ELEMENTARY       TREATISE 


ON 


PHYSICS 


EXPERIMENTAL     AND     APPLIED 


FOR     THE     USE    OF    COLLEGES    AND    SCHOOLS 


(■ 


TRANSLATED   AND   EDITED   FROM 


GANOT'S     ELEMENTS     DE     PHYSIQUE 

{wi'ik  M£  Author^ s  sanction) 


/.     A  E.    ATiUNSON,    Ph.D.,-  F.C.S. 


v'* 


<"i«[-EssoR    Qf  >exm;rimental    science,    staff    college,    sandhukst 


xntb   ^bilion,    ^bis^b   anb   (Sitlargib 


ILLUSTRATED    BY  \    COLOURED   PLATES   AND    758    WOODCUTS 


NEW     YORK 
WILLIAM     WOOD     AND     CO.,     PUBLISHERS 

27     GREAT    JONES     STREET 

1875  '^^    t 


In 


QCI'h 


I T""^  ADVERTISEMENT 

THE   SEVENTH    EDITION. 


The  present  edition  contains  seventeen  entirely  new  illustrations. 
A  very  large  number  of  the  old  illustrations  have  been  recut. 

The  additions  to  the  text  amount  to  twenty-seven  pages.  In 
making  these  additions,  while  I  have  consulted  the  wants  of  the  general 
reader,  my  principal  aim  has  been,  as  in  former  editions,  to  render 
the  book  more  usefulYor  the  student  of  Physical  Science.  ^ 

I  have  also  added  an  Appendix  containing  a  series  of  numerical 
A)roblems  and  examples  in  Physics.  This  Appendix  is  based  upon  a 
similar  one  contained  in  the  French  edition  of  the  work.  But  I 
have  been  able  to  use  only  a  sanall  proportion  of  the  problems  con- 
tained in  that  Appendix,  as  the  interest  of  the  solution  was  in  most 
cases  geometrical  or  algebraical.  Hence  I  have  substituted  or  added 
others,  which  have  been  so  selected  as  to  involve  in  the  solution  a 
knowledge  of  some  definite  physical  principle. 

Such  an  Appendix  has  from  time  to  time  been  urged  upon  me  b^ 
teachers  and  others  who  use  the  work.  It  will,  I  conceive,  be  more 
useful  to  those  students  who  have  not  the  advantage  of  regular 
instruction ;  affording  to  them  a  means  of  personally  testing  their 
knowledge.  Such  a  student  should  not  aim  solely  at  getting  a  result 
which  numerically  agrees  with  the  answer.  He  should  habituate 
himself  to  write  out  at  length  the  several  steps  by  which  the  result 
is  obtained,  so  that  he  may  bring  clearly  before  himself  the  physical 
principles  involved  in  each  stage.  Some  of^^the  solution^  of  the 
problems  are  therefore  worked  out  at  lengtii. 

Those  of  the  questions  which  are  not  original,  have  been  taken 
from  various  sources.  My  thanks^re  especially  due  to  my  friend 
Mr.  Eve,  of  Wellington  College,  wht)  has  placed  at  my  disposal  a 
collection  of  problems  in  Electricity  of  which  I  have  extensively 
availed  myself. 

E.  A. 

Staff  College  :  yune  iS-JS. 


^  I  Q'r  *)• 


• 


TRANSLATOR'S    PREFACE 

TO 

THE   FIRST   EDITION. 


The  Elements  de  Physique  of  Professor  Ganot,  of  which  the  present 
work  is  a  translation,  has  acquired  a  high  reputation  as  an   Intro- 
duction to  Physical  Science.     In  France  it  has  passed  through  Nine 
large  editions  In  little  more  than  as  many  years,  and  it  has  been, 
translated  into  German  and  Spanish. 

This  -reputation  it  doubtless  owes  to  the  clearness  and  conciseness 
with  which  the  principal  physical  laws  and  phenomena  are  explained, 
to  its  methodical  arrangement,  and  to  the  excellence  of  its  illustra- 
tions. In  undertaking  a  translation,  I  was  influenced  by  the  favour- 
able opinion  which  a  previous  use  of  it  in  teaching  had  enabled  me 
to  form. 

I  found  that  its  principal  defect  consisted  in  its  too  close  adapta- 
tion to  the  French  systems  of  instruction,  and  accordingly,  my  chief 
labour,  beyond  that,  of  mere  translation,  has  been  expended  in 
making  such  alterations  and  additions  as  might  render  it  more  useful 
to  the  English  student. 

I  have  retained  throughout  the  use  of  the  cdhtigrade  thermometer, 
and  in  some  cases  have  expressed  the  smaller  linear  measures  on  the 
metrical  system.  These  systems  are  now  everywhere  gaining  ground, 
and  an  apology  is  scarcely  needed  for  an  innovation  which  may  help 
to  familiarise  the  English  student  with  their  use  in  the  perusal  of  the 
larger  and  more  complete  works  on  Physical  Science  to  which  this 
work  may  serve  as  an  introductJoR. 

E.  ATKINSON. 

Royal  Military  College,  Sandhurst  : 

1863. 


CONTENTS. 


BOOK   I. 
ON    MATTER,  FORCE,  AND   MOTION. 

CHAPTER  I'AGES 

I.     General  Notions  ......  i 

II.     General  Properties  of  Bodies  ....  3 

III.     On  Force,  Equilibrium,  and  Motion  ....  9 

BOOK   II. 

GRAVITATION   AND    MOLECULAR  ATTRACTION. 

# 
I.     Gravity,  Centre  of  Gravity,  the  Balance   .  .  -        43 

II.  Laws    of    Falling    Bodies.       Intensity    of    Terrestrial 

Gravity.     The  Pendulum  .  .  .  .  .52 

III,  Molecular  Forces  .  .  .  .  .  .61 

IV.  Properties  peculiar  to  Solids  .  .  .  -63 

BOOK  in. 

ON   LIQUIDS. 

I.     Hydrostatics         .  .  .  .  .  .  .70 

II.     Capillarity,    Endosmose,    Effusion,    Absorption,   and    Im- 
bibition .  .  .  ".  .  .  '97 

BOOK   IV. 
ON   GASES. 

I.  Properties  of  Gases.     Atmosphere,     Barometers  .  .       109 

11.  Measurement  of  the  Elastic  Force  of  Qases  .  .       127 

III.  Pressure  on  Bodies  in  Air,     Balloons          .  .  -137 

IV.  Apparatus  founded  on  the  Properties  of  Air  .  .       141 


Vlll 


•        Contents. 


CHAl'TER 
I. 
II. 
III. 

IV. 
V. 

^    VI. 


BOOK   V. 
ACOUSTICS. 

PAGE 

Production,  Propagation,  and  Reflection  of  Sound       .       i66 
Measurement  of  the  Number  of  Vibrations         .  .       i8i 

The  Physical  Theory  of  Music         .  .  .  .186 

Vibrations  of  Stretched  Strings,  and  of  Columns  of  Air      201 
Vibrations  of  Rods,  Plates,  and  Membranes  .  .214 

Graphical  Method  of  Studying  Vibratory  Motions       .      217 


BOOK  VI. 
ON    HEAT. 


I.  Preliminary  Ideas.     Thermometers 

II.  Expansion  of  Solids     .... 

III.  Expansion  of  Liquids  .... 

IV.  Expansion  and  Density  of  Gases 
►      V.  Changes  of  Condition.     Vapours 

VI.  Hygrometry       .  .  . 

VII.  Conductivity  of  Solids,  Liquids,  and  Gases 

VIII.  Radiation  of  Heat       .... 

IX.  Calorimetry       ..... 

X.  Steam  Engines  ..... 

XI.  Sources  of  Heat  and  Cold    . 

XII.  Mechanical  Equivalent  of  Heat     . 


227 
240 
247 
253 
262 
306 

315 
321 

358 
375 
388 
401 


BOOK   VII. 
ON   LIGHT. 


I.  Transmission,  Velocity,  and  Intensity  of  Light 

II.  Reflection  of  Light.     Mirrors 

III.  Single  Refraction.     Lenses  . 

IV.  Dispersion  and  Achromatism. 
V.  Optical  Instruments   .  . 

VI.  The  Eye  considered  as  an  Optical  Instrument 

VII.  Sources  of  Light.     Phosphorescence 

VIII.  Double  Refraction.     Interference.     Polarisation 


409 

420 

439 

459 
480 
508 

dn 

525 
528 

Contents. 


IX 


BOOK  VIII. 
ON    MAGNETISM. 

CHAPTER 

I.  Properties  of  Magnets 

II.  Terrestrial  Magnetism.      Compasses 

III.  Laws  of  Magnetic  Attractions  and  Repulsions 

IV.  Processes  of  Magnetisation  . 


566 

572 
585 
589 


BOOK   IX. 

FRICTIONAL   ELECTRICITY. 

I,     Fundamental  Principles         .....       597 
II.     Quantitative  Laws  of  Electrical  Action  .  .       604 

III.  Action  of  Electrified  Bodies  on  Bodies  in  the  Natural 

State.    Induced  Electricity.     Electrical  Machines  .       612 

IV.  Condensation  of  Electricity  ....       636 


BOOK  X. 
DYNAMICAL   ELECTRICITY. 


I.     Voltaic  Pile.     Its  Modifications     . 
II.     Detection  and  Measurement  of  Voltaic  Currents 

III.  Effects  of  the  Current        .... 

IV.  Electrodynamics.  Attraction  and  Repulsion  of  Currents 

BY  Currents  ..... 

V.     Magnetisation  by  Currents.    Electromagnets.    Electric 
Telegraphs   ...... 

VI.     Voltaic  Induction        ..... 

VII.     Optical  Effects  of  Powerful  Magnets.      Diamagnetism 
VIIL     Thermo-electric  Current      .... 

IX.     Determination  of  Electrical  Conductivhy 
X.     Animal    Electricity.      Application    of    Electricity   to 
Therapeutics  ..... 

Elementary  Outlines  of  Meteorology  and  Cllmatology 
INDEX     .  .  .  .  . 


667 
688 
700 

726 

745 
767 
805 
809 
819 

830 
836 
889 


LIST   OF   TABLES. 


Absorbing  powers    . 
Absorption  of  gases    . 

—  heat  by  gases 
liquids 

vapours     346,  349,  351 

Breaking  weight  of  substances 
Boiling  point 

Combustion,  heat  of 
Conducting  powers  of  solids  for 
heat    . 

liquids  for  heat 

Conductors  of  electricity 

Densities  of  gases    . 

—  of  vapours 
Density  of  water 
Diathermanous  power 
Diffusion  of  solutions . 
Diamagnetism    . 

Endosmotic  equivalents 
Elasticity  , 
Electrical  series . 

—  conductivity  . 
Electromotive  force   of  different 

elements 
Expansion,  coefficients  of  solids, 

liquids 

gases 

Eye,  dimensions  of     . 

—  refractive  indices  of  media  of 

Freezing  mixtures    . 
Fusing  points  of  bodies 


243 


PAGE 

333 
107 

345 
344 
352 

68 
280 

395 

317 
319 
599 

261 
305 
253 
345 
104 
808 


103 

65 
602 
825 

685 
,244 
250 
257 
511 
511 

267 
263 


Glaisher's  factors     .         .         .312 
Gravity,  force  of,  at  different  levels       5  8 


Hardness,  scale  of  . 

Latent  heat,  of  evaporation 
liquefaction 

Magnetic  declination 

—  inclination     .... 

—  intensity        .... 

Radiating  powers    ,        .      333, 
Radiation  of  powders 
Refraction,  angle  of  double 
Refractive  indices 

of  media  of  eye 

Reflecting  powers       .         .     332, 


Specific  gravity  of  solids  . 

—  elasticity 
liquids 

—  heat  of  solids  and  liquids 
gases 

—  inductive  capacities 

Temperatures,  various  remark 
able    ... 

—  of  different  latitudes 

—  thermal  springs 
Tension  of  aqueous  vapour 

—  different  liquids     . 
Thermo-electric  series 

Undulations,  length  of  . 

Velocity  of  sound  in  rocks 

gases  . 

liquids 

metals  and  woods 


PAGE 

69 

286 
371 

574 
581 
583 

334 
356 
534 
449 
511 
333 

92 
65 

94 
365 
369 
617 


239 
866 
867 

276 

277 
810 

529 1 

172 

174 
176 
176 


LIST   OF    PLATES. 


Table  of  Spectra        .         .         .         .         .         .         .         .  Frontispiece 

Coloured    Rings    produced    by    Polarised    Light     in     Double 

Refracting  Crystals 552 

IsoGONic  Lines  for  the  Year  i860 575 

IsocLiNic  Lines  for  the  Year  i860 580 


1     1     1     1     M     1     1     |ii.-h                             |2                                   1^5                                4 

llllllllll' 

Millimetres 

|2           13           |4           15           |6           17           |« 

Centimetres 

The  area  of  the  figure  within  the  heavy  Hnes  is 
that  of  a  square  decimetre.  A  cube,  one  of  whose 
sides  is  this  area,  is  a  cubic  decimetre  or  litre.  A 
litre  of  water  at  the  temperature  of  4°  C.  weighs  a 
kilogramme.  A  litre  of  air  at  0°  C.  and  760™™ 
pressure  weighs  i  -293  grammes. 

A  litre  is  rj6  pints ;  a  pint  is  0-568  of  a  litre. 

The  smaller  figures  in  dotted  lines  represent  the 
areas  of  a  square  centimetre  and  of  a  square  inch. 

A  cubic  centimetre  of  water  at  4°  C.  weighs  a 
gramme. 

|9         10 

9 

Square  Inch 

Square      ! 
Centimetre; 

! 

Metres. 

Feet. 

0-03937 

0  00328 I 

0-39371 

0032819 

3 '93708 

0*328090 

39*37079 

3*280899 

7070000 

3280-899167 

f  Millimetre 

Centimetre 
Decimetre 
Metre 
Kilometre 

A  Hectare  or  loooo  square  metres  is  equal  to  2 -471 14  acres,  each  of  which  is  43560 
square  feet.  A  kilometre  is  0-6214  of  a  statute  mile,  A  statute  mile  is  i  -609  kilometres. 
A  knot  (in  telegraphy)  is  2029  yards  or  i'i528  statute  miles. 


Measures  of  Capacity. 


Cubic  centimetre  or  millitre 
Litre  or  cubic  decimetre 
Kilolitre  or  cubic  metre 


Cubic  Inches. 
0-06103 
61  "02705 
.   61027 -05152 


Measures  of  Weight. 


Milligramme 
Gramme     , 
Kilogramme  . 


English  grains. 

001543 

15  "43235 
15432-34880 


Cubic  Feet. 

C728  c.  in.  =1  c.  ft. 

0-000035 

0-035317 

35-316581 


Avoirdupois  pounds 

of  7000  grains . 

0-0000022 

0-0022046 

2-2046213 


I  grain =0-064799  gramme  ;  i  pound  avoirdupois  is  0-453593  kilogramme. 


Errata 


Page    17, 

line  28  from  top, 

for  -129-9 

reac 

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„      67, 

,, 

27 

,,       „ 

,, 

inversely 

>h 

directly 

„    235, 

,, 

29 

,,       ,, 

,, 

+ 

,j 

X 

,,      J, 

,, 

33 

,,       ,, 

,, 

(F.=32) 

„ 

(F.-32) 

,,      ,, 

,, 

4 

,,     bottom, 

1    5, 

33 

,, 

32 

,,   255, 

,, 

17 

,,     top. 

,, 

V  +  760 

,, 

VX760 

„    302, 

,, 

18 

,,       ,, 

,, 

yellow 

,, 

violet 

„    330, 

bottom  line, 

,, 

fig.  304 

,, 

fig.  303 

.,    363, 

line 

8  from  top, 

,, 

M  (T-    ) 

,, 

M  (T-fl) 

„    405, 

top 

line, 

,, 

p{h-h) 

,, 

p{h-h) 

„    447, 

line 

5  from  top, 

,, 

LDL 

,j 

LDC 

„    487, 

,, 

16 

,,       ,j 

,j 

fig-  435 

J, 

fig.  434 

,,      ,, 

,, 

21 

>,       », 

,, 

„    424 

,, 

„    436 

In  fig.  437  the  positions  of  the  letters  r  Rv'  and  v  Vv'  should  be 

interchanged 
Page  595,  line  17  from  bottom,  y^/-  n  read  n, 
„    700,    „    10    ,,     top,/?r4'3  rmi/4-6 


Gnnot's  Physics 


«? 


i 


ELEMENTARY    TREATISE 

ON 

PHYSICS. 

BOOK   I. 

ON    MATTER,  FORCE,  AND   MOTION. 


CHAPTER    I. 
GENERAL  NOTIONS. 


1.  Object  of  Pbyslcs. — The  object  oi  Physics  is  the  study  of  the  phe- 
nomena presented  to  us  by  bodies.  It  should,  however,  be  added,  that 
changes  in  the  nature  of  the  body  itself,  such  as  the  decomposition  of  one 
body  into  others,  are  phenomena  whose  study  forms  the  more  immediate 
object  of  chemistry. 

2.  laatter.— That  which  possesses  the  properties  whose  existence  is 
revealed  to  us  by  our  senses,  we  call  matter  or  substance. 

All  substances  at  present  known  to  us  may  be  considered  as  chemical 
combinations  of  sixty-five  elementary  or  simple  substances.  This  number, 
however,  may  hereafter  be  diminished  or  increased  by  a  more  powerful 
chemical  analysis. 

3.  Atoms,  Molecules. — From  various  properties  of  bodies  we  con- 
clude that  the  matter  of  which  they  are  formed  is  not  perfectly  continuous, 
but  consists  of  an  aggregate  of  an  immense  number  of  exceedingly  small 
portions  or  atoms  of  matter.  These  atoms  cannot  be  divided  physically, 
they  are  retained  side  by  side,  without  touching  each  other,  being 
separated  by  distances  which  are  great  in  comparison  with  their  supposed 
dimensions. 

A  group  of  two  or  more  atoms  forms  a  molecule^  so  that  a  body  may 
be  considered  as  an  aggregate  of  very  small  molecules,  and  these  again  as 
aggregates  of  still  smaller  atoms.  The  smallest  masses  of  matter  we  ever 
obtain  artificially  are  particles  and  not  molecules  or  atoms.  Molecules 
retain  their  position  in  virtue  of  the  action  of  certain  forces  called  mole- 
cular foixes. 

B 


2  On  Matter,  Force,  and  Motion.  [4- 

From  considerations  based  upon  various  physical  phenomena  Sir  W. 
Thomson  has  calculated  that  in  ordinary  solids  and  liquids  the  average 
distance  between  contiguous  molecules  is  less  than  the  hundred  millionth 
and  greater  than  the  two  thousand  millionth  of  a  centimetre. 

To  give  an  idea  of  the  degree  of  the  size  of  the  molecules  Sir  W. 
Thomson  gives  this  illustration  :  *  Imagine  a  drop  of  rain,  or  a  glass 
sphere  the  size  of  a  pea,  magnified  to  the  size  of  the  earth,  the  molecules 
in  it  being  increased  in  the  same  proportion.  The  structure  of  the  mass 
would  then  be  coarser  than  that  of  a  heap  of  fine  shot,  but  probably  not 
so  coarse  as  that  of  a  heap  of  cricket-balls.' 

4.  Molecular  state  of  bodies. — With  respect  to  the  molecules  of 
bodies  three  different  states  of  aggregation  present  themselves. 

First,  the  solid  state,  as  observed  in  woods,  stones,  metals,  etc.,  at  the 
ordinary  temperature.  The  distinctive  character  of  this  state  is,  that  the 
relative  positions  of  the  molecules  of  the  bodies  cannot  be  changed  with- 
out the  expenditure  of  more  or  less  force.  As  a  consequence,  solid  bodies 
tend  to  retain  whatever  form  may  have  been  given  to  them  by  nature  or 
by  art. 

Secondly,  the  liquid  state,  as  observed  in  water,  alcohol,  oil,  etc.  Here 
the  relative  position  of  the  molecules  is  no  longer  permanent,  the  mole- 
cules glide  past  each  other  with  the  greatest  ease,  and  the  body  assumes 
with  readiness  the  form  of  any  vessel  in  which  it  may  be  placed. 

Thirdly,  the  gaseous  state,  as  in  air.  In  gases  the  mobility  of  the 
molecules  is  still  greater  than  in  liquids  ;  but  the  distinctive  character  of 
a  gas  is  its  incessant  struggle  to  occupy  a  greater  volume,  or  the  tendency 
of  its  molecules  to  recede  from  each  other. 

The  general  ttrm  Jluid  is  applied  to  both  liquids  and  gases. 

We  shall  see  in  the  sequel  that  the  state  of  a  body  depends  upon  the 
relations  which  exist  between  its  molecular  attractions  and  repulsions,  and 
that  for  one  and  the  same  body  these  relations  vary  with  the  temperature. 
On  this  account  most  simple  bodies,  and  many  compound  ones,  may  be 
made  to  pass  successively  through  all  the  three  states.  Water  presents 
the  most  familiar  example  of  this. 

5.  Physical  phenomena,  laxirs,  and  theories. — Every  change  which 
can  happen  to  a  body,  mere  alteration  of  its  chemical  constitution  being 
excepted,  may  be  regarded  as  a.  physical phe?to?nenon.  The  fall  of  a  stone, 
the  vibration  of  a  string,  and  the  sound  which  accompanies  it,  the  rippling 
of  the  surface  of  a  lake,  and  the  freezing  of  water,  are  examples  of  such 
phenomena. 

A  physical  law  is  the  constant  relation  which  exists  between  any  phe- 
nomenon and  its  cause.  As  an  example,  we  have  the  phenomenon  of  the 
diminution  of  the  volume  of  a  gas  by  the  application  of  pressure ;  the 
corresponding  law  has  been  determined,  and  is  expressed  by  saying  that 
the  volume  of  a  gas  is  inversely  proportional  to  the  pressure. 

In  order  to  explain  whole  classes  of  phenomena  suppositions,  or  hypo- 
theses are  made  use  of ;  the  utility  and  probability  of  an  hypothesis  or 
theory  is  the  greater  the  simpler  it  is,  and  the  more  varied  and  numerous 
are  the  phenomena  which  are  explained  by  it ;  that  is  to  say,  are  brought 


-7]  General  Properties  of  Bodies.  3 

into  regular  causal  connection  among  themselves  and  with  other  natural 
phenomena.  Thus  the  adoption  of  the  undulatory  theory  of  light  is 
justified  by  the  simple  and  unconstrained  explanation  it  gives  of  all  lumi- 
nous phenomena,  and  by  the  connection  it  reveals  with  the  phenomena 
of  heat. 

6.  Physical  agrents. — In  our  attempts  to  ascend  from  a  phenomenon 
to  its  cause,  we  assume  the  existence  oi  physical  agents^  or  natural  forces^ 
acting  upon  matter ;  as  examples  of  such  we  have  gravitation^  heat,  lights 
magnetism,  and  electricity. 

Since  these  physical  agents  are  disclosed  to  us  only  by  their  effects, 
their  intimate  nature  is  completely  unknown.  In  the  present  state  of 
science,  we  cannot  say  whether  they  are  properties  inherent  in  matter,  or 
whether  they  result  from  movements  impressed  on  the  mass  of  subtile 
and  imponderable  forms  of  matter  diffused  through  the  universe.  The 
latter  hypothesis  is  however  generally  admitted.  This  being  so  it  may 
be  further  asked  are  there  several  distinct  forms  of  imponderable  matter, 
or  are  they  in  reality  but  one  and  the  same  ?  As  the  physical  sciences 
extend  their  limits,  the  opinion  tends  to  prevail  that  there  is  a  subtile, 
imponderable,  and  eminently  elastic  fluid  called  the  ether  distributed 
through  the  entire  universe;  pervading  the  mass  of  all  bodies,  the  densest 
and  most  opaque,  as  well  as  the  lightest  or  the  most  transparent.  It  is 
also  considered  that  the  intimate  particles  of  which  matter  is  made 
up  are  capable  of  definite  motions  varying  in  character  and  velocity, 
and  which  can  be  communicated  to  the  ether.  A  motion  of  a  particular 
kind  communicated  to  the  ether  can  give  rise  to  the  phenomenon 
of  heat  ;  a  motion  of  the  same  kind,  but  of  greater  velocity,  produces 
light ;  and  it  may  be  that  a  motion  different  in  form  or  in  character 
is  the  cause  of  electricity.  Not  merely  do  the  atoms  of  bodies  commu- 
nicate motion  to  the  atoms  of  the  ether,  but  this  latter  can  impart  it  to 
the  former.  Thus  the  atoms  of  bodies  are  at  once  the  sources  and  the 
recipients  of  the  motion.  All  physical  phenomena,  referred  thus  to  a 
single  cause,  are  but  transformations  of  motion. 


CHAPTER  II; 

GENERAL  PROPERTIES  OF   BODIES. 

7.  Different  kinds  of  properties. — By  the  term  properties  as  ap- 
plied to  bodies,  we  understand  the  different  ways  in  which  bodies  present 
themselves  to  our  senses.  We  distinguish  general  from  specific  properties. 
The  former  are  shared  by  all  bodies,  and  amongst  them  the  most  impor- 
tant are  ijnpenetrability ,  extension,  divisibility,  porosity,  compressibility , 
elasticity,  mobility,  and  inertia. 

Specific  properties  are  such  as  are  observed  in  certain  bodies  only,  or 
in  certain  states  of  these  bodies  ;  such  are  solidity ,  fiuidity ,  tenacity,  duc- 
tility, malleability,  hardness,  transparency,  colour,  etc. 

With  respect  to  the  above  general  properties,  it  may  be  remarked 


At  On  Matter^  Force^  and  Motion.  [8- 

that  impenetrability  and  extension  might  be  more  aptly  termed  essential 
attributes  of  matter,  since  they  suffice  to  define  it ;  and  that  divisibility, 
porosity,  compressibility,  and  elasticity,  do  not  apply  to  atoms,  but  only 
to  bodies  or  aggregates  of  atoms  (3). 

8.  Impenetrability. — Impenetrability  is  the  property  in  virtue  of 
which  two  portions  of  matter  cannot,  at  the  same  time,  occupy  the  same 
portion  of  space. 

Strictly  speaking,  this  property  applies  only  to  the  atoms  of  a  body. 
In  many  phenomena  bodies  appear  to  penetrate  each  other  ;  thus,  the 
volume  of  a  compound  body  is  always  less  than  the  sum  of  the  volumes 
of  its  constituents  ;  for  instance,  the  volume  of  a  mixture  of  water  and  sul- 
phuric acid,  or  of  water  and  alcohol,  is  less  than  the  sum  of  the  volumes 
before  mixture.  In  all  these  cases,  however,  the  penetration  is  merely 
apparent,  and  arises  from  the  fact  that  in  every  body  there  are  interstices 
or  spaces  unoccupied  by  matter. 

9.  Extension. — Extension  or  magnitude  is  the  property  in  virtue  of 
which  every  body  occupies  a  limited  portion  of  space. 

Many  instruments  have  been  invented  for  measuring  linear  extension 
or  lengths  with  great  precision.  Two  of  these,  the  vernier  and  micro- 
meter screw,  on  account  of  their  great  utility,  deserve  to  be  here  mentioned. 

10.  Vernier. — The  vernier  forms  a  necessary  part  of  all  instruments 
where  lengths  or  angles  have  to  be  estimated  with  precision  ;  it  derives 
its  name  from  its  inventor,  a  French  mathematician,  who  died  in  1637, 
and  consists  essentially  of  a  short  graduated  scale,  ab,  which  is  made  to 


A 

B 

! 

i\ 

1C\ 

^'\ 

) 

1      1      1      1      1  .  1      1      1      1      1     1           1      i      1      1      1    I 

1     1     1 

1       1             1       1 

I       ' 

1 

A. 

a 

b 

S\                                      10, 

/il 

^^^^^^^^^^^;n 

1         1         1         1          III 

1          1         1 

1      1     1 

m 

ii 

1C\ 

Fig.  I. 

slide  along  a  fixed  scale,  AB,  so  that  the  graduations  of  both  may  be 
compared  with  each  other.  The  fixed  scale,  AB,  being  divided  into 
equal  parts,  the  whole  length  of  the  vernier,  ab,  may  be  taken  equal  to 
nine  of  those  parts,  and  itself  divided  into  ten  equal  parts.  Each  of  the 
parts  of  the  vernier,  ab^  will  then  be  less  than  a  part  of  the  scale  by  one 
tenth  of  the  latter. 

This  granted,  in  order  to  measure  the  length  of  any  object,  mn,  let  us 
suppose  that  the  latter,  when  placed  as  in  the  figure,  has  a  length  greater 
than  four  but  less  than  five  parts  of  the  fixed  scale.  In  order  to  determine 
by  what  fraction  of  a  part  mn  exceeds  four,  one  of  the  ends,  a,  of  the  ver- 
nier, ab^  is  placed  in  contact  with  one  extremity  of  the  object,  mn^  and 
the  division  on  the  vernier  is  sought  which  coincides  with  a  division  on 
the  scale,  AB.  In  the  figure  this  coincidence  occurs  at  the  eighth  divi- 
sion of  the  vernier,  counting  from  the  extremity,  ;/,  and  indicates  that  the 


-12]  Micrometer  Srew.  5 

fraction  to  be  measured  is  equal  to  /oths  of  a  part  of  the  scale,  AB.  In 
fact,  each  of  the  parts  of  the  vernier  being  less  than  a  part  of  the  scale  by 
j^^th  of  the  latter,  it  is  clear  that  on  proceeding  towards  the  left  from  the 
point  of  coincidence,  the  divisions  of  the  vernier  are  respectively  one,  two, 
three,  etc.,  tenths  behind  the  divisions  of  the  scale ;  so  that  the  extremity, 
;/,  of  the  object  (that  is  to  say,  the  eighth  division  of  the  vernier)  is  jo^hs 
behind  the  division  marked  4  on  the  scale ;  in  other  words,  the  length  of 
inn  is  equal  to  4/0^^^  ^^  ^^  parts  into  which  the  scale  AB  is  divided. 
Consequently,  if  the  scale  AB  were  divided  into  inches,  the  length  of  mn 
would  be  4yo  =  4|  inches.  The  divisions  on  the  scale  remaining  the  same, 
it  would  be  necessary  to  increase  the  length  of  the  vernier  in  order  to 
measure  the  length  mil  more  accurately.  For  instance,  if  the  length  of 
the  vernier  were  equal  to  nineteen  of  the  parts  on  the  scale,  and  this 
length  were  divided  into  twenty  equal  parts,  the  length  mn  could  be  deter- 
mined to  the  twentieth  of  a  part  on  a  scale,  and  so  on.  In  instruments 
like  the  theodolite,  intended  for  measuring  angles,  the  scale  and  vernier 
have  a  circular  form,  and  the  latter  usually  carries  a  magnifier,  in  order 
to  determine  with  greater  precision  the  coincident  divisions  of  vernier 
and  scale. 

11.  micrometer  screw. — Another  useful  little  instrument  for  mea- 
suring small  lengths  with  precision  is  the  micrometer  screw.  It  is  used 
under  various  forms,  but  the  principle  is  the  same  in  all,  and  may  be 
illustrated  by  a  simple  example.  Suppose  the  distance  between  the 
threads  of  an  accurately  cut  screw  to  be  equal  to  j^th  of  an  inch,  and  the 
head  of  the  screw  to  be  a  tolerably  large  circle  divided  into  one  hundred 
equal  parts.  If  the  screw  is  fixed  in  such  a  manner  that  it  can  only  turn 
on  its  axis,  but  neither  advance  nor  recede,  and  if  it  work  in  a  nut  held 
between  guides  which  prevent  it  from  turning,  then  every  turn  of  the 
screw  will  cause  the  nut  to  advance  through  the  tenth  part  of  an  inch.  If 
a  fixed  pointer  be  placed  before  the  divided  circle  at  the  head  of  the  screw, 
and  the  latter  turned  through  so  small  an  angle  that  only  one  division  of 
the  circle  passes  under  the  pointer,  the  hundredth  part  of  a  turn  will 
have  been  given  to  the  screw,  and  the  nut  thereby  caused  to  advance  o4» 
recede  through  the  hundredth  part  of  the  distance  between  two  threads* 
— that  is  to  say,  through  the  jo^oo^^  P^^^  °^  ^^  inch.  Applications  of  this 
principle  to  the  measurement  of  small  lengths  are  met  with  in  the  sphe- 
rometer,  and  in  the  dividing  machitie^  and  will  be  readily  understood 
when  seen. 

12.  Bivisibility — is  the  property  in  virtue  of  which  a  body  may  be 
separated  into  distinct  parts. 

Numerous  examples  may  be  cited  of  the  extreme  divisibility  of  matter. 
The  tenth  part  of  a  grain  of  musk  will  continue  for  years  to  fill  a  room 
with  its  odoriferous  particles,  and  at  the  end  of  that  time  will  scarcely  be 
diminished  in  weight. 

Blood  is  composed  of  red,  flattened  globules,  floating  in  a  colourless 
liquid  called  serum.  In  man  the  diameter  of  one  of  these  globules  is 
less  than  the  3,500th  part  of  an  inch,  and  the  drop  of  blood  which  might 
be  suspended  from  the  point  of  a  needle  would  contain  about  a  million  of 
globules. 


On  Matter,  Force,  and  Motion. 


[12- 


Again,  the  microscope  has  disclosed  to  us  the  existence  of  insects 
smaller  even  than  these  particles  of  blood;  the  struggle  for  existence 
reaches  even  to  these  little  creatures,  for  they  devour  still  smaller  ones. 
If  blood  runs  in  the  veins  of  these  devoured  ones,  how  infinitesimal  must 
be  the  magnitude  of  its  component  globules  ! 

Has  then  the  divisibility  of  matter  no  limit  ?  Although  experiment 
fails  to  determine  such  limit,  many  facts  in  chemistry,  such  as  the  in- 
variability in  the  relative  weights  of  the  elements  which  combine  with 
each  other,  would  lead  us  to  believe  that  a  limit  does  exist.  It  is  on  this 
account  that  bodies  are  conceived  to  be  composed  of  extremely  minute 
and  indivisible  parts  called  atoms  (3). 

13.  Porosity. — Porosity  is  the  quality  in  virtue  of  which  interstices  or 
^ores  exist  between  the  molecules  of  a  body. 

Two  kinds  of  pores  may  be  distin- 
guished :  physical  pores,  where  the  inter- 
stices are  so  small  that  the  surrounding 
molecules  remain  within  the  sphere  of 
each  other's  attracting  or  repelling  forces; 
and  sensible  pores,  or  actual  cavities  across 
which  these  molecular  forces  cannot  act. 
The  contractions  and  dilatations  resulting 
from  variations  of  temperature  are  due  to 
the  existence  of  physical  pores,  whilst  in 
the  organic  world  the  sensible  pores  are 
the  seat  of  the  phenomena  of  exhalation 
and  absorption. 

In  wood,  sponge,  and  a  great  number 
of  stones,  for  instance,  pumice  stone,  the 
sensible  pores  are  apparent ;  physical 
pores  never  are.  Yet,  since  the  volume 
of  every  body  may  be  diminished,  we 
conclude  that  all  possess  physical  pores. 

The  existence  of  sensible  pores  may 
be  shown  by  the  following  experiment:  — 
A  long  glass  tube,  A  (fig.  2),  is  provided 
with  a  brass  cup,  in,  at  the  top,  and  a  brass 
foot  made  to  screw  on  to  the  plate  of  an 
air-pump.  The  bottom  of  the  cup  con- 
sists of  a  thick  piece  of  leather.  After 
pouring  mercury  into  the  cup  so  as  en- 
tirely to  cover  the  leather,  the  air-pump 
is  put  in  action,  and  a  partial  vacuum 
produced  within  the  tube.  By  so  doing 
a  shower  of  mercury  is  at  once  produced  within  the  tube,  for  the  atmos- 
pheric pressure  on  the  mercury  forces  that  liquid  through  the  pores  of 
the  leather.  In  the  same  manner  water  or  mercury  may  be  forced 
through  the  pores  of  wood,  by  replacing  the  leather  in  the  above  experi- 
ment by  a  disc  of  wood  cut  perpendicular  to  the  fibres. 


Fig.  2. 


r 


^ 


-16]  Compressibility.  *  7 

When  a  piece  of  chalk  is  thrown  into  water,  air-bubbles  at  once  rise 
to  the  surface,  in  consequence  of  the  air  in  the  pores  of  the  chalk  being 
expelled  by  the  water.  The  chalk  will  be  found  to  be  heavier  after  im- 
mersion than  it  was  before,  and  from  the  increase  of  its  weight  the  volume 
of  its  pores  may  be  easily  determined. 

The  porosity  of  gold  was  demonstrated  by  the  celebrated  Florentine 
experiment  made  in  1661.  Some  academicians  at  Florence,  wishing  to 
try  whether  water  was  compressible,  filled  a  thin  globe  of  gold  with  that 
liquid,  and,  after  closing  the  orifice  hermetically,  they  exposed  the  globe 
to  pressure  with  a  view  of  altering  its  form,  well  knowing  that  any  altera- 
tion in  form  must  be  accompanied  by  a  diminution  in  volume.  The 
consequence  was,  that  the  water  forced  its  way  through  the  pores  of  the 
gold,  and  stood  on  the  outside  of  the  globe  like  dew.  More  than  twenty 
years  previously  the  same  fact  was  demonstrated  by  Francis  Bacon  by 
means  of  a  leaden  sphere,  the  experiment  has  since  been  repeated  with 
globes  of  other  metals,  and  similar  results  obtained. 

14.  Apparent  and  real  volumes. — In  consequence  of  the  porosity  of 
bodies,  it  becomes  necessary  to  distinguish  between  their  real  and  appa- 
rent volumes.  The  real  volume  of  a  body  is  the  portion  of  space  actually 
occupied  by  the  matter  of  which  the  body  is  composed  ;  its  apparent 
vohcine  is  the  sum  of  its  real  volume  and  the  total  volume  of  its  pores. 
The  real  volume  of  a  body  is  invariable,  but  its  apparent  volume  can  be 
altered  in  various  ways. 

15.  Applications. — The  property  of  porosity  is  utilised  in  filters  of 
paper,  felt,  stone,  charcoal,  etc.  The  pores  of  these  substances  are  suffi- 
ciently large  to  allow  liquids  to  pass,  but  small  enough  to  arrest  the 
passage  of  any  substances  which  these  liquids  may  hold  in  suspension 
Again,  large  blocks  of  stone  are  often  detached  in  quarries  by  introducing 
wedges  of  dry  wood  into  grooves  cut  in  the  rock.  These  wedges  being 
moistened,  water  penetrates  their  pores,  and  causes  them  to  swell  with 
considerable  force.  Dry  cords,  when  moistened,  increase  in  diameter  and 
diminish  in  length,  a  property  of  which  advantage  is  sometimes  taken  in 
order  to  raise  great  weights. 

16.  Compressibility. — Compressibility  is  the  property  in  virtue  of 
which  the  volume  of  a  body  m.ay  be  diminished  by  pressure.  This  pro- 
perty is  at  once  a  consequence  and  a  proof  of  porosity. 

Bodies  differ  greatly  with  respect  to  compressibility.  The  most  com- 
pressible bodies  are  gases  ;  by  sufficient  pressure  they  may  be  made  to 
occupy  ten,  twenty,  or  even  a  hundred  times  less  space  than  they  do 
under  ordinary  circumstances.  In  most  cases,  however,  there  is  a  limit 
beyond  which,  when  the  pressure  is  increased,  they  become  liquids. 

The  compressibility  of  solids  is  much  less  than  that  of  gases,  and  is 
found  in  all  degrees.  Cloths,  paper,  cork,  woods,  are  amongst  the  most 
compressible.  Metals  are  so  also  to  a  great  extent,  as  is  proved  by  the 
process  of  coining,  in  which  the  metal  receives  the  impression  from  the 
die.  There  is,  in  most  cases,  a  limit  beyond  which,  when  the  pressure  is 
increased,  bodies  are  fractured  or  reduced  to  powder. 

The  compressibility  of  liquids  is  so  small  as  to  have  remained  for  a 


8  On  Matter,  Force,  and  Motion.  [17- 

long  time  undetected  :  it  may,  however,  be  proved  by  experiment,  as  will 
be  seen  in  the  chapter  on  Hydrostatics. 

17.  Elasticity. — Elasticity  is  the  property  in  virtue  of  which  bodies 
resume  their  original  form  or  volume,  when  the  force  which  altered  that 
form  or  volume  ceases  to  act.  Elasticity  may  be  developed  in  bodies  by 
pressure,  by  traction  or  pullinf^,  flexion  or  bending,  and  by  torsion  or 
twisting.  In  treating  of  the  general  properties  of  bodies,  the  elasticity 
developed  by  pressure  alone  requires  consideration  ;  the  other  kinds  of 
elasticity  being  peculiar  to  solid  bodies,  will  be  considered  amongst  their 
specific  properties  (arts.  81,  82,  83). 

Gases  and  liquids  are  perfectly  elastic ;  in  other  w^ords,  after  under- 
going a  change  in  volume  they  regain  exactly  their  original  volume 
when  the  pressure  becomes  what  it  originally  was.  Solid  bodies  present 
different  degrees  of  elasticity,  though  none  present  the  property  in  the 
same  perfection  as  liquids  and  gases,  and  in  all  it  varies  according  to  the 
time  during  which  the  body  has  been  exposed  to  pressure.  Caoutchouc, 
ivory,  glass,  and  marble  possess  considerable  elasticity ;  lead,  clay,  and 
fats,  scarcely  any. 

There  is  a  limit  to  the  elasticity  of  solids,  beyond  which  they  either 
break  or  are  incapable  of  regaining  their  original  form  and  volume.  This 
is  called  the  limit  of  elasticity .  In  sprains,  for  instance,  the  elasticity  of 
the  tendons  has  been  exceeded.  In  gases  and  liquids,  on  the  contrary, 
no  such  limit  can  be  reached  ;  they  always  regain  their  original  volume. 

If  a  ball  of  ivory,  glass,  or  marble,  be  allowed  to  fall  upon  a  slab  of 
polished  marble,  which  has  been  previously  slightly  smeared  with  oil,  it 
will  rebound  and  rise  to  a  height  nearly  equal  to  that  from  which  ii  fell. 
On  afterwards  examining  the  ball  a  circular  blot  of  oil  will  be  found  upon 
it,  more  or  less  extensive  according  to  the  height  of  the  fall.  From  this 
we  conclude  that  at  the  moment  of  the  shock  the  ball  was  flattened,  and 
that  its  rebound  was  caused  by  the  effort  to  regain  its  original  form. 

18.  Mobility,  motion,  rest. — Mobility  is  the  property  in  virtue  of 
which  the  position  of  a  body  in  space  may  be  changed. 

Motion  and  rest  may  be  either  relative  or  absolute.  By  the  7-elative 
motion  or  rest  of  a  body  w^e  mean  its  change  or  permanence  of  position 
with  respect  to  surrounding  bodies  ;  by  its  absolute  motion  or  rest  we 
mean  the  change  or  permanence  of  its  position  with  respect  to  ideal  fixed 
points  in  space. 

Thus  a  passenger  in  a  railway  carriage  may  be  in  a  state  of  relative 
rest  with  respect  to  the  train  in  which  he  travels,  but  he  is  in  a  state  of 
relative  motion  with  respect  to  the  objects,  such  as  trees,  houses,  etc., 
past  which  the  train  rushes.  These  houses  again  enjoy  merely  a  state  of 
relative  rest,  for  the  earth  itself  which  bears  them  is  in  a  state  of  inces- 
sant relative  motion  with  respect  to  the  celestial  bodies  of  our  solar 
system,  inasmuch  as  it  moves  at  the  rate  of  more  than  eighteen  miles  in  a 
second.  In  short,  absolute  motion  and  rest  are  unknown  to  us  ;  in 
nature,  relative  motion  and  rest  are  alone  presented  to  our  observation. 

19.  Inertia. — Inertia  is  a  purely  negative  property  of  matter  ;  it  is  the 
incapability  of  matter  to  change  its  own  state  of  motion  or  rest. 


^ 


-21]  Measure  of  Time,  9 

A  body  when  unsupported  in  mid-air  does  not  fall  to  the  earth  in  virtue 
of  any  inherent  property,  but  because  it  is  acted  upon  by  the  force  of 
gravity.  A  billiard  ball  gently  pushed  does  not  move  more  and  more 
slowly,  and  finally  stop,  because  it  has  any  preference  for  a  state  of  rest, 
but  because  its  motion  is  impeded  by  the  friction  on  the  cloth  on  which  it 
rolls,  and  by  the  resistance  of  the  air.  If  all  impeding  causes  were  with- 
drawn, a  body  once  in  motion  would  continue  to  move  for  ever. 

20.  Applic£ition. — Numerous  phenomena  may  be  explained  by  the 
inertia  of  matter.  For  instance,  before  leaping  a  ditch  we  run  towards  it, 
in  order  that  the  motion  of  our  bodies  at  the  time  of  leaping  may  add 
itself  to  the  muscular  effort  then  made. 

On  descending  carelessly  from  a  carriage  in  motion,  the  upper  part  of 
the  body  retains  its  motion,  whilst  the  feet  are  prevented  from  doing  so 
by  friction  against  the  ground  ;  the  consequence  is  we  fall  towards  the 
moving  carriage.  A  rider  falls  over  the  head  of  a  horse  if  it  suddenly 
stops.  In  fixing  the  head  of  a  hammer  by  striking  the  handle  against  the 
ground  w€  have  an  application  of  inertia. 

The  terrible  accidents  on  qur  railways  are  chiefly  due  to  inertia.  When 
the  motion  of  the  engine  is  suddenly  arrested  the  carriage^  strive  to 
continue  the  motion  they  had  acquired,  and  in  doing  so  are  shattered 
against  each  other. 

Hammers,  pestles,  stampers  are  applications  qf  inertia.  So  are  also 
the  enormous  iron  fly-wheels,  by  which  the  motion  of  steam  engines  is 
regulated. 

CHAPTER   III, 
ON  force;,  e;quilibrium,  and,  motion, 

21.  XMCeti'Sure  of  Time. — To  obtain  a  proper  measure  of  force  it  is 
necessary,  as  a  preliminary,  to  define  certain  conceptions  which  are  pre- 
supposed in  that  measure  ;  and,  in  the  first  place,  it  is  necessary  to  define 
the  unit  of  time.  Whenever  a  second  is  spoken  of  without  qualification  it 
is  understood  to  be  a  second  of  mean  solar  time.  The  exact  length  of 
this  unit  is  fixed  by  the  following  consideration.  The  instant  when  the 
sun's  centre  is  on  an  observer's  meridian — in  other  words,  the  instant  of 
the  transit  of  the  sun's  centre — can  be  determined  with  exactitude,  and 
thus  the  interval  which  elapses  between  two  successive  transits  also  admits 
of  exact  determination,  and  is  called  an  apparent  day.  The  length  of 
this  interval  differs  slightly  from  day  to  day,  and  therefore  does  not  serve 
as  a  convenient  measure  of  time.  Its  average  length  is  free  from  this 
inconvenience,  and  therefore  serves  as  the  required  measure,  and  is  called 
a  mean  solar  day.  The  short  hand  of  a  common  clock  w^ould  go  exactly 
twice  round  the  face  in  a  mean  solar  day  if  it  went  perfectly.  The  mean 
solar  day  consists  of  24  equal  parts  called  hours,  these  of  60  equal  parts 
called  minutes^  and  these  of  6q  equal  parts  called  seconds.  Consequently, 
the  second  is  the  86,400th  part  of  a  mean  solar  day,  and  is  the  generally 
received  unit  of  time, 


10  On  Matter,  Force,  and  Motion.  [22- 

22.  Measure  of  Space. — Space  may  be  either  length  or  distance,  which 
is  space  of  one  dimension  ;  area,  which  is  space  of  two  dimensions ;  or 
volume,  which  is  space  of  three  dimensions.  In  England  the  standard  of 
length  is  the  British  Imperial  Yard,  which  is  the  distance  between  two 
points  on  a  certain  metal  rod,  kept  in  the  Tower  of  London,  when  the 
temperature  of  the  whole  rod  is  6o°  F.  =  i5°-5  C.  It  is,  however,  usual  to 
employ  as  a  unit,  difoot,  which  is  the  third  part  of  a  yard.  In  France  the 
standard  of  length  is  the  metre ;  this  is  approximately  equal  to  the  ten- 
millionth  part  of  a  quadrant  of  the  earth's  meridian,  that  is  of  the  arc 
from  the  Equator  to  the  North  Pole  ;  it  is  practically  fixed  by  the  distance 
between  two  rnarks  on  a  certain  standard  rod.  The  relation  between 
these  standards  is  as  follows  : 

I  yard     =0*914383  metre. 
I  metre  =  i  "093633  yard. 

The  unit  of  length  having  been  fixed,  the  units  of  area  and  volume  are 
connected  with  it  thus  :  the  unit  of  area  is  the  area  of  a  square,  one  side 
of  which  is  the  unit  of  length.  The  unit  of  volunie  is  the  volume  of  a 
cube,  one  edge  of  which  is  the  unit  of  length.  These  units  in  the  case  of 
English  measures  are  the  square  yard  (or  foot)  and  the  cubic  yard  (or 
foot)  respectively  ;  in  the  case  of  French  measures,  the  square  metre  and 
cubic  metre  respectively. 

23.  Measure  of  XMEass. — Two  bodies  are  said  to  have  equal  masses 
when,  if  placed  in  a  perfect  balance  in  vacuo,  they  counterpoise  each 
other.  Suppose  we  take  lumps  of  any  substance,  lead,  butter,  wood, 
stone,  etc.,  and  suppose  that  any  of  them  when  placed  on  one  pan  of  a 
balance  will  exactly  counterpoise  any  other  of  them  when  placed  on  the 
opposite  pan — the  balance  being  perfect  and  the  weighing  performed  in 
vacuo  ;  this  being  the  case,  these  lumps  are  said  to  have  equal  masses. 
That  these  lumps  differ  in  many  respects  from  each  other  is  plain  enough  ; 
in  what  respects  they  have  the  same  properties  in  virtue  of  the  equality 
of  their  masses  is  to  be  ascertained  by  subsequent  enquiry. 

The  British  unit  of  mass  is  the  standard  pound  (avoirdupois),  which 
is  a  certain  piece  of  platinum  kept  in  the  Exchequer  Office  in  London. 
This  unit  having  been  fixed,  the  mass  of  a  given  substance  is  expressed 
as  a  multiple  or  submultiple  of  the  unit. 

It  need  scarcely  be  mentioned  that  many  distances  are  ascertained  and 
expressed  in  yards  which  it  would  be  physically  impossible  to  measure 
directly  by  a  yard  measure.  In  like  manner  the  masses  of  bodies  are 
frequently  ascertained  and  expressed  numerically  which  could  not  be 
placed  in  a  balance  and  subjected  to  direct  weighing. 

24.  Density  and  Relative  Density. — If  we  consider  any  body  or 
portion  of  matter,  and  if  we  conceive  it  to  be  divided  into  any  number  of 
parts  having  equal  volumes,  then,  if  the  masses  of  these  parts  are  equal, 
in  whatever  way  the  division  be  conceived  as  taking  place,  that  body  is 
one  of  uniform  density.  The  density  of  such  a  body  is  the  mass  of  the 
unit  of  volume.  Consequently  if  M  denote  the  mass,  V  the  volume,  and 
D  the  density  of  the  body,  we  have 

M=VD. 


-25]  Velocity.  1 1 

If  now  we  have  an  equal  volume  V  of  any  second  substance  whose  mass 
is  M'  and  density  D',  we  shall  have 

M'  =  VD'. 
Consequently  D  :  D'  ::  M  :  M^ ;  that  is  the  densities  of  substances  are 
in  the  same  ratio  as  the  masses  of  equal  volumes  of  those  substances.  If 
now  we  take  the  density  of  distilled  water  at  4°  C.  to  be  unity,  the 
relative  density  of  any  other  substance  is  the  ratio  which  the  mass  of 
any  given  volume  of  that  substance  at  that  temperature  bears  to  the  mass 
of  an  equal  volume  of  water.  Thus  it  is  found  that  the  mass  of  any 
volume  of  platinum  is  22-069  times  that  of  an  equal  volume  of  water, 
consequently  the  relative  density  of  platinum  is  22*069. 

The  relative  density  of  a  substance  is  generally  called  its  specific 
gravity.     Methods  of  determining  it  are  given  in  Book  III. 

In  French  measures  the  cubic  deciinetre  or  litre  of  distilled  water  at  4° 
C.  contains  the  unit  of  mass,  the  kilogramme  ;  and  therefore  the  mass  in 
kilogrammes  of  V  cubic  decimetres  of  a  substance  whose  specific  gravity 
is  D,  will  be  given  by  the  equation 

M  =  VD. 
The  same  equation  will  give  the  mass  in  grammes  of  the  body,  if  V  is 
given  in  cubic  centimetres. 

It  has  been  ascertained  that  277274  cubic  inches  of  distilled  water 
at  the  temperature  1 5°-5  C.  or  60°  F.  contain  a  pound  of  matter.  Conse- 
quently, if  V  is  the  vohime  of  a  body  in  cubic  inches,  D  its  specific  gravity, 
its  mass  M  in  lbs.  avoirdupois  will  be  given  by  the  equation 

M  = ^• 

277274 

In  this  equation  D  is,  properly  speaking,  the  relative  density  of  the  sub- 
stance at  60°  F.  when  the  density  of  water  at  60°  F.  is  taken  as  the  unit. 

25.  Velocity  and  Its  measure. — When  a  material  point  moves,  it 
describes  a  continuous  line  which  may  be  either  straight  or  curved,  and 
is  called  its  path  and  sometimes  its  trajectory.  Motion  which  takes 
place  along  a  straight  line  is  called  rectilinear  motion  ;  that  which  takes 
place  along  a  curved  line  is  called  curvilinear  motion.  The  rate  of  the 
motion  of  a  point  is  called  its  velocity.  Velocity  may  be  either  uniform  or 
variable  ;  it  is  u7iiform  when  the  point  describes  equal  spaces  of  portions 
of  its  path  in  all  equal  times  ;  it  is  variable  when  the  point  describes  un- 
equal portions  of  its  path  in  any  equal  times. 

Uniform  velocity  is  measured  by  the  number  of  units  of  space  de- 
scribed in  a  given  unit  of  time.  The  units  commonly  employed  are  feet 
and  seconds.  If,  for  example,  a  velocity  5  is  spoken  of  without  qualifica- 
tion, this  means  a  velocity  of  5  feet  per  second.  Consequently,  if  a  body 
moves  for  /  seconds  with  a  uniform  velocity  7/,  it  will  describe  vt  feet. 

The  following  are  a  few  examples  of  different  degrees  of  velocity  ex- 
pressed in  this  manner.  A  snail  0*005  feet  in  a  second;  the  Rhine 
between  Worms  and  Mainz  3-3  ;  military  quick  step  4-6  ;  moderate  wind 
10  ;  fast  sailing  vessel  i8-o  ;  channel  steamer  22*0  ;  railway  train  36  to  75 
feet;  racehorse  and  storm  50  feet  ;  eagle  100  feet  ;  carrier  pigeon  12a 


1 2  On  Matter y  Force ^  and  Motion.  [26- 

feet ;  a  hurricane  i6o  feet  ;  sound  at  0^1090  ;  a  point  on  the  Equator  in 
its  rotation  about  the  earth's  axis  1520  ;  a  Martini-Henry  rifle  bullet  1330  ; 
a  shot  from  an  Armstrong  gun  1 180 ;  the  centre  of  the  earth  loiooo  ;  light 
and  also  electricity  in  a  medium  destitute  of  resistance  192000  miles. 

Variable  velocity  is  measured  at  any  instant  by  the  number  of  units  of 
space  a  body  would  describe  if  it  continued  to  move  uniformly  from  that 
instant  for  a  unit  of  time.  Thus,  suppose  a  body  to  run  down  an  inclined 
plane,  it  is  a  matter  of  ordinary  observation  that  it  moves  more  and  more 
quickly  during  its  descent ;  suppose  that  at  any  point  it  has  a  velocity 
15,  this  means  that  at  that  point  it  is  moving  at  the  rate  of  15  ft.  per 
second,  or  in  other  words,  if  from  that  point  all  increase  of  velocity 
ceased,  it  would  describe  15  ft.  in  the  next  second. 

26.  Force. — When  a  material  point  is  at  rest,  it  has  no  innate  power 
of  changing  its  state  of  rest ;  when  it  is  in  motion  it  has  no  innate  power 
of  changing  its  state  of  uniform  motion  in  a  straight  line.  This  property 
of  matter  is  termed  its  inertia  (19).  Any  cause  which  sets  a  point  in 
motion,  or  which  changes  the  magnitude  or  direction  of  its  velocity  if  in 
motion,  is  a  force.  Gravity ,  friction,  elasticity  of  springs  or  gases,  elec- 
trical or  magnetic  attraction  or  repulsion,  etc.  are  forces.  All  changes 
observed  in  the  motion  of  bodies  can  be  referred  to  the  action  of  one  or 
more  forces. 

27.  Accelerative  effect  of  force. — If  we  suppose  a  force  to  con- 
tinue unchanged  in  magnitude,  and  to  act  along  the  line  of  motion  of  a 
point,  it  will  communicate  in  each  successive  second  a  constant  increase 
of  velocity.  This  constant  increase  is  the  accelerative  effect  of  the  force. 
Thus,  if  at  any  given  instant  the  body  has  a  velocity  10,  and  if  at  the  end 
of  the  first,  second,  third,  etc.,  second  from  that  instant  its  velocity  is 
13,  16,  19,  etc.,  the  accelerative  effect  of  the  force  is  3  ;  a  fact  which  is 
expressed  by  saying  that  the  body  has  been  acted  on  by  an  accelerating 
force  3. 

If  the  force  vary  from  instant  to  instant,  its  accelerative  effect  will  also 
vary  ;  when  this  is  the  case  the  accelerative  effect  at  any  instant  is  mea- 
sured by  the  velocity  it  would  communicate  in  a  second  if  the  force 
continued  constant  from  that  instant. 

By  means  of  an  experiment  to  be  described  below  (76)  it  can  be  shown 
that  at  any  given  place  the  accelerative  effect  of  gravity^  is  constant ;  but 
it  is  found  to  have  different  values  at  different  places  ;  adopting  the 
units  of  feet  and  seconds  it  is  found  that  with  sufficient  approximation 

^=/  (l 0-00256  cos  20) 

at  a  place  whose  latitude  is  0,  where/"  denotes  the  number  32 "1724,  that 
is  the  effect  of  gravity  in  latitude  45°. 

If  we  adopt  th^units  of  metres  and  seconds,  then/  =  9-8059. 

28.  AKomentum  or  quantity  of  motion  is  a  magnitude  varying  as  the 
mass  of  a  body  and  its  velocity  jointly,  and  therefore  is  expressed  nume- 
rically by  the  product  of  the  number  of  units  of  mass  which  it  contains 
and  the  number  of  units  of  velocity  in  its  motion.  Thus  a  body  con- 
taining 5  lbs.  of  matter,  and  moving  at  the  rate  of  12  ft.  per  second,  has 
a  momentum  of  60. 


-30]  Representation  of  Forces,  13 

29.  Measure  of  force. — Force,  when  constant,  is  measured  by  the 
momentiun  it  communicates  to  a  body  in  a  unit  of  time.  If  the  force 
varies,  it  is  then  measured  at  any  instant  by  the  momentum  it  would 
communicate  if  it  continued  constant  for  a  unit  of  time  from  the  instant 
under  consideration.  The  unit  of  force  is  that  force  which  acting  on  a 
pound  of  matter  would  produce  in  one  second  a  velocity  of  one  foot  per 
second.  Consequently  if  a  body  contains  m  lbs.  of  matter,  and  is  acted 
pn  by  a  force  whose  accelerative  effect  is^^  that  force  contains  a  number 
of  units  of  force  (F),  given  by  the  equation 

F  =  mf. 

The  weight  of  a  body,  when  that  term  denotes  a  force,  is  the  force 
exerted  on  it  by  gravity  ;  consequently,  if  m  is  the  mass  of  the  body,  and 
g  the  accelerating  force  of  gravity,  the  number  of  units  of  force  W  exeited 
on  it  by  gravity  is  given  by  the  equation 

W  =^  mg 
or  (27)  ^  =  mf{i — 0-00256  cos  20). 

From  this  it  is  plain  that  the  weight  of  the  same  body  will  be  different  at 
different  parts  of  the  earth's  surface  ;  this  could  be  verified  by  attaching 
a  piece  of  platinum  (or  other  metal)  to  a  delicate  spring,  and  noting  the 
variations  in  the  length  of  the  spring  during  a  voyage  from  a  station  in 
the  Northern  Hemisphere  to  another  in  the  Southern  Hemisphere,  for 
instance,  from  London  to  the  Cape  of  Good  Hope. 

When,  therefore,  3.potmd\s  used  as  a  unit  of  force  it  must  be  under- 
stood to  mean  the  force  W  exerted  by  gravity  on  a  pound  of  matter  in 
London.  Now,  in  London,  the  latitude  of  which  is  51-30,  the  numerical 
value  of  ^is  32-1912,  so  that 

W=  I  X  32-1912  ; 

in  other  words,  when  a  pound  is  taken  as  the  unit  of  force  it  contains 
32-1912  units  of  force  according  to  the  measure  given  above.  It  will  be 
observed  that  a  pound  of  matter  is  a  completely  determinate  quantity  of 
matter  irrespective  of  locality,  but  gravity  exerts  on  a  pound  of  matter 
a  pound  (or  32*1912  units)  of  force  at  London  and  other  places  in  about 
the  same  latitude  as  London  only  ;  this  ambiguity  in  the  term  pound 
should  be  carefully  noticed  by  the  student ;  the  context  in  any  treatise 
will  always  show  in  which  sense  the  term  is  used. 

30.  Representation  of  forces. — Draw  any  straight  line  AB,  and  fix 
on  any  point  O  in  it.  We  may  suppose  a  force  to  act  on  the  point  O, 
along  the  line  AB,  either  towards  A  or  B  :  then  O 

is  called  the  point  of  application  of  the  force,  AB    b    m         o ]« — a 

its  line  of  action ;  if  it  acts  towards  A,  its  direction  p. 

is  OA,  if  towards  B,  its  direction  is  OB.     It  is 

rarely  necessary  to  make  the  distinction  between  the  line  of  action  and 

direction  of  a  force  ;  it  being  very  convenient  to  make  the  convention 

that  the  statement — a  force  acts  on  a  point  O  along  the  line  OA — means 

that  it  acts  from  O  to  A.     Let  us  suppose  the  force  which  acts  on  O  along 

OA  to  contain  P  units  of  force  ;  from  O  towards  A  measure  ON  coni 


14  Oil  Matter,  Force,  and  Motion.  [30- 

taining  P  units  of  length,  the  hne  ON  is  said  to  represent  the  force.  It 
will  be  remarked  that  the  analogy  between  the  line  and  the  force  is  very- 
complete  ;  the  line  ON  is  drawn  from  O  in  a  given  direction  OA,  and 
contains  a  given  number  of  units  P,  just  as  the  force  acts  on  O  in  the 
direction  OA,  and  contains  a  given  number  of  units  P.  It  is  scarcely 
necessary  to  add,  that  if  an  equal  force  were  to  act  on  O  in  the  opposite 
direction,  it  would  be  said  to  act  in  the  direction  OB,  and  would  be  re- 
presented by  OM,  equal  in  magnitude  to  ON. 

When  we  are  considering  several  forces  acting  along  the  same  line  we 

may  indicate  their  directions  by  the  positive  and  negative  signs.     Thus 

the  forces  mentioned  above  would  be  denoted  by  the  symbols  +  P  and 

—  P  respectively. 

;         31.  Forces  acting-  along:  the  same  line. — If  forces  act  on  the  point 

i  O  in  the  direction  OA  equal  to  P  and  Q  units  respectively,  they  are 

\  equivalent  to  a  single  force  R  containing  as  many  units  as  P  and  Q 

together,  that  is, 

R  =  P  +  Q. 

If  the  sign  +  in  the  above  equation  denote  algebraical  addition,  the  equation 
will  continue  true  whether  one  or  both  of  the  forces  act  along  OA  or  OB. 
It  is  plain  that  the  same  rule  can  be  extended  to  any  number  of  forces, 
and  if  several  forces  have  the  same  line  of  action  they  are  equivalent  to 
one  force  containing  the  same  number  of  units  as  their  algebraical  sum. 
Thus  if  forces  of  3  and  4  units  act  on  O  in  the  direction  OA,  and  a  force 
of  8  in  the  direction  OB,  they  are  equivalent  to  a  single  force  containing 
R  units  given  by  the  equation 

R=3+4-8=-i; 

that  is,  R  is  a  force  containing  one  unit  acting  along  OB.  This  force  R 
is  called  their  resultant.  If  the  forces  are  in  equilibrium  R  is  equal  to 
zero.  In  this  case  the  forces  have  equal  tendencies  to  move  the  point  O 
in  opposite  directions. 

32.  Resultant  and  components. — In  the  last  article  we  saw  that  a 
single  force  R  could  be  found  equivalent  to  several  others  ;  this  is  by  no 
J,  I  means  peculiar  to  the  case  in  which  all  the  forces  have 

the  same  line  of  action  ;  in  fact,  when  a  material 
point,  A  (fig.  4),  remains  in  equilibrium  under  the 
action  of  several  forces,  S,  P,  Q,  it  does  so  because 
any  one  of  the  forces,  as  S,  is  capable  of  neutralising 
the  combined  effects  of  all  the  others.  If  the  force  S, 
therefore,  had  its  direction  reversed,  so  as  to  act  along 
\  AR,  the  prolongation  of  AS,  it  would  produce  the 

\         same  effect  as  the  system  of  forces  P,  Q. 
\  Now,  a  force  whose  effect  is  equivalent  to  the  com- 

\    bined  effects  of  several  other  forces  is  called  their  re- 
P    sultanty  and  with  respect  to  this  resultant,  the  other 
^^  ^  forces  are  termed  components. 

When  the  forces,  P,  Q,  act  on  a  point  they  can  only  have  otie  resultant  ; 


-33]  Parallelogram  of  Forces.  15 

but  any  single  force  can  be  resolved  into  components  in  an  indefinite 
number  of  ways. 

If  a  point  move  from  rest  under  the  action  of  any  number  of  forces  it 
will  begin  to  move  in  the  direction  of  their  resultant. 

33.  Parallelograxu  of  forces. — When  two  forces  act  on  a  point  their 
resultant  is  found  by  the  following  theorem,  known  as  the  principle  of 
the  parallelogram  of  forces: — If  two  forces  act  on  a  point ,  arid  if  lines  be 
drawn  from  that  point  representing  the  forces  in  magnitude  and  direction, 
and  oji  these  lines  as  sides  a  parallelogram  be  cotistructed,  their  resultant 
will  be  represented  in  7nagnitude  and  direction  by  that  diagonal  which 
passes  through  the  point.  Thus  let  P  and  Q  (fig.  5)  be  two  forces  acting 
on  the  point  A  along  AP  and  AQ  respectively,  and  let  AB  and  AC  be 
taken  containing  the  same  number  of  units  of  length  that  P  and  Q  con- 
tain units  of  force  ;  let  the  parallelogram  AB  DC  be  completed,  and  the 
diagonal  AD  drawn  ;  then  the  theorem  states  that  the  resultant,  R,  of  P 
and  Q  is  represented  by  AD  ;  that  is  to  say,  P  and  Q  together  are  equal 
to  a  single  force  R  acting  along  the  line  AD,  and  containing  as  many 
units  of  force  as  AD  contains  units  of  length. 


Fie.  6. 

Proofs  of  this  theorem  are  given  in  treatises  on  Mechanics ;  we  will 
here  give  an  account  of  a  direct  experimental  verification  of  its  truth;  but 
before  doing  so  we  must  premise  an  account  of  a  very  simple  experiment. 

Let  A  (fig.  6)  be  a  small  pulley,  and  let  it  turn  on  a  smooth,  hard,  and 
thin  axle  with  little  or  no  friction  :  let  W  be  a  weight  tied  to  the  end  of  a  fine 
thread  which  passes  over  the  pulley ;  let  a  spring  CD  be  attached  by  one 
end  to  the  end  C  of  the  thread  and  by  the  end  D  to  another  piece  of 
thread,  the  other  end  of  which  is  fastened  to  a  fixed  point  B;  a  scale  CE 
can  be  fastened  by  one  end  to  the  point  C  and  pass  inside  the  spring  so 
that  the  elongation  of  the  spring  can  be  measured.  Now  it  will  be  found 
on  trial  that  with  a  given  weight  W  the  elongation  of  the  spring  will  be 
the  same  whatever  the  angle  contained  between  the  parts  of  the  string 
WA  and  BA.  Also  it  would  be  found  that  if  the  whole  were  suspended 
from  a  fixed  point,  instead  of  passing  over  the  pulley,  the  weight  would 
in  this  case  stretch  the  spring  to  the  same  extent  as  before.  This  experi- 
ment shows  that  when  care  is  taken  to  diminish  to  the  utmost  the  friction 
of  the  axle  of  the  pulley,  and  the  imperfect  flexibility  of.  the  thread,  the 


i6 


On  Matter,  Force,  and  Motio7i. 


[33- 


weight  of  W  is  transmitted  without  sensible  diminution  to  B,  and  exerts 
on  that  point  a  pull  or  force  along  the  line  BA  virtually  equal  to  W. 

This  being  premised,  an   experimental  proof,    or   illustration  of  the 
parallelogram  of  forces,  may  be  made  as  follows  : — 

Suppose  H  and  K  (fig.  7)  to  be  two  pulleys  with  axles  made  as  smooth 
and  fine  as  possible  ;  let  P  and  Q  be  two  weights  suspended  from  fine 
and  flexible  threads  which,  after  passing  over 
H  and  K,  are  fastened  at  A  to  a  third 
thread  AL  from  which  hangs  a  weight  R ; 
let  the  three  weights  come  to  rest  in  the 
positions  shown  in  the  figure.  Now  the  point 
A  is  acted  on  by  three  forces  in  equilibrium, 
viz.,  P  from  A  to  H,  Q  from  A  to  K,  and  R 
from  A  to  L,  consequently  any  one  of  them 
must  be  equal  and  opposite  to  the  resultant 
of  the  other  two.  Now  if  we  suppose  the 
apparatus  to  be  arranged  immediately  in  front  of  a  large  slate,  we  can 
draw  lines  upon  it  coinciding  with  AH,  AK,  and  AL,  If  now  we  mea^ 
sure  off  along  AH  the  part  AB- containing  as  many  inches  as  P  contains 
pounds,  and  along  AK  the  part  AC  containing  as  many  inches  as  Q  con- 
tains pounds,  and  complete  the  parallelogram  ABCD,  it  will  be  found 
that  the  diagonal  AD  is  in  the  same  Hne  as  AL,  and  contains  as  many 
inches  as  R  weighs  pounds.  Consequently,  the  resultant  of  P  and  Q  is 
represented  by  AD.  Of  course,  any  other  units  of  length  and  force  might 
have  been  employed.  Now  it  will  be  found  that  when  P,  Q,  and  R 
are  changed  in  any  way  whatever,  consistent  with  equilibrium,  the  same 
construction  can  be  made, — the  point  A  will  have  different  positions  in 
the  different  cases  ;  but  when  equilibrium  is  established,  and  the  paral- 
lelogram ABCD  is  constructed,  it  will  be  found  that  AD  is  vertical,  and 
contains  as  many  units  of  length  as  R  contains  units  of  force,  and  conse- 
quently it  represents  a  force  equal  and  opposite  to  R,  that  is,  it  represents 
the  resultant  of  P  and  Q. 

34.  Resultant  of  any  number  of  forces  acting:  in  one  plane  on 
a  point. — Let  the  forces  P,  Q,  R,  S  (fig.  8)  act  on  the  point  A,  and  let 
them  be  represented  by  the  lines  AB,  AC,  AD, 
Y\  AE,  as  shown  in  the  figure.  First,  complete  the 
parallelogram  ABFC  and  join  AF ;  this  line 
represents  the  resultant  of  P  and  Q.  Secondly, 
complete  the  parallelogram  AFGD  and  join 
AG;  this  line  represents  the  resultant  of  P,  Q,  R. 
Thii'dly,  complete  the  parallelogram  AG  HE 
and  join  AH  ;  this  line  represents  the  resultant 
of  P,  Q,  R,  S.  It  is  manifest  that  the  construc- 
tion can  be  extended  to  any  number  of  forces. 
A  little  consideration  will  show  that  the  line 
AH  might  be  determined  by  the  following 
through  B  draw  BF  parallel  to,  equal  to,  and  towards  the 
same  part  as  AC;  through  F  draw  FG  parallel  to,  equal  to,  and  towards 


^36] 


Conditions  of  Equilibrium  of  Forces. 


17 


Fig.  9. 


the  same  part  as  AD;  through  G  draw  GH  parallel  to,  equal  to,  and  towards 
the  same  part  as  AE;  join  AH,  then  AH  represents  the  required  resultant. 
In  place  of  the  above  construction,  the  resultant  can  be  determined 
by  calculation  in  the  following  manner  : — Through  A  draw  any  tvvo 
rectangular  axes  Ax  and  Ay  (fig.  9),  and  let  a,  a:?,  y 
be  the  angles  made  with  the  axis  Ax  by  the  lines 
representing  the  pressures,  then  P,  Q,  R  can  be 
resolved  into  P  cos  a,  O  cos  |8,  R  cos  y,  acting 
along  Ax,  and  P  sin  a,  Q  sin  (5,  R  sin  7,  acting 
along  Ay.  Now  the  former  set  of  forces  can  be 
reduced  to  a  single  force  X  by  addition,  attention 
being  paid  to  the  sign  of  each  component ;  and  in 
like  manner  the  latter  forces  can  be  reduced  to  a 
single  force  Y,  that  is, 

X  =  P  cos  a  +  Q  cos  /3  +  R  cos  y  + . . . 

Y  =  P  sin  a  +  Q  sin  ^3  +  R  sin  y  + . . . 
Since  the  addition  denotes  the  algebraical  sum  of  the  quantities  on  the 
right  hand  side  of  the  equations,  both  sign  and  magnitude  of  X  and  Y  are 
known.     Suppose  U  to  denote  the  required  resultant,  and  ^  the  angle 
made  by  the  line  representing  it  with  the  axis  Ax ; 
then  U  cos  ^  =  X,  and  U  sin  •/>  =  Y. 

These  equations  give  U2  =  X2  +  Y2,  which  determines  the  magnitude 
of  the  resultant,  and  then,  since  both  sin  ^  and  cos  ^  are  known,  0  is 
determined  without  ambiguity. 

Thus  let  P,  Q,  and  R  be  forces  of  100,  150,  and  120  units,  respectively, 
and  suppose  xAP,  xAO,  and  xAR  to  be  angles  of  45°,  120*',  and  210°  re- 
spectively. Then  their  components  along  Ax  are  707, — 75, — 103'9,  ^^id 
their  components  along  Ay  are  707, — 129*9, — 60.  The  sums  of  these 
two  sets  being  respectively — 108*2  and  140*6,  we  have  U  cos  0=  —108*2 
and  U  sin  ^=  140*6. 

therefore  U^  =  (108*2)2  ^.  (140*6)= 

or  U  =177-4 

therefore  I77'4  cos  ^  =  -  108*2,  and  177*4  sin  ^  =  140-6. 

If  we  made  use  of  the  former  of  these  equations  only,  we  should  obtain 
^  equal  to  232°  25',  or  127°  35',  and  the  result  would  be  ambiguous  :  in 
like  manner,  if  we  determined  ^  from  the  second  equation  only,  we  should 
have  0  equal  to  52°  25',  or  127°  35';  but  as  we  have  both  equations,  we 
know  that  ^  equals  127°  35',  and  consequently  the  force  U  is  completely 
determined  as  indicated  by  the  dotted  line  AU. 

35.  Conditions  of  equilibrium  of  any  force  actingr  in  one  plane 
on  a  point. — If  the  resultant  of  the  forces  is  zero,  they  have  no  joint 
tendency  to  move  the  point,  and  consequently  are  in  equilibrium.  This 
obvious  principle  enables  us  to  deduce  the  following  constructions  and 
equations,  which  serve  to  ascertain  whether  given  forces  will  keep  a  point 
at  rest. 

Suppose  that  in  the  case  represented  in  fig.  8,  T  is  the  force  which  will 
balance  P,  Q,  R,  S.    It  is  plain  that  T  must  act  on  A  along  HA  produced, 


i8 


On  Matter,  Force,  and  Motio7t. 


[35- 


and  in  magnitude  must  be  proportional  to  HA  ;  for  then  the  resultant  of 
the  five  forces  will  equal  zero,  since  the  broken  line  ABFGHA  returns  to 
the  point  A.  This  construction  is  plainly  equivalent  to  the  following  : 
Let  P,  Q,  R  (fig.  lo)  be  forces  acting  on  the  point  O,  as  indicated,  their 
magnitudes  and  directions  being  given.  It  is  known  that  they  are  balanced 
by  a  fourth  force,  S,  and  it  is  required  to  determine  the  magnitude  and 
direction  of  S.  Take  any  point  D,  and  draw  any  line  parallel  to  and 
towards  the  same  part  as  OP,  draw  AB  parallel  to  and  towards  the  same 
parts  as  OQ,  and  take  AB  such  that  P  :  Q : :  DA  :  AB.  Through  B  draw 
BC  parallel  to  and  towards  the  same  part  as  OR,  taking  BC  such  that 
O  :  R::AB  :  BC;  join  CD;  through  O  draw  OS  parallel  to  and  towards 
the  same  part  as  CD,  then  the  required  force  S  acts  along  OS,  and  is  in 
magnitude  proportional  to  CD. 


Fig.  lo. 


Fig. 


It  is  to  be  observed  that  this  construction  can  be  extended  to  any 
number  of  forces,  and  will  apply  to  the  case  in  which  these  directions  are 
not  in  one  plane,  only  in  this  case  the  broken  line  ABCD  would  not  lie 
wholly  in  one  plane.  The  above  construction  is  frequently  called  the 
Polygon  of  Forces. 

The  case  of  three  forces  acting  on  a  point  is,  of  course,  included  in  the 
above ;  but  its  importance  is  such  that  we  may  give  a  separate  statement 
of  it.  Let  P,  Q,  R  (fig.  1 1)  be  three  forces  in  equilibrium  on  the  point  O. 
From  any  point  B  draw  BC  parallel  to  and  towards  the  same  part  OP, 
from  C  draw  CA  parallel  to  and  towards  the  same  part  as  00,  and  take 
CA  such  that  P  :  Q::BC  :  CA;  then,  on  joining  AB,  the  third  force  R 
must  act  along  OR  parallel  to  and  towards  the  same  part  as  AB,  and  must 
be  proportional  in  magnitude  to  AB.  This  construction  is  frequently 
called  the  Triangle  of  Forces.  It  is  evident  that  while  the  sides  of  the 
triangle  are  severally  proportional  to  P,  O,  R,  the  angles  A,  B,  C  are 
supplementary  to  QOR,  ROP,  POQ  respectively,  consequently  every 
trigonometrical  relation  existing  between  the  sides  and  angles  of  ABC 
will  equally  exist  between  the  forces  P,  Q,  R,  and  the  supplements  of  the 
angles  between  their  directions.  Thus  in  the  triangle  ABC  it  is  known  that 
the  sides  are  proportional  to  the  sines  of  the  opposite  angles  ;  now  since 
the  sines  of  the  angles  are  equal  to  the  sines  of  their  supplements,  we  at 
once  conclude  that  when  three  forces  are  in  eqtiilibrium,  each  is  propor- 
tional to  the  sine  of  the  angle  between  the  directio7is  of  the  other  two. 


-36]  Parallel  Forces.  1 9 

We  can  easily  obtain  from  the  equations  which  determine  the  resultant 
of  any  number  of  forces  (34),  equations  which  express  the  conditions  of 
equilibrium  of  any  number  of  forces  acting  in  one  plane  on  a  point  ;  in 
fact,  if  U  =  O  we  must  have  X  =  o  and  Y  =  O  ;  that  is  to  say,  the  required 
conditions  of  equilibrium  are  these  : — 

O  =  P. cos  a  +  Q  cos  |3  +  R  cos  y  +  .. . 
and  O  =>  P  sin  a  +  Q  sin  /3  +  R  sin  y  + . . . 

The  first  of  these  equations  shows  that  no  part  of  the  motion  of  the  point 
can  take  place  along  Ax,  the  second  that  no  part  can  take  place  along  Ay. 
In  other  words,  the  point  cannot  move  at  all. 
V  36.  Composition  and  resolution  of  parallel  forces. — The  case  of 
the  equilibrium  of  three  parallel  forces  is  merely  a  particular  case  of  the 
equilibrium  of  three  forces  acting  on  a  point.  In  fact  let  P  and  O  be 
two  forces  whose  directions  pass  through  the  points  A  and  B,  and  inter- 
sect in  O ;  let  them  be  balanced  by  a  third  force  R  whose  direction 
produced  intersects  the  line  AB  in  C.  Now  suppose 
the  point  O  to  move  along  AO,  gradually  receding 
from  A,  the  magnitude  and  direction  of  R  will  con- 
tinually change,  and  also  the  point  C  will  continually 
change  its  position,  but  will  always  lie  between  A  and 
B.  In  the  limit  P  and  Q  become  parallel  forces, 
acting  towards  the  same  part  balanced  by  a  parallel 
force  R  acting  towards  the  contrary  part  through  a 
point  X  between  A  and  B.  The  question  is  : — First^ 
on  this  limiting  case  what  is  the  value  of  R  ;  secondly., 
what  is  the  position  of  X  ?  Now  with  regard  to  the  a, 
first  point  it  is  plain,  that  if  a  triangle  a  b  c  were  drawn  iv 
as    in   art.  35,  the   angles  a  and  b  in  the  limit  will  Fig.  12. 

vanish,  and  ^  will  become  180°,  consequently rt;  b  ultimately  equals  ac  -v  cb; 
or  R  =  P  +  Q. 

With  regard  to  the  second  point  it  is  plain  that 

OC  sin  POR  =  OC  sin  AOC  =  AC  sin  CAO, 
and  OC  sin  ROQ  =  OC  sin  BOC  =  CB  sin  CBO; 

therefore    AC  sin  CAO  :  CB  sin  CBO ::  sin  POR  :  sin  ROQ 

::Q:P(35).  \ 

Now  in  the  limit,  when  OA  and  OB  become  parallel,  OAB  and  OB  A 
become  supplementary ;  that  is,  their  sines  become  equal ;  also  AC  and  CB 
become  respectively  AX  and  XB  ;  consequently 

AX:XB::Q:P, 

a  proportion  which  determines  the  position  of  X.     This  theorem  at  once 
leads  to  the  rules  for  the  composition  of  any  two  parallel  forces,  viz. 

I.  When  two  parallel  forces  P  and  O  act  towards  the  same  part,  at 
rigidly  connected  points  A  and  B,  their  resultant  is  a  parallel  force  acting 
towards  the  same  part,  equal  to  their  sum,  and  its  direction  divides  the 


/ 


20  On  Mattel',  Force,  and  Motion.  [36- 

line  AR  into  two  parts  AC  and  CB  inversely  proportional  to  the  forces 
P  and  Q. 

J  II.  When  two  parallel  forces  P  and  O 

J  act  towards  contrary  parts  at  rigidly  con- 

/  nected  points  A  and  B,  of  which  P  is  the 

greater,  their  resultant  is  a  parallel  force 

acting  towards  the  same  part  as  P,  equal 

to  the  excess  of  P  over  Q,  and  its  direc- 

'P^  tion  divides  BA  produced  in  a  point  C 

such  that  CA  and  CB  are  inversely  pro- 

^'^-  '3-  ^^  portional  to  P  and  O. 

In  each  of  the  above  cases  if  we  were 
to  apply  R  at  the  point  C,  in  opposite 
direction  to  those  shown  in  the  figure,  it 
would  plainly  (by  the  above  theorem) 
balance  P  and  O,  and  therefore  when  it 
acts  as  shown  in  figs.  13  and  14  it  is  the 
resultant  of  P  and  Q  in  those  cases  re- 
spectively. It  will  of  course  follow  that 
/  the  force  R  acting  at  C  can  be  resolved 

^'  into  P  and  Q  acting  at  A  and  B  respect- 

'^'  ^^'  ively. 

If  the  second  of  the  above  theorems  be  examined,  it  will  be  found  that 
no  force  R  exists  equivalent  to  P  and  Q  when  those  forces  are  equal. 
Two  such  forces  constitute  a  couple,  which  may  be  defined  to  be  two 
equal  parallel  forces  acting  towards  contrary  parts  ;  they  possess  the 
remarkable  property  that  they  are  incapable  of  being  balanced  by  any 
single  force  whatsoever. 

In  the  case  of  more  than  two  parallel  forces  the  resultant  of  any  two 
can  be  found,  then  of  that  and  a  third,  and  so  on  to  any  number  ;  it  can 
be  shown  that  however  great  the  number  of  forces  they  will  either  be  in 
^  equilibrium  or  reduce  to  a  single  resultant  or  to  a  couple. 
3c  37.  Centre  of  parallel  forces.— On  referring  to  figs.  13  and  14,  it  will 
be  remarked  that  if  we  conceive  the  points  A  and  B  to  be  fixed  in  the 
directions  AP  and  BQ  of  the  forces  P  and  Q,  and  if  we  suppose  those 
directions  to  be  turned  round  A  and  B,  so  as  to  continue  parallel  and  to 
make  any  given  angles  with  their  original  directions,  then  the  direction 
of  their  resultant  will  continue  to  pass  through  C  ;  that  point  is  therefore 
called  the  centre  of  the  parallel  forces  P  and  O. 

It  appears  from  investigation,  that  whenever  a  system  of  parallel  forces 
reduces  to  a  single  resultant,  those  forces  will  have  a  centre  ;  that  is  to 
say,  if  we  conceive  each  of  the  forces  to  act  at  a  fixed  point,  there  will  be 
a  point  through  which  the  direction  of  their  resultant  will  pass  when  the 
directions  of  the  forces  are  turned  through  any  equal  angles  round  their 
points  of  application  in  such  a  manner  as  to  retain  the  parallelism  of 
their  directions. 

The  most  familiar  example  of  a  centre  of  parallel  forces  is  the  case  in 
which  the  forces  are  the  weights  of  the  parts  of  a  body  ;  in  this  case  the 


-39]  Equality  of  Action  and  Reaction.  21 

forces  all  acting  towards  the  same  part  will  have  a  resultant,  viz.  their 
Varum  ;  and  their  centre  is  called  the  ce7itre  of  gravity  of  the  body. 

"^  38.  Moments  of  forces.— Let  P  denote  any  force  acting  from  B  to  P, 
take  A  any  point,  let  fall  AN  a  perpendicular  from  A  on  BP.  The 
product  of  the  number  of  units  of  force  in  P,  and  the  number  of  units  of 
length  in  AN,  is  called  the  moment  of  P  with  respect  to  A.  Since  the 
force  P  can  be  represented  by  a  straight  line,  the 
moment  of  P  can  be  represented  by  an  area.  In  fact, 
if  BC  is  the  line  representing  P,  the  moment  is 
properly  represented  by  twice  the  area  of  the  triangle 
ABC.  The  perpendicular  AN  is  sometimes  called 
the  arm  of  the  pressure.  Now  if  a  watch  were  placed 
with  its  face  upward  on  the  paper,  the  force  P  would  *»  N"  c  p 
cause  the  arm  AN  to  turn  round  A  in  the  contrary  Fig-  ^5- 

direction  to  the  hands  of  the  watch.  Under  these  circumstances,  it  is 
usual  to  consider  the  moment  of  P  with  respect  to  the  point  A  to  be 
positive.  If  P  acted  from  C  to  B,  it  would  turn  NA  in  the  satne  direction 
as  the  hands  of  the  watch,  and  now  its  moment  is  reckoned  negative. 

The  following  remarkable  relation  exists  between  any  forces  acting  in 
one  plane  on  a  body  and  their  "resultant.  Take  the  moments  of  the  forces 
and  of  their  resultant  with  respect  to  any  one  point  in  the  plane.  Then 
the  moment  of  the  resultant  equals  the  sum  of  the  moments  of  the  several 
forces,  regard  being  had  to  the  signs  of  the  moments. 

If  the  point  about  which  the  moments  are  measured  be  taken  in  the 

direction  of  the  resultant,  its  moment  with  respect  to  that  point  will  be 

zero  ;  and  consequently  the  sum  of  the  moments  with  respect  to  such 

point  will  be  zero. 

\        39.  Equality  of  Action  an  d  Reaction. — We  will  proceed  to  exemplify 

*^^ome  of  the  principles  now  laid  down  by  investigating  the  conditions  of 
equilibrium  of  bodies  in  a  few  simple  cases  ;  but  before  doing  so  we  must 
notice  a  law  which  holds  good  whenever  a  mutual  action  is  called  into 
play  between  two  bodies.  Reaction  is  always  equal  and  contrary  to, 
action  :  that  is  to  say,  the  mutual  actiotis  of  two  bodies  on  each  other  ai'e 
always  forces  equal  in  amount  and  opposite  in  direction.  This  law  is  per- 
fectly general,  and  is  equally  true  when  the  bodies  are  in  motion  as  well 
as  when  they  are  at  rest.  A  very  instructive  example  of  this  law  has 
already  been  given  (33),  in  which  the  action  on  the  spring  CD  (fig.  6)  is 
the  weight  W  transmitted  by  the  spring  to  C,  and  balanced  by  the  re- 
action of  the  ground  transmitted  from  B  to  D.  Under  these  circum- 
stances, the  spring  is  said  to  be  stretched  by  a  force  W.  If  the  spring 
were  removed,  and  the  thread  were  continuous  from  A  to  B,  it  is  clear  that 
any  part  of  it  is  stretched  by  two  equal  forces,  viz.  an  action  and  reaction, 
each  equal  to  W,  and  the  thread  is  said  to  sustain  a  tension  W.  When  a 
body  is  urged  along  a  smooth  surface,  the  mutual  action  can  only  take 
place  along  the  common  perpendicular  at  the  point  of  contact.  If,  how- 
ever, the  bodies  are  rough,  this  restriction  is  partially  removed,  and  now 
the  mutual  action  can  take  place  in  any  direction  not  making  an  angle 
greater  than  some  determinate  angle  with  the  common  perpendicular. 


22 


On  Matter^  Force,  and  Motion. 


[40 


This  determinate  angle  has  different  values  for  different  substances,  and 
is  sometimes  called  the  limititig  angle  of  resistance,  sometimes  the  angle 
of  repose. 

40.  Tlie  lever  is  a  name  given  to  any  bar  straight  or  curved,  AB,  rest- 
ing on  a  fixed  point  or  edge  c  called  the 
fulcrum.  The  forces  acting  on  the  lever 
are  the  weight  or  resistance  Q,  Xho.  power 
P,  and  the  reaction  of  the  fulcrum. 
Since  these  are  in  equilibrium,  the  re- 
sultant of  P  and  Q  must  act  through  C, 
for  otherwise  they  could  not  be  balanced 
.  "■"""'""""'  by  the  reaction.     Draw  cb  at  right  angles 

"^  to  QB  and  ca  to  PA  produced  ;  then  ob- 

serving that  P  X  ca,  and  (^xcb  are  the 
moments  of  P  and  Q  with  respect  to  c, 
and  that  they  have  contrary  signs,  we 
have  by  (38), 

V  X  ca  =  Oy.  cb  ; 

^an  equation  commonly  expressed  by  the 
Fig-  16.  rule,  that  in  the  lever  the  power  is  to  the 

weight  in  the  i^iverse  ratio  of  their  arms. 
Levers  are  divided  into  three  kinds,  according  to  the  position  of  the 
fulcrum  with  respect  to  the  points  of  application  of  the  power  and  the 
weight.  \Ti2.lever  of  the  frst  kind  the  {ulcrum  is  between  the  power 
and  resistance,  as  in  fig.  16,  and  as  in  a  poker  and  in  the  common  steel- 
yard ;  a  pair  of  scissors  and  a  carpenter's  pincers  are  double  levers  of  this 
kind.  In  a  lever  of  the  second  kind  Xhe  resistance  is  between  the  power 
and  the  fulcrum,  as  in  a  wheelbarrow,  or  a  pair  of  nutcrackers,  or  a  door; 
in  a  lever  of  the  third  kind  the  power  is  between  the  fulcrum  and  the 
resistance,  as  in  a  pair  of  tongs  or  the  treadle  of  a  lathe. 
_V^  41.  The  single  pulley. — In  the  case  of  the  single  fixed  pulley,  shown 
m  fig.  17,  it  follows  at  once  from  (33)  that  when  the  forces  P  and  Q  are 
in  equilibrium  they  will  be  equal,  the  axle  of  the  pulley  being  supposed 

perfectly  smooth  and  the  thread  perfectly 
}    \      ^.  flexible.       The  same   conclusion   follows 

directly  from  the  principle  of  m.oments  ; 
for  the  resultant  of  P  and  Q  must  pass 
through  C,  or  otherwise  they  would  cause 
the  pulley  to  turn  ;  now  their  moments 
are  respectively  P  x  CM  and  Q  x  CN, 
and  since  these  have  opposite  signs  we 
I  have  (38) 

Go  PxCM  =  QxCN. 

Fig.  18.         But    CM    and    CN     being     equal,    this 

equation    shows     that     P     and     Q    are 

equal.     In  the  case  of  the  single  moveable  pulley,  shown  in  fig.  18,  we 

have  one  end  of  the  rope  fastened  to  a  point  A  in  a  beam.     The  pulley 


p      ^ 


Fig.  17. 


-43] 


The  Wedge, 


23 


V 


Fig.  19. 


is  consequently  supported  by  two  forces,  viz.  P  and  the  reaction  of  the 
fixed  point  which  is  equal  to  P  ;  these  two  forces  support  Q  and  the 
weight  of  the  pulley  w.  In  the  case  represented  in  the  figure  the  parts 
of  the  rope  are  parallel,  consequently  (36) 

2P  =  Q  +  7t'. 

When  several  pulleys  are  united  into  one  machine,  they  constitute  a 
system  of  pulleys  ;  such  are — the  Block  and  Tackle,  the  Barton,  White's 
Pulley,  etc. 

42.  The  Inclined  plane. — A  very  instructive  and  useful  application  of 
"^  the  resolution  of  forces  is  to  be  found  in  the  case  of  a  body  supported  on 

an  inclined  plane.  Let  AB  (fig.  19)  be  the  plane,  AC  its  base,  and  BC  its 
height ;  let  a  body  M  considered  as  a  point, 
whose  mass  is  M  and  weight  M^  or  Q,  be  sup- 
ported on  it  by  a  force  P  acting  along  MB.  The 
plane  is  supposed  to  be  smooth,  and  therefore 
reacts  on  M  with  a  force  R  at  right  angles  to  AB. 
Draw  CD  at  right  angles  to  AB,  then  the  point 
M  is  held  at  rest  by  forces  P,  Q,  R,  whose  direc- 
tions are  severally  parallel  to  the  sides  of  the  triangle  DBC  which  is 
similar  to  CBA.  ..Hence 

P  :  R  :  Q  : :  BD  :  DC  :  CB  :  :  BC  :  CA  :  AB  ; 

or  since  BC  =  AB  sin  A  and  CA  =  AB  cos  A, 

we  have  P  =  Q  sin  A  and  R  =  Q  cos  A. 

Or  the  same  fact  may  be  stated  in  this  form  : — When  a  mass  M  is  placed 
on  an  inclined  plane,  its  pressure  on  the  plane  is  M^  cos  A  and  its  force 
down  the  plane  is  M^  sin  A.  In  the  above  case  these  forces  are  balanced 
by  P  and  R  respectively. 

Thus  suppose  BC  and  CA  to  be  9  ft.  and  12  ft,  respectively,  then  AB 
will  equal  1 5  ft.  Consequently,  if  the  weight  of  Q  is  360  lbs.  it  produces 
on  the  plane  a  perpendicular  pressure  of  288  lbs,,  and  requires  for  its 
support  a  force  of  216  lbs.  acting  up  the  plane. 

43.  Tne  wedgre. — This  instrument  is  nothing  but  a  moveable  inclined 
plane.  It  is  used  inseveral  forms,  of  which  the 
annexed  is,  perhaps,  the  best  for  showing  the 
action  of  the  forces  called  into  play.  AB  is  a 
fixed  table.  ACDE  is  a  piece  which  is  pre- 
vented from  moving  in  a  lateral  direction  by 
a  fixed  guide  F.  ABC  is  a  wedge  whose  angle 
is  such  that  one  of  its  faces  is  in  contact  with  a 
face  of  ACDE  as  shown  in  the  figure.  ABC 
being  forced  forward  by  P,  overcomes  the  re- 
sistance  Q    acting    on  ACDE.     The  various 

forces  called  into  play  are  represented  in  the  diagram,  namely,  P,  O,  the 
reaction  of  the  table  S,  the  mutual  action  between  the  pieces  R,  R^  and 
the  reaction  T  of  the  guide  F.  We  will  suppose  the  angles  B,  D,  E,  and 
EAB  to  be  right  angles,  and  that  P  and  Q  act  at  right  angles  to  DE  and 


^: 


X. 

^  11 


24  On  Matter,  Force,  and  Motion.  [43- 

BC  respectively.  Moreover,  since  the  surfaces  in  contact  are  smooth,  S 
acts  in  a  direction  at  right  angles  to  AB,  R  and  R^  to  AC,  and  T  to  AE. 
Through  C  draw  CG  at  right  angles  to  AC  ;  then  the  body  ABC  being 
kept  in  equilibrium  by  three  forces,  P,  R,  S,  whose  directions  are  re- 
spectively parallel  to  the  sides  of  the  triangle  DGC,  we  have 
P  :  R  :  :  DO  :  GC. 

The  body  ACDE  being  kept  in  equilibrium  by  three  forces,  T,  Rj,  Q, 
whose  directions  are  respectively  parallel  to  the  side  of  the  triangle  DGC, 
we  have 

Ri  :  Q  : :  GC  :  CD. 

Now  R  and  Rj  are  equal,  being  the  mutual  actions  of  the  two  bodies^ 
ABC,  ACDE  ;  therefore  compounding  the  ratios,  we  have 

P  :  Q  ::DG  :  DC; 
or,  by  similar  triangles, 

P  :  Q  :  :  CB  :  BA, 

a  proportion  equivalent  to  the  equation  ', 

P  =  O  tan  A. 


44.  The  screw. — It  will  be  remarked  that  when  the  wedge  is  used  as 
in  the  last  article,  Q  cannot  be  many  times  greater  than  P,  and  also  that 
the  space  through  which  P  can  lift  Q  is  limited.  The  screw  is  merely  a 
modification  of  the  wedge  by  which  the  limits  of  its  application  in  both 
these  respects  are  extended.  To  explain  this,  it  may  be  observed  that  if 
the  thread  of  a  screw  were  reduced  to  a  line,  it  would  become  a  curve 
called  the  helix,  running  in  whorls  round  the  cylinder;  the  distance 
between  any  two  consecutive  turns  measured  parallel  to  the  axis  of  the 
cylinder  being  constant,  and  called  the  pitch  of  the  screw.  Now  if  ABC 
(fig.  20)  were  wrapped  round  a  cylinder,  whose  dimensions  were  such  that 
the  base  AB  coincided  with  the  circumference  of  the  base  of  the  cylinder, 
and  the  height  BC  with  the  pitch,  the  hypothenuse  CA  could  be  brought 
into  coincidence  with  one  whorl  of  the  helix.  Under  these  circumstances, 
the  angle  BAC  (A)  is  called  the  inclination  of  the  thread,  and  if  r  denote 
the  radius  of  the  base  of  the  cylinder,  h  the  pitch  of  the  screw,  we  shall 
have,  since  AB  tan  A  equals  BC  (fig.  20), 

2  Trr  tan  A  =  /z. 

Moreover,  if  ACDE  were  wrapped  round  the  inside  of  a  hollow  cylinder 
or  nut  (fig.  21)  of  equal  radius  it  would  take  the  form  of  a  helix,  or  com- 
panion screw  cut  on  the  inside  of  the  nut  ;  and  if  the  screw  were  placed 
within  the  nut  the  two  helices  would  be  in  exact  contact.  If  now  we  sup- 
pose the  power  to  act  at  the  end  of  an  arm,  we  shall  have  transformed 
the  wedge  of  fig.  20  into  a  screw,  one  end  of  which  works  on  a  fixed  table 
with  a  moveable  nut.  The  annexed  figure  shows  the  arrangement,  half 
the  nut  being  removed  in  order  to  show  how  the  thread  of  the  screw 
works  within  the  groove  of  the  companion.  When  the  arm  is  turned  in 
the  direction  indicated  by  P  the  point  B  will  pass  to  B',  but  as  the  nut  is 
kept  by  the  guides  G,  H  from  turning  with  the  screw,  it  must  now  occupy 


-45] 


The  Screw.     Friction. 


25 


/ 


\ 


the  point  C  of  the  companion,  and  consequently  the  nut  must  be  lifted  so 
that  C  comes  to  B'.  If  the  nut  were  fixed  the  screw  would  be  depressed 
by  the  same  amount,  when  P  acts  as  indicated. 

If  the  screw  were  turned  by  a  force  P'  acting  tangentially  to  the  base 
of  the  cylinder,  it  is  plain  that  when  all  frictions  are  neglected  the  relation 
between  P'  and  Q  must  be  the  same 
as  that  between  P  and  Q  in  the  last 
article,  that  is, 

P'  =  Q  tan  A 
27rrP'=Q>^; 

but  P  acting  perpendicularly  at  the 
end  of  an  arm  a  will  have  (by  equality 
of  moments)  the  same  tendency  as  P' 
to  turn  the  screw,  provided 

PV=P^, 

and  therefore  the  relation  between  P 
and  Q  is  given  by  the  equation 

i-Ka  P  =  O/i ; 

or  the  power  has  to  the  resistance 
the  same  ratio  which  the  pitch  of  the 
screw  has  to  the  circumference  of  the 
circle  described  by  the  end  of  the  arm  ; 
for  example,  if  h  equal  i  inch,  and  a 
equals  lix.,?^  power  of  100  lbs.  would 
overcome  a  resistance  not  exceeding 
1 5,000  lbs. 

45.  Friction. — In  the  cases  of  the  actions  of  machines  which  have 
een  described,  the  resistances  which  are  offered  to  motion  have  not  been 
at  all  considered.  The  surfaces  of  bodies  in  contact  are  never  perfectly 
smooth  ;  even  the  smoothest  present  inequalities  which  can  neither  be 
detected  by  the  touch  nor  by  ordinary  sight ;  hence  when  one  body  moves 
over  the  surface  of  another  the  elevations  of  one  sink  into  the  depressions 
of  the  other,  like  the  teeth  of  wheels,  and  thus  offer  a  certain  resistance  to 
motion  ;  this  is  what  is  called  frictioti.  It  must  be  regarded  as  a  force 
which  continually  acts  in  opposition  to  actual  or  possible  motion. 

Friction  is  of  two  kinds  :  sliding,  as  when  one  body  glides  over  another  ; 
this  is  least  when  the  two  surfaces  in  contact  remain  the  same,  as  in  the 
motion  of  an  axle  in  its  bearing  ;  and  rollifig  friction,  which  occurs  when 
one  body  rolls  over  ^nother,  as  in  the  case  of  an  ordinary  wheel.  The 
latter  is  less  than  the  former,  for  by  the  rolling  the  inequalities  of  one  body 
are  raised  over  those  of  the  other. 

The  force  which  is  required  to  overcome  friction  and  which  is  briefly 
spoken  of  as  friction  is  proportional  to  the  pressure  of  the  two  bodies 
against  each  other.  That  fraction  of  the  pressure  which  is  required  to 
overcome  friction  is  called  the  coefficient  of  friction. 

Friction  is  independent  ot  the  extent  of  surfaces  in  contact,  it  is  dimi- 

c 


26  On  Matter,  Force,  and  Motion.  I^S- 

nished  by  polishing  and  by  smearing,  but  is  increased  by  heat.  It  is 
greater  as  a  body  passes  from  the  state  of  rest  to  that  of  motion  than 
%  during  motion,  but  seems  independent  of  the  velocity.  The  coefficient  of 
friction  depends  on  the  nature  of  the  substances  in  contact  ;  thus,  for  oak 
upon  oak  it  is  0*418  when  the  fibres  are  parallel,  and  0-293  when  they 
•  cross  ;  for  beech  upon  beech  it  is  o*  36.  Greasy  substances  which  are  not 
absorbed  by  the  body  diminish  friction  ;  but  increase  it  if  they  are  ab- 
sorbed. Thus  moisture  and  oil  increase,  while  tallow,  soap,  and  graphite 
diminish,  the  friction  of  wooden  surfaces.  In  the  sliding  friction  of  cast 
iron  upon  bronze  the  coefficient  was  found  to  be  0-25  without  grease  ; 
with  oil  it  was  0-17,  fat  o'li,  soap  0-03,  and  with  a  mixture  of  fat  and 
graphite  0*02.  The  coefficient  of  rolling  friction  for  cast  iron  wheels  on 
iron  rails  is  o"oo4 ;  for  ordinary  wheels  on  an  ordinary  road  it  is  0*04. 

As  rolling  friction  is  considerably  less  than  sliding  friction,  it  is  a  great 

^  saving  of  power  to  convert  the  latter  into  the  former,  as  is  done  in  the 

case  of  the  castors  of  chairs  and  other  furniture.     On  the  other  hand,  it 

is  sometimes  useful  to  change  rolling  into  sliding  friction,  as  when  drags 

are  placed  on  carriage  wheels. 

Without  friction  on  the  ground,  neither  men  nor  animals,  neither  or- 
dinary carriages  nor  railway  carriages  could  move.     Friction  is  necessary 
for  the  transmission  of  power  from  one  wheel  to  another  by  means  of 
<      bands  or  ropes  ;  and  without  friction  we  could  hold  nothing  in  the  hands. 
X/     46.  TTniformly  accelerated  rectilinear  motion. — Let  us  suppose  a 
t^body  containing  m  units  of  mass  to  move  from  rest  under  the  action  of  a 
force,  of  F  units,  the  body  will  move  in  the  line  of  action  of  the  force, 
and  will  acquire  in  each  second  an  additional  velocity/  given  by  the 
equation  Y  =  mf 

consequently,  if  v  is  its  velocity  at  the  end  of  /  seconds,  we  have 

v=ft,  (I) 

To  determine  the  space  it  will  describe  in  /  seconds,  we  may  reason  as 
follows  : — The  velocity  at  the  time  t  being//,  that  at  a  time  t  +  r  will  be 
fit  +  r).  If  the  body  moved  uniformly  during  the  time  r  with  the  former 
velocity  it  would  describe  a  space  s  equal  to  fir,  if  with  the  latter  velocity 
■^  space  s^  equal  to  f{t  +  t)t.     Consequently, 

jj  :  j::/  +  r  :  /, 

is  indefinitely  small,  the  limiting  values  of  s  and  s^ 
are  equal.  Now  since  the  body's  velocity 
is  continually  increasing  during  the  time  r, 
the  space  actually  described  is  greater 
than  J,  and  less  than  s^  But  since  the 
limiting  values  of  s  and  Sy  are  equal,  the 
limiting  value  of  the  space  described  is  the 
same  as  that  of  s  or  s^  In  other  words,  if 
we  suppose  the  whole  time  of  the  body's 
motion  to  be  divided  into  any  number  of 
equal  parts,  if  we  determine  the  velocity  of 
the  body   at  the  beginning  of  each  of  these  parts,  and  if  we  ascertain 


1 


therefore, 

when  T 

is 

inde 

B 

S 

5^ 

t 

^ 

e 

f 

^          D        K        K        «       H        C 

Fig 

22. 

-46]  Uniformly  accelerated  Motion.  27 

the  spaces  described  on  the  supposition  that  the  body  moves  uniformly 
during  each  portion  of  time,  the  hmiting  value  of  the  sum  of  these 
spaces  will  be  the  space  actually  described  by  the  body.  Draw  a 
line  AC,  and  at  A  construct  an  angle  CAB,  whose  tangent  equals  /; 
divide  AC  into  any  number  of  equal  parts  in  D,  E,  F,...and  draw 
PD,  QE,  RF,...BC  at  right  angles  to  AC,  then  since  PD=ADx/ 
QE  =  AE  x/,  RF  =  AF  x/  EC  =  AC  -</,  etc.,  PD  will  represent  the  velocity 
of  the  body  at  the  end  of  the  time  represented  by  AD,  and  similarly  QE, 
RF,...BC,  will  represent  the  velocity  at  the  end  of  the  times  AE.AF,... 
AC.  Complete  the  rectangles  D^,  Y.f^  F^...  These  rectangles  represent 
the  space  described  by  the  body  on  the  above  supposition  during  the 
second,  third,  fourth,... portions  of  the  time.  Consequently,  the  space 
actually  described  during  the  time  AC  is  the  limit  of  the  sum  of  the 
rectangles  ;  the  limit  being  continually  approached  as  the  number  of  parts 
into  which  AC  is  divided  is  continually  increased.  But  this  limit  is  the 
area  of  the  triangle  ABC  :  that  is  ^AC  x  CB  or  ^AC  x  AC  x/  Therefore, 
if  AC  represents  the  time  t  during  which  the  body  describes  a  space  j, 
we  have 

s-\ft\  (2) 

Since  this  equation  can  be  written 

we  find,  on  comparing  this  with  equation  (i),  that 

^^  =  2A  (3) 

To  illustrate  these  equations,  let  us  suppose  the  accelerative  effect  of  the 
force  to  be  6,  that  is  to  say,  that  in  virtue  of  the  action  of  the  force,  the 
body  acquires  in  each  successive  second  an  additional  velocity  of  6  ft.  per 
second,  and  let  it  be  asked  what,  on  the  supposition  of  the  body  moving 
from  rest,  will  be  the  velocity  acquired  and  the  space  described  at  the 
end  of  12  seconds  ;  equations  i  and  2  enable  us  to  answer  that  at  that 
instant  it  will  be  moving  at  the  rate  of  72  ft.  per  second  and  will  have 
described  432  ft. 

The  following  important  result  follows  from  equation  2.  At  the  end 
of  the  first,  second,  third,  fourth,  etc.  second  of  the  motion  the  body  will 
have  described  \f,  ^fx  4,  |/x  9,  |/x  16,  etc.,  ft.,  and  consequently 
during  the  first,  second,  third,  fourth,  etc.  second  of  the  motion  will  have 
described  ^f,  ^/x  3,  f/x  5,  ^/"x  7,  etc.  ft.,  namely,  spaces  in  arithmetical 
progression. 

The  results  of  the  above  article  can  be  stated  in  the  form  of  laws  which 
apply  to  the  state  of  a  body  moving  from  a  state  of  rest : — 

I.  The  velocities  are  proportional  to  the  times  during  which  the  motion 
has  lasted. 

II.  The  spaces  described  are  proportional  to  the  squares  of  the  times 
employed  in  their  description. 

III.  The  spaces  described  are  proportional  to  the  squares  of  tJie  velo- 
cities acquired  during  their  description. 

IV.  The  spaces  described  in  equal  successive  periods  of  time  increase  by 
a  constant  qtta?itity. 


y 


28  On  Matter i  Force,  and  Motion.  [46-  1 

Instead  of  supposing  the  body  to  begin  to  move  from  a  state  of  rest,  we 
may  suppose  it  to  have  an  initial  velocity  V,  in  the  direction  of  the  force. 
In  this  case  equations  i,  2,  and  3  can  be  easily  shown  to  take  the  follow- 
ing forms  respectively  : — 

v  =  N  +ft 

s  =  Vt  +  ^/t^ 

If  the  body  move  in  a  direction  opposite  to  that  of  the  force, /must  be 
reckoned  negative. 

The  laws  stated  in  the  present  article  apply  directly  to  the  case  of  a 
body  falling  freely  m  vacuo.  In  this  case  the  force  causing  the  accelera- 
tion is  that  of  gravity,  and  it  is  usual  to  denote  the  acceleration  produced, 
by  the  letter^ ;  it  has  already  been  stated  (27  and  29)  that  the  numerical 
value  of  g,  is  32"i9i?.  at  London,  when  the  unit  of  time  is  a  second  and 
the  unit  of  distance  a  foot. 

Adopting  the  metre  as  unit  of  distance  the  value  of  g  at  London 
is  9-8117. 

47.  Motion  on  an  inclined  plane. — Referring  to  (42),  suppose  the 
force  P  not  to  act  ;  then  the  mass  M  is  acted  on  by  an  unbalanced 
force  M^  sin  A,  in  the  direction  MA,  consequently  the  accelerating  force 
down  the  plane  is  g  sin  A,  and  the  motion  becomes  a  particular  case  of 
that  discussed  in  the  last  article.  If  it  begin  to  move  from  rest,  it  will 
at  the  end  of  /  seconds  acquire  a  velocity  v  given  by  the  equation 

v=gt  sin  A, 
and  will  describe  a  length  s  (ft.)  of  the  plane  given  by  the  equation 

s  =  Igt^  sin  A. 
Also,  if  V  is  the  velocity  acquired  while  describing  s  feet  of  the  plane 

v^=.2gs  sin  A. 
Hence  (fig.  19)  if  a  body  slides  down  the  plane  from  B  to  A  the  velocity 
which  it  acquires  at  A  equals  a/2^.AB  sin  A  or  ^2g.  EC.  that  is  to  say, 
the  velocity  which  the  body  has  at  A  does  not  depend  on  the  angle  A, 
but  only  on  the  perpendicular  height  EC.  The  same  would  be  true  if 
'  for  EA  we  substituted  any  smooth  curve,  and  hence  we  may  state 
generally,  that  when  a  body  moves  along  any  smooth  line  under  the 
action  of  gravity,  the  change  of  velocity  it  experiences  in  moving  from 
one  point  to  another  is  that  due  to  the  vertical  height  of  the  former  point 

y  above  the  latter. 
48.  Composition  of  velocities. — The  rule  for  the  composition  of 
velocities  is  the  same  as  that  for  the  composition  of  forces  ;  this  follows 
evidently  from  the  fact  that  forces  are  measured  by  the  momentum  they 
communicate,  and  are  therefore  to  one  another  in  the  same  ratio  as  the 
velocities  they  communicate  to  the  same  body.  Thus  (fig.  5,  art.  33)  if 
the  point  has  at  any  instant  a  velocity  AB,  in  the  direction  AP,  and 
there  is  communicated  to  it  a  velocity  AC  in  the  direction  AO,  it  will 
move  in  the  direction  AR  with  a  velocity  represented  by  AD.  And 
conversely,  the  velocity  of  a  body  represented  by  AD  can  be  resolved  into 


^49] 


Motion  in  a  Circle. 


29 


two  component  velocities  AB  and  AC.  This  suggests  the  method  of 
determining  the  motion  of  a  body  when  acted  on  by  a  force  in  a  direction 
transverse  to  the  direction  of  its  velocity  ;  namely,  suppose  the  time  to  be 
divided  into  a  great  number  of  intervals,  and  suppose  the  velocity  actually 
communicated  by  the  force  to  be  communicated  at  once,  then  by  the  com- 
position of  velocities  we  can  determine  the  motion  during  each  interval, 
and  therefore  during  the  whole  time  ;  the  actual  motion  is  the  limit  to 
which  the  motion,  thus  determined,  approaches  when  the   number  of 

"V  inpetvals  is  increased. 

yC^  49.  MIotion  in  a  circle. — Let  ABC D... be  a  regular  polygon  inscribed 
in  a  circle  whose  centre  is  O.  Draw  the  diameter  BOM.  Produce  AB 
to  H,  makmg  BH  equal  to  AB,  join  CH,  this  line  is  parallel  to  BO. 
Draw  CK  parallel  to  BH  ;  and  CL  at  right  angles  at  BO.  Join  CM. 
Suppose  a  body  whose  mass  is  M  to  describe  AB  with  a  velocity  V  in  a 
time  /,  suppose  that  at  B  there  is  suddenly  communicated  to  it  in  the 
direction  BO,  a  velocity  _/^  which  is  the  same 
velocity  as  a  force  M/ would  communicate 
gradually  in  the  same  time  /,  it  will  move 
during  the  next  short  time  /,  with  the  velocity 
compounded  of  V  and  ft ;  now  since  BH 
equals  V/,  if  /  is  such  that  BK  equals  //  x  /, 
the  body  will  describe  BC,  in  the  second 
interval.  It  will  be  observed  that  as  BC  and 
AB  are  equal  and  are  described  in  equal 
times  /,  the  velocity  along  BC  is  the  same  as 
along  AB,  that  is,  the  effect  of  the  composi- 
tion is  to  change  the  direction,  not  the 
amount  of  the  velocity.  When  the  body  is 
at  the  point  C  we  may  suppose  a  velocity  ft 
to  be  communicated  in  the  direction  CO,  and 

then  at  the  end  of  the  third  interval  the  body  will  be  at  D.  On  this 
supposition  therefore  the  body  will  describe  the  polygon,  ABCD...with  a 
uniform  velocity  V.     Now  from  similar  triangles  MCB,  BCL  we  have 

MB  :  BC::BC  :  BL 
or  2r:Yt\:Vt:\{ft)xt 

where  r  denotes  the  radius  of  the  circle  ; 
therefore  fr  =  V^. 

This  is  true  for  all  values  of  /,  and  therefore  also  when  /  is  indefinitely 
small.  Now  by  diminishing  /  we  merely  increase  the  number  of  sides  of 
the  polygon,  therefore  when  t  is  indefinitely  small,  the  motion  takes  place 
in  the  circle,  and  the  force  M/acts  continuously  towards  the  centre. 

This  is  a  most  important  mechanical  truth,  it  may  therefore  be  well 
to  illustrate  as  well  as  prove  it.  Suppose  a  mass  of  6  lbs.  of  matter 
to  describe  a  circle  whose  radius  is  5  ft.  with  an  uniform  velocity  of  20  ft. 
per  second.  The  force  acting  on  it  tending  to  the  centre  will  contain 
6  X  2o'^-T-5  or  480  units  of  force.  In  virtue  of  its  inertia  the  body  tends 
at  each  point  to  move  along  the  tangent  at  that  point,  concequently  aforce 


30 


On  Matter^  Force,  and  Motion. 


[50- 


must  continually  act  on  it  towards  the  centre  to  deflect  it  from  the  tangent, 
and  keep  it  moving  in  the  circle ;  in  the  above  case  the  force  contains 
480  units,  which  is  nearly  15  lbs.  of  force. 

50.  Motion  in  a  vertical  circle. — Let  ACDB  be  a  circle  whose  plane 
is  vertical  and  radius  denoted  by  r.  Suppose  a 
point  placed  at  A,  and  allowed  to  slide  down  the 
curve,  what  velocity  will  it  have  acquired  on  reach- 
ing any  given  point  P  1  Draw  the  vertical  diameter 
CD,  join  CA,  CP,  and  draw  the  horizontal  lines 
AMB  and  PNP^  Now  assuming  the  curve  to  be 
smooth  the  velocity  acquired  in  falling  from  A  to  P 
is  that  due  to  MN  the  vertical  height  of  A  above  P 
(47);  if,  therefore,  v  denote  the  velocity  of  the  point 
at  P,  we  shall  have 

Fig.  24.  V^-2gW^. 

Now  by  similar  triangles  DCP,  PCN  we  have 
DC  :CP  ::  CP  :  CN 
consequently,  if  we  denote  by  s  the  chord  CP, 

2rNC=j-2 
in  like  manner  if  a  denote  the  chord  CA, 
2r  MC=rt^ 


therefore 


ir  MN^rt--^^ 


and 


i{a-^s'^\ 


It  will  be  remarked  that  v  will  have  equal  values  when  s  has  the  same 
value  whether  positive  or  negative,  and  for  any  one  value  of  s  there  are 
two  equal  values  of  ?7,  one  positive  and  one  negative.  That  is  to  say,  since 
CP'  is  equal  to  CP,  the  body  will  have  the  same  velocity  at  P'  that  it  has 
at  P,  and  at  any  point  the  body  will  have  the  same  velocity  whether 
it  is  going  up  the  curve  or  down  the  curve.  Of  course  it  is  included  in 
this  statement,  that  if  the  body  begins  to  move  from  A  it  will  just  ascend 
to  a  point  B  on  the  other  side  of  C,  such  that  A  and  B  are  in  the  same 
horizontal  hne.  It  will  also  be  remarked  that  at  C  the  value  of  ^  is  zero  ; 
consequently,  if  V  is  the  velocity  acquired  by  the  body  in  falling  from  A 
to  C  we  have 


Vf' 


and,  on  the  other  hand,  if  the  body  begins  to  move  from  C  with  a  velo- 
city V  it  will  reach  a  point  A  such  that  the  chord  AC  or  a  is  given  by 
the  same  equation.  In  other  words,  the  velocity  at  the  lowest  point  is 
proportional  to  the  chord  of  the  arc  described. 


-51]         \.-v*v^.  Motion  of  a  simple  Pendiiliim.  3 1 

51.  Motion  of  a  simple  pendulum. — By  a  simple  pendulum  is  meant 
a  heavy  particle  suspended  by  a  fine  thread  from  a  fixed  point,  about 
which  it  oscillates  without  friction.     So  far  as  t 

its  changes  of  velocity  are  concerned  they  will 
be  the  same  as  those  of  the  point  in  the  pre- 
vious article,  for  the  tension  of  the  thread  acting 
at  each  position  in  a  direction  at  right  angles  to 
that  of  the  motion  of  the  point,  will  no  more 
affect  its  motion  than  the  reaction  of  the  smooth 
curve  affects  that  of  the  point  in  the  last  article. 
The  time  of  an  oscillation,  that  is,  the  time  in 
which  the  point  moves  from  A  to  B,  can  be 
easily  ascertained  when  the  arc  of  vibration  is  '^"  ^^' 

small,  that  is,  when  the  chord  and  the  arc  do  not  sensibly  differ. 

Thus,  let  AB  (fig.  25)  equal  the  arc  or  chord  ACB  (fig.  24),  with  centre 
C  and  radius  AC  or  a  describe  a  circle,  and  suppose  a  point  to  describe 

the  circumference  of  that  circle  with  a  uniform  velocity  V  or  a     /  i'^.      At 

any  instant  let  the  point  be  at  Q,  join  CQ,  draw  the  tangent  OT,  alsp 
draw  OP  at  right  angles  and  QN  parallel  to  AB,  then  the  angles  NQT 
and  COP  are  equal.     Now  the  velocity  of  Q  resolved  parallel  to  AB  is  V 

cosTQNor<i!^^  /cos  CQP,  that  is,  if  CP  equals  j,  the  velocity  of  O 
parallel  to  A B  is 


y^PQory^K-.^). 


But  if  we  suppose  a  point  to  move  along  AB  in  such  a  manner  that  its 
velocity  in  each  position  is  the  same  as  that  of  the  oscillating  body,  its 


velocity  at  P  would  also  equal  ^^/ ■/ (^'^  —  j''^) ;    and,  therefore,   this   point 

would  describe  AB  in  the  same  time  that  Q  describes  the  semicircum- 
ference  ACB.     If  then  /  be  the  required  time  of  an  oscillation  we  have 

/   =    TT  «-i-^  -/    /  =  TT  ^/ -. 

V     ^         V    ^ 

This  result  is  independent  of  the  length  of  the  arc  of  vibration,  provided 
its  ampliticde,  that  is  AB,  be  small.  It  is  evident  from  the  formula  that 
the  time  of  a  vibration  is  directly  proportional  to  the  square  root  of  the 
length  of  the  pendulum,  and  inversely  proportional  to  the  square  root  of 
the  accelerating  force  of  gravity. 

As  an  example  of  the  use  of  the  formula  we  may  take  the  following  : 
— It  has  been  found  by  careful  experiments  that  39*13983  inches  is  the 
length  of  a  simple  pendulum,  whose  time  of  oscillation  at  Greenwich  is 
one  second;  the  formula  at  once  leads  to  an  accurate  determination  of  the 
accelerating  force  of  gravity^;  for  using  feet  and  seconds  as  our  units  we 


y 


32  On  Matter,  Force,  and  Motion.  [52- 

have   /  =  l,  r=- 3-26165,  and   tt  stands  for  the  known  number  3-14159, 
therefore  the  formula  gives  us 

g=  (3-14159)'  X  3-26165  =  32-1912. 
This  is  the  value  employed  in  (29). 

Other  examples  will  be  met  with  in  the  Appendix. 

52.  Graphic  representation  of  tbe  ctaangres  of  velocity  of  an  oscil- 
tingr  body. — The  changes  which  the  velocity  of  a  vibrating  body  under- 
goes may  be  graphically  represented  as  follows: — Draw  a  line  of  indefinite 
length  and  mark  off  AH  to  represent  the  time  of  one  vibration.  HH'  to 
represent  the  time  of  the  second  vibration,  and  so  on.  During  the  first 
vibration  the  velocity  increases  from  zero  to  a  maximum  at  the  halt 


Fig.  26. 

vibration,  and  then  decreases  during  the  second  half  vibration  from  the 
maximum  to  zero.  Consequently,  if  a  curved  line  or  arc  AQH  is  drawn, 
the  ordinate  QM  at  any  point  Q  will  represent  the  velocity  of  the  body 
at  the  time  represented  by  AM.  If  a  similar  curved  line  or  arc  HPH' 
be  drawn,  the  ordinate  PN  of  any  point  P  will  represent  the  velocity  at 
a  time  denoted  by  AN.  But  since  the  direction  of  the  velocity  in  the 
second  oscillation  is  contrary  to  that  of  the  velocity  in  the  first  oscil- 
lation, the  ordinate  NP  must  be  drawn  in  the  contrary  direction  to  that 
of  MQ.  If,  then,  the  curve  be  continued  by  a  succession  of  equal  arcs 
alternately  on  opposite  sides  of  AD,  the  variations  of  the  velocity  of  the 
vibrating  body  will  be  completely  represented  by  the  varying  magnitudes 
of  the  ordinates  of  successive  points  of  the  curve. 

53.  Conical  pendulum. — When  a  point  P  is  suspended  from  a  point 
A  as  a  simple  pendulum,  it  can  be  caused  to  describe  a  horizontal  circle 
with  a  uniform  velocity  V.  A  point  moving  in  such  a  manner  constitutes 
what  is  called  a  conical  pendultmz,  and  admits  of 
many  useful  and  interesting  applications.  We  will, 
in  this  place,  ascertain  the  relation  which  exists 
between  the  length  r  of  the  thread,  AP,  the  angle  of 
the  cone  PAN  or  P,  and  the  velocity  V.  Since  the 
point  P  moves  in  a  circle,  whose  radius  is  PN  with  a 
velocity  V,  a  force  R  must  act  on  it  in  the  direction 
PN  given  by  the  equation  (49) 

R  =  M-^. 
Fig.  27.  PN 

Now  the  only  forces  acting  are  the  tension  of  the  thread  T  along  PA, 
and  the  weight  of  the  body  M^  vertically,  consequently  their  resultant 
must  be  a  force  R  acting  along  PN.  And  therefore  these  forces  will  be 
parallel  to  the  sides  of  the  triangle  ANP.     So  that  (35) 


/ 

^ 

X 

M*8r 

-p- 

-54]  Impulsive  Forces,  33 

therefore 

M  ^'  =  Mi^PN 


Now 


•^AN 


PN 

PN  =  r  sin  0  and  £4:  =  tan  P, 

AN 


therefore 

V^  =^r  sin  0  tan  0. 

One  conclusion  from  this  may  be  noticed.  With  centre  A  and  radius 
AP,  describe  the  arc  PC.  Now  when  the  angle  PAC  is  small,  the  sine, 
PN,  does  not  sensibly  differ  from  the  chord,  nor  the  cosine,  AN,  from 
the  radiuSj  therefore  in  this  case  we  have 

y,^     (chdPCr  o,v  =  chdPC    /I. 
radius  V    , 

On  comparing  this  result  with  (50)  we  see  that  when  the  angle  PAN 
is  small,  the  velocity  of  P  moving  in  a  conical  penduluin  is  the  same  as  P 
would  have  at  the  lowest  point  C  if  it  oscillated  as  a  simple  pendulum ; 
consequently,  if  we  conceive  the  point  P  to  be  making  small  oscillations 
about  the  point  A,  and  denote  the  velocity  at  the  lowest  point  by  V,  and 
if  when  at  the  extreme  point  of  the  arc  of  vibration,  there  is  communi- 
cated to  it  a  velocity  V  in  a  direction  at  right  angles  to  the  plane  of 

,>/Wbration,  its  motion  will  be  changed  into  that  of  a  conical  pendulum. 

^  54.  Impulsive  forces. — When  a  force  acts  on  a  body  for  an  inappreci- 
ably short  time,  and  yet  sensibly  changes  its  velocity,  it  is  termed  an 
mstaiitaneous  or  impulsive  force.  Such  a  force  is  called  into  play  when 
one  body  strikes  against  another.  A  force  of  this  character  is  nothing  but 
a  finite  though  very  large  force,  acting  for  a  time  so  short  that  its  duration , 
is  nearly,  or  quite,  insensible.  In  fact,  if  M  is  the  mass  of  the  body,  and 
the  force  contains  M/  units,  it  will,  in  a  time  /,  communicate  a  velocity 
//;  now,  however  small  /may  be,  M/  and  therefore  /  may  be  so  large 
that  ft  may  be  of  sensible  or  even  considerable  magnitude.  Thus  if  M 
contain  a  pound  of  matter,  and  if  the  force  contain  ten  thousand  units, 
though  /  were  so  short  as  to  be  only  the  jo^oo^^  °^  ^  second,  the  velocity 
communicated  by  the  force  would  be  one  of  10  ft,  per  second.  It  is  also 
to  be  remarked  that  the  body  will  not  sensibly  move  while  this  velocity 
is  being  communicated  ;  thus,  in  the  case  supposed,  the  body  would  only 
move  through  ^  //~  or  the  o^o^h  of  a  foot  while  the  force  acts  upon  it. 

When  one  body  impinges  on  another  it  follows  from  the  law  of  the 
equality  of  action  and  reaction  (39)  that  whatever  force  the  first  body 
exerts  upon  the  second,  the  second  will  exert  an  equal  force  upon  the  first 
in  the  opposite  direction  ;  now  forces  are  proportional  to  the  momenta 
generated  in  the  same  time  ;  consequently,  these  forces  generate,  during 
the  whole  or  any  part  of  the  time  of  impact,  in  the  bodies  respectively, 

C3 


34 


On  Matter,  Force,  and  Motion. 


[54- 


Fig.  28. 


equal  momenta  with  contrary  signs  ;  and  therefore  the  sum  of  the  mo- 
menta of  the  two  bodies  will  remain  constant  during  and  at  the  end  of 
the  impact.  It  is  of  course  understood  that  if  the  two  bodies  move  in 
contrary  directions  their  momenta  have  opposite  signs  and  the  sum  is  an 
algebraical  sum.  In  order  to  test  the  physical  validity  of  this  conclusion, 
Newton  made  a  series  of  experiments,  which  may  be  briefly  described 
thus  :— two  balls  A  and  B  are  hung  from  points  C,  D,  in  the  same  hori- 
zontal line  by  threads  in  such  a  manner 
that  their  centres  A  and  B  are  in  the 
same  horizontal  line.  With  centre  C 
and  radius  CA  describe  a  semicircle 
EAF,  and  with  centre  D  and  radius 
DB  describe  a  semicircle  GBH  on  the 
wall  in  front  of  which  the  balls  hang. 
Let  A  be  moved  back  to  R,  and  be 
allowed  to  descend  to  A  ;  it  there  im- 
pinges on  B,  both  A  and  B  will  now 
move,  along  the  arcs  AF  and  BH  respectively  ;  let  A  and  B  come  to  their 
highest  points  at  r  and  k  respectively.  Now  if  V  denote  the  velocity 
with  which  A  reaches  the  lowest  point,  v  and  u  the  velocities  with  which 
A  and  B  leave  the  lowest  points  after  impact,  and  r  the  radius  AC,  it 
appears  from  (50)  that    _ 

V  =  chd  AR    /C,  V  =  chd  Ar    /f ,  and  u  =  chd  Bk/-^, 

therefore  if  A  and  B  are  the  masses  of  the  two  balls,  the  momentum  at 
the  instant  before  impact  was  A  x  chd  AR  and  the  momentum  after 
impact  was  A  x  chd  Ar+Bxchd  Bk  Now  when  the  positions  of  the 
points  R,  r,  and  k  had  been  properly  corrected  for  the  resistance  of  the 
air,  it  was  found  that  these  two  expressions  were  equal  to  within  quanti- 
ties so  small  that  they  could  be  properly  referred  to  errors  of  observation. 
The  experiment  succeeded  equally  under  every  modification,  whether  A 
impinged  on  B  at  rest  or  in  motion,  and  whatever  the  materials  of  A  and 
B  might  be. 

55.  Direct  collision  of  two  bodies. — Let  A  and  B  be  two  bodies 
moving  with  velocities  V  and  U  respectively,  along  the  same  line,  and  let 
their  mutual  action  take  place  in  that  line  ;  if  the  one  overtake  the  other, 
I  what  will  be  their  respective  velocities  at  the  instant  after  impact  ?  We 
will  answer  this  question  in  two  extreme  cases. 

i.  Let  us  suppose  the  bodies  to  be  giii'te  inelastic.  In  this  case,  when 
A  touches  B,  it  will  continue  to  press  against  B  until  their  velocities  are 
equalised,  when  the  mutual  action  ceases.  For  whatever  deformation  the 
bodies  may  have  undergone,  they  have  no  tendency  to  recover  their 
shapes.  If,  therefore,  x  is  their  common  velocity  after  impact,  we  shall 
have  hx  +  Bx  their  joint  momentum  at  the  end  of  impact,  but  their 
momentum  before  impact  was  AV  +  BU.  Whence 
(A+B);ir  =  AV  +  BU, 


an  equation  which  determines  x. 


56]  Work:  Meaning-  of  the  Term.  35 

ii.  Let  us  suppose  the  bodies  perfectly  elastic.  In  this  case  they 
recover  their  shapes,  with  a  force  exactly  equal  to  that  with  which  they 
were  compressed.  Consequently,  the  whole  momentum  lost  by  the  one, 
and  gained  by  the  other,  must  be  exactly  double  of  that  lost  while  com- 
pression took  place,  that  is  up  to  the  instant  at  which  their  velocities  were 
equalised.  But  these  are  respectively  AV-A;ir  and  Bjit-BU  ;  therefore, 
if  V  and  u  are  the  required  final  velocities, 

A?y  =  AV -  2(AV  -  A;f)  or  z/ =  -  V  +  2:f 

B?/  =  BU  +  2(B;t--BU)  or  ?/  =  2.r-U, 
hence 

(A  +  B)-6/  =  2BU  +  (A-B)V 
and 

(A  +  B)u  =  2AV  -  (A  -  B)U. 

The  following  conclusion  from  these  equations  may  be  noticed  :  suppose 
a  ball  A,  moving  with  a  velocity  V,  to  strike  directly  an  equal  ball  B  at 
rest.  In  this  case  A  =  B,  and  U  =0,  consequently  ?7  =  o  and  u  =  V,  that 
is,  the  former  ball  A  is  brought  to  rest,  and  the  latter  B  moves  on  with  a 
velocity  V.  If  now  B  strike  on  a  third  equal  ball  C  at  rest,  B  will  in  turn 
be  brought  to  rest,  and  C  will  acquire  the  velocity  V.  And  the  same  is 
true  if  there  is  a  fourth,  or  fifth,  or  indeed  any  number  of  balls.  This 
result  may  be  shown  with  ivory  balls,  and  if  carefully  performed  is  a  very 
jy  remarkable  experiment. 

56.  "Work  :  meaning:  of  tbe  term. — It  has  been  pointed  out  (19,  26) 
that  a  moving  body  has  no  power, of  itself  to  change  either  the  direction 
or  the  speed  of  its  motion,  and  that,  if  any  such  change  takes  place,  it  is  a 
proof  that  the  body  is  acted  upon  by  some  external  force.  But  although 
change  of  motion  thus  always  implies  the  action  of  force,  forces  are  often 
exerted  without  causing  any  change  in  the  motion  of  the  bodies  on 
which  they  act.  For  instance,  when  a  ship  is  sailing  at  a  uniform  speed 
the  force  exerted  on  it  by  the  wind  causes  no  change  in  its  motion,  but 
simply  prevents  such  a  change  being  produced  by  the  resistance  of  the 
water ;  or,  when  a  railway-train  is  running  with  uniform  velocity,  the 
force  of  the  engine  does  not  change,  but  only  maintains  its  motion  in 
opposition  to  the  forces,  such  as  friction  and  the  resistance  of  the  air, 
which  tend  to  destroy  it. 

These  two  classes  of  cases,  namely,  first,  those  in  which  forces  cause 
a  change  of  motion  ;  and  secondly,  those  in  which  they  prevent,  wholly 
or  in  part,  such  a  change  being  produced  by  other  forces,  include  all  the 
effects  to  which  the  action  of  forces  can  give  rise.  When  acting  in 
either  of  these  ways,  a  force  is  said  to  do  work  :  an  expression  which  is 
used  scientifically  in  a  sense  somewhat  more  precise,  but  closely  accord- 
ant with  that  in  which  it  is  used  in  common  language.  A  little  reflection 
will  make  it  evident  that,  in  all  cases  in  which  we  are  accustomed  to 
speak  of  work  being  done,— whether  by  men,  horse-power  or  steam- 
power,  and  however  various  the  products  may  be  in  different  cases, — the 
physical  part  of  the  process  consists  solely  in  producing  or  changing 


!>' 


36  On  Matter,  Force,  and  Motion.  [66- 

motion,  or  in  keeping  up  motion  in  opposition  to  resistance,  or  in  a 
combination  of  these  actions.  The  reader  will  easily  convince  himself  of 
this  by  calling  to  mind  what  the  definite  actions  are  which  constitute  the 
work  done  by  (say)  a  navvy,  a  joiner,  a  mechanic,  a  weaver ;  that  done 
by  a  horse,  whether  employed  in  drawing  a  vehicle  or  in  turning  a  gin  ; 
or  that  of  a  steam-engine,  whether  it  be  used  to  drag  a  railway-train  or 
to  drive  machinery.  In  all  cases  the  work  done  is  reducible,  from  a 
mechanical  point  of  view,  to  the  elements  that  have  been  mentioned, 
although  it  may  be  performed  on  different  materials,  with  different  tools, 
and  with  different  degrees  of  skill. 

It  is,  moreover,  easy  to  see  (comp.  48,  49)  that  any  possible  change  of 
n\otion  may  be  represented  as  a  gain  by  the  moving  body  of  an  addi- 
tional (positive  or  negative)  velocity  either  in  the  direction  of  its  previous 
motion,  or  at  right  angles  to  it ;  but  a  body  which  gains  velocity  is 
(27)  said  to  be  accelerated.  Hence,  what  has  been  said  above  may  be 
summed  up  as  follows  : — When  a  force  produces  acceleration,  or  when 
it  maintai7is  motion  unchanged  in  opposition  to  resistance,  it  is  said  to  do 
WORK. 

57.  nceasure  of  "Work. — In  considering  how  work  is  to  be  measured, 
or  how  the  relation  between  different  quantities  of  work  is  to  be  ex- 
pressed numerically,  we  have,  in  accordance  with  the  above,  to  consider 
first,  work  of  acceleration  ;  and  secondly,  work  against  resistance.  But 
in  order  to  make  the  evaluation  of  the  two  kinds  of  work  consistent,  we 
must  bear  in  mind  that  one  and  the  same  exertion  of  force  will  result  in 
work  of  either  kind,  according  to  the  conditions  under  which  it  takes 
place  :  thus,  the  force  of  gravity  acting  on  a  weight  let  fall  from  the  hand 
causes  it  to  move  with  a  continually  accelerated  velocity  until  it  strikes 
the  ground  ;  but  if  the  same  weight,  instead  of  being  allowed  to  fall 
freely  through  the  air,  be  hung  to  a  cord  passing  round  a  cylinder  by 
means  of  which  various  degrees  of  friction  can  be  applied  to  hinder  its 
descent,  it  can  be  made  to  fall  with  a  very  small  and  practically  uniform 
velocity.  Hence,  speaking  broadly,  it  may  be  said  that,  in  the  former 
case,  the  work  done  by  gravity  upon  the  weight  is  work  of  acceleration 
only,  while  in  the  latter  case  it  is  work  against  resistance  (friction)  only. 
But  it  is  very  important  to  note  that  an  essential  condition,  without 
which  a  force,  however  great,  cannot  do  work  either  of  one  kind  or  the 
other,  is  that  the  thing  acted  on  by  it  shall  move  while  the  force  continues 
to  act.  This  is  obvious,  for  if  no  motion  takes  place  it  clearly  cannot  be 
either  accelerated  or  maintained  against  resistance.  The  motion  of  the 
body  on  which  a  force  acts  being  thus  necessarily  involved  in  our  notion 
of  work  being  done  by  the  force,  it  naturally  follows  that,  in  estimating 
how  much  work  is  done,  we  should  consider  how  much — that  is  to  say, 
how  far — the  body  moves  while  the  force  acts  upon  it.  This  agrees  with 
the  mode  of  estimating  quantities  of  work  in  common  life,  as  will  be 
evident  if  we  consider  a  very  simple  case,  for  instance,  that  of  a  labourer 
employed  to  carry  bricks  up  to  a  scaffold  :  in  such  a  case  a  double  number 
of  bricks  carried  would  represent  a  double  quantity  of  work  done,  but  so 
also  would  a  doubled  height  of  the  scaffold,  for  whatever  amount  of  work 


-57]  Measure  of  Work.  37 

is  done  in  raising  a  certain  number  to  a  height  of  twenty  feet,  the  same 
amount  must  be  done  again  to  raise  them  another  twenty  feet,  or  the 
amount  of  work  done  in  raising  the  bricks  forty  feet  is  twice  as  great 
as  that  done  when  they  are  raised  only  twenty  feet.  It  is  also  to  be 
noted  that  no  direct  reference  to  time  enters  into  the  conception  of 
a  quantity  of  work  :  if  we  want  to  know  how  much  work  a  labourer  has 
done,  we  do  not  ask  how  long  he  has  been  at  work,  but  what  he  has  done, 
—for  instance,  how  many  bricks  he  has  carried,  and  to  what  height; — and 
our  estimate  of  the  total  amount  of  work  is  the  same  whether  the  man 
has  spent  hours  or  days  in  doing  it. 

The  foregoing  relations  between  force  and  work  may  be  put  into 
definite  mathematical  language  as  follows  : — If  the  point  of  appHcation  of 
a  force  moves  in  a  straight  line,  and  if  the  part  of  the  force  resolved  along 
this  line  acts  in  the  direction  of  the  motion,  the  product  of  that  component 
and  the  length  of  the  line  is  the  work  done  by  the  force.  If  the  com- 
ponent acts  in  the  opposite  direction  to  the  motion,  the  component  may 
be  considered  as  a  resistance  and  the  product  is  work  done  against  the 
resistance.  Thus,  in  (42)  if  we  suppose  M  to  move  up  the  plane  from  A 
to  B,  the  work  done  by  P  is  P  x  AB  ;  the  work  done  against  the  resist- 
ance O  is  Q  sin  A  X  AB.  It  will  be  observed  that  if  the  forces  are  in 
equilibrium  during  the  motion,  so  that  the  velocity  of  M  is  uniform,  P 
equals  O  sin  A,  and  consequently  the  work  done  by  the  power  equals 
that  done  against  the  resistance.  Also  since  AB  sin  A  equals  BC,  the 
work  done  against  the  resistance  equals  Q  x  BC.  In  other  words,  to 
raise  Q  from  A  to  B  requires  the  same  amount  of  work  as  to  raise  it 
from  C  to  B. 

If,  however,  the  forces  are  not  in  equilibrium,  the  motion  of  M  will 
not  be  uniform,  but  accelerated  ;  the  work  done  upon  it  will  neverthe- 
less still  be  represented  by  the  product  of  the  force  into  the  distance 
through  which  it  acts.  In  order  to  ascertain  the  relation  between  the 
amount  of  work  done  a.nd  the  change  produced  by  it  in  the  velocity  of 
the  moving  mass,  we  must  recall  one  or  two  elementary  mechanical 
principles.  Let  F  be  the  resultant  force  resolved  along  the  direction  of 
motion,  and  S  the  distance  through  which  its  point  of  application  moves: 
then,  according  to  what  has  been  said,  the  work  done  by  the  force  =  FS. 
Further,  it  has  been  pointed  out  (29),  that  a  constant  force  is  measured 
by  the  momentum  produced  by  it  in  a  unit  of  time :  hence,  if  T  be 
the  time  during  which  the  force  acts,  Vq  the  velocity  of  the  mass  M  at 
the  beginning  of  this  period,  and  V^  the  velocity  at  the  end  of  it,  the 
momentum  produced  during  the  time  T  is  MVi  — MV.,  and  consequently 
the  momentum  produced  in  a  unit  of  time,  or,  in  other  words,  the  measure 
of  the  force  is — 

M(V,-V.) 
F=  ^         . 

The  distance  S  through  which  the  mass  M  moves  while  its  velocity 
changes  from  the  value  V.  to  the  value  V^,  is  the  same  as  if  it  had  moved 
during  the  whole  period  T  with  a  velocity  equal  to  the  average  value  of 
the  varying  velocity  which  it  actually  possesses.     But  a  constant  force 


38  On  Matter,  Force,  and  Motion.  [57- 

acting  upon  a  constant  mass  causes  its  velocity  to  change  at  a  uniform 
rate ;    hence,   in  the  present   case,  the  average  velocity  is   simply   the 
arithmetical  mean  of  the  initial  and  final  velocities,  or 
S  =  HVi  +  V.)T. 
Combining  this  with  the  last  equation,  we  get  as  the  expression  for  the 
work  done  by  the  force  F—  - 

FS  =  ^M(Vi2-V„2); 

or,  in  words,  when  a  constajit  force  acts  on  a  mass  so  as  to  change  its 
velocity,  the  work  done  by  the  force  is  equal  to  half  the  product  of  the 
mass  into  the  change  of  the  square  of  the  velocity. 

The  foregoing  conclusion  has  been  arrived  at  by  supposing  the  force 
F  to  be  constant,  but  it  is  easy  to  show  that  it  holds  good  equally  if  F  is 
the  average  magnitude  of  a  force  which  varies  from  one  part  to  another 
of  the  total  distance  through  which  it  acts.  To  prove  this,  let  the 
distance  S  be  subdivided  into  a  very  great  number  ?i  of  very  small  parts 
each  equal  to  s,  so  that  n  s  =  S.  Then,  by  supposing  s  to  be  sufficiently 
small,  we  may  without  any  appreciable  error' consider  the  force  as  constant 
within  each  of  these  intervals  and  as  changing  suddenly  as  its  point  of 
application  passes  from  one  interval  to  the  next.  Let  F^,  Fg,  F3  .  .  .  .  F„, 
be  the  forces  acting  throughout  the  ist,  2nd,  3rd  ....  ;/th  interval 
respectively,  and  let  the  velocity  at  the  end  of  the  same  intervals  be 
<z/j,  7/3,  7/3,  ....  7/,,  ( =  VJ  respectively ;  then,  for  the  work  done  in  the 
successive  intervals  we  have — 

FiJ  =  ^M  (V-V.,=^) 

Y,s=^^M{v^-v^) 

Y,s^^,U{v,^-v,') 


■^.,S)=iM(\V-7/„S), 


F.,j  =  ^  M  (2/., 
or,  for  the  total  work, 

(F,  +  F,  +  F3+ +F.)^  =  iM(V,2-V„=^); 

where  the   quantity  on  the  left-hand  side  of  the  equation  may  also  be 

"P      -4-    T"'       ■+•  4-  F 

written  -^-— — ? '— —  n  s  =  F  S,  if  we   put   F   to    stand  for    the 

n 

average  (or  arithmetical  mean)  of  the  forces  Fj,  Fo,  etc. 

An  important  special  case  of  the  application  of  the  above  formula 
arises  when  either  the  initial  or  the  final  velocity  of  the  mass  M  is 
nothing,  that  is  to  say,  when  the  effect  of  the  force  is  to  make  a  body  pass 
from  a  state  of  rest  into  one  of  motion,  or  from  a  state  of  motion  into  one 
of  rest.  The  general  expression  then  assumes  one  of  the  following  forms, 
namely  : — 

F  S  =  *MV,-or, 

-FS  =  ^MV„2; 

the  first  of  which  denotes  the  quantity  of  work  which  must  be  done  on  a 


-59]  *  Energy.  39. 

body  of  mass  M  in  order  to  give  to  it  the  velocity  V^,  while  the  second 
expresses  the  work  that  must  be  done  in  order  to  bring  the  same  mass  to 
rest  when  it  is  moving  with  the  velocity  V„,  the  negative  sign  in  the  latter 
case  showing  that  the  force  here  acts  in  oppositio7i  to  the  actual  motion, 
and  is  therefore  to  be  regarded  as  a  resistance. 

In  practice,  the  case  which  most  frequently  occurs  is  where  work  of 
acceleration  and  work  against  resistance  are  performed  simultaneously. 
Thus,  recurring  to  the  inclined  plane  already  referred  to  in  page  37  ;  if 
the  force  P  be  greater  than  M^  sin  A,  the  body  M  will  move  up  the  in- 
cline with  a  continually  increasing  velocity,  and  if  the  point  of  application 
of  P  be  displaced  from  A  to  B,  the  total  amount  of  work  done,  namely, 
P.  AB,  consists  of  a  portion  =  IV^  sin  A.  AB,  done  against  the  resistance 
of  the  weight  Q  or  M^,  and  of  a  portion  =  (P  —  M^  sin  A)  A  B  expended 
in  accelerating  the  mass  M.  Hence,  to  determine  the  velocity  v  with 
which  M  arrives  at  the  top  of  the  incline  we  have  the  equation 

(P-M^sin  A)  AB  =  iM2/2; 

for  the  portion  of  P  which  is  in  excess  of  what  is  required  to  produce 
•equilibrium  with  the  weight  O,  namely,  I*  — M^  sin  A,  corresponds  to  the 
resultant  force  F  supposed  in  the  foregoing  discussion,  and  AB  in  the 
distance  through  which  this  resultant  force  acts. 

58.  Unit  of  "Work. — For  strictly  scientific  purposes  a  unit  of  work  is 
taken  to  be  the  work  done  by  a  unit  of  force  when  its  point  of  application 
moves  through  one  foot  in  the  direction  of  its  action  ;  but,  as  a  convenient 
and  sufficiently  accurate  standard  for  practical  purposes,  the  quantity  of 
work  which  is  done  in  lifting  i  pound  through  the  height  of  i  foot  is  com- 
monly adopted  as  the  unit,  and  this  quantity  of  work  is  spoken  of  as  one 
'  foot-pound  ! '  It  is,  however,  important  to  observe  that  the  foot-pound  is 
not  perfectly  invariable,  since  the  weight  of  a  pound,  and  therefore  the 
work  done  in  lifting  it  through  a  given  height,  differs  at  different  places  ; 
being  a  little  greater  near  the  Poles  than  near  the  Equator. 

59.  Energy. — The  fact  that  any  agent  is  capable  of  doing  work  is 
usually  expressed  by  saying  that  it  possesses  Energy,  and  the  quantity  of 
energy  it  possesses  is  measured  by  the  amount  of  work  it  can  do.  For  ex- 
ample, in  the  case  of  the  inclined  plane  above  referred  to,  the  working  power 
or  energy  of  the  force  P  is  P  x  AB  ;  and  if  this  force  acts  under  the  condi- 
tions last  supposed,  by  the  time  its  own  energy  is  exhausted  (in  consequence 
of  its  point  of  application  having  arrived  at  B,  the  limit  of  the  range  through 
which  it  is  supposed  able  to  act),  it  has  conferred  upon  the  mass  M  a  quantity 
of  energy  equal  to  that  which  has  been  expended ;  for,  in  the  first  place, 
the  mass  M  has  been  raised  through  a  vertical  height  equal  to  BC,  and 
could  by  falling  again  through  the  same  height  do  an  amount  of  work 
represented  by  M^x  BC  or  0  x  BC  ;  and  in  the  second  place  M  can  do 
work  by  virtue  of  the  velocity  that  has  been  imparted  to  it,  and  can  con- 
tinue moving  in  opposition  to  any  given  resistance  R  through  a  distance 
S,  such  that 

The  energy  possessed  by  the  mass  M  in  consequence  of  having  been 


40  Oji  Matter y  Force,  and  Motion.  [59 

raised  from  the  ground,  is  commonly  distinguished  as  energy  of  position 
or  potential  energy,  and  is  measured  by  the  product  of  the  force  tending 
to  cause  motion  into  the  distance  through  which  the  point  of  application 
of  the  force  is  capable  of  being  displaced  in  the  direction  in  which  the 
force  acts.  The  energy  possessed  by  the  mass  M  in  consequence  of  its 
velocity,  is  commonly  distinguished  as  enei'gy  of  motion  ox  kinetic  energy  : 
it  is  measured  by  half  the  product  of  the  moving  mass  into  the  square  of 

Kjtg  velocity. 
60.  Varieties  of  Energ^y. — It  will  be  seen,  on  considering  the  defini- 
tion of  work  given  above,  that  a  force  is  said  to  do  work  when  it  produces 
any  change  in  the  condition  of  bodies,  for  the  only  changes  which,  ac- 
cording to  the  definition  of  force  given  previously  (26),  a  force  is  capable 
of  producing,  are  changes  in  the  state  of  rest  or  motion  of  bodies  and 
changes  of  their  place  in  opposition  to  resistances  tending  to  prevent 
motion  or  to  produce  motion  in  an  opposite  direction.  There  are,  how- 
ever, many  other  kinds  of  physical  changes  which  can  be  produced  under 
appropriate  conditions,  and  the  recent  progress  of  investigation  has  shown 
that  the  conditions  under  which  changes  of  all  kinds  occur  are  so  far 
analogous  to  those  required  for  the  production  of  work  by  mechanical 
forces,  that  the  term  work  has  come  to  be  used  in  a  more  extended  sense 
than  formerly,  and  is  now  often  used  to  signify  the  production  of  any  sort 
of  physical  change. 

Thus  work  is  said  to  be  done  when  a  body  at  a  low  temperature  is 
raised  to  a  higher  temperature,  just  as  much  as  when  a  weight  is  raised 
from  a  lower  to  a  higher  level ;  or  again,  work  is  done  when  any  electrical, 
magnetic,  or  chemical  change  is  produced.  This  extension  of  the  mean- 
ing of  the  term  work  involves  a  similar  extension  of  the  meaning  of  ene?gy, 
which  in  this  wider  sense  may  be  defined  as  the  capacity  for  producijig 
physical  change. 

As  examples  of  energy  in  this  more  general  sense  the  following  may 
be  mentioned  :  {a)  the  energy  possessed  by  gunpowder  in  virtue  of  the 
mutual  chemical  affinities  of  its  constituents,  whereby  it  is  capable  of 
doing  work  by  generating  heat  or  by  acting  on  a  cannon  ball  so  as  to 
change  its  state  of  rest  into  one  of  rapid  motion  ;  {b)  the  energy  of  a 
charged  Leyden  jar,  which,  according  to  the  way  in  which  the  jar  is  dis- 
charged, can  give  rise  to  changes  of  temperature,  changes  of  chemical 
composition,  to  mechanical  changes,  or  to  changes  of  magnetic  or  electri- 
cal condition  ;  {c)  the  energy  of  a  red-hot  ball  which,  amongst  other  effects 
it  is  capable  of  producing,  can  raise  the  temperature  and  increase  the 
volume  of  bodies  colder  than  itself,  or  can  change  ice  into  water  or  water 
into  steam. 

61.  Transformations  of  Energ^y. — It  has  been  found  by  experiment 
that  when  one  kind  of  energy  disappears  or  is  expended,  energy  of  some 
other  kind  is  produced,  and  that,  under  proper  conditions,  the  disappear- 
ance of  any  one  of  the  known  kinds  of  energy  can  be  made  to  give  rise  to 
a  greater  or  less  amount  of  any  other  kind.  One  of  the  simplest  illustra- 
tions that  can  be  given  of  this  transformation  of  energy  is  afforded  by  the 
oscillations  of  a  pendulum.     When  the  pendulum  is  at  rest  in  its  lowest 


k 


-62]  Conservation  of  Energy.  41 

position  it  does  not  possess  any  energy,  for  it  has  no  power  of  setting 
either  itself  or  other  bodies  in  motion  or  of  producing  in  them  any  kind  of 
change.  In  order  to  set  the  pendulum  oscillating,  work  must  be  done 
upon  it,  and  it  thereafter  possesses  an  amount  of  energy  corresponding  to 
the  work  that  has  been  expended.  When  it  has  reached  either  end  of  its 
path,  the  pendulum  is  for  an  instant  at  rest,  but  it  possesses  energy  by 
virtue  of  its  position,  and  can  do  an  amount  of  work  while  falling  to  its 
lowest  position  which  is  represented  by  the  product  of  its  weight  into  the 
vertical  height  through  which  its  centre  of  gravity  descends.  When  at 
the  middle  of  its  path  the  pendulum  is  passing  through  its  position  of 
equilibrium  and  has  no  power  ot  doing  work  by  falling  lower,  but  it  now 
possesses  energy  by  virtue  of  the  velocity  which  it  has  gained,  and  this 
energy  is  able  to  carry  it  up  on  the  second  side  of  its  lowest  position  to  a 
height  equal  to  that  from  which  it  has  descended  on  the  first  side.  By 
the  time  it  reaches  this  position  the  pendulum  has  lost  all  its  velocity,  but 
it  has  regained  the  power  of  falling  :  this,  in  its  turn,  is  lost  as  the  pen- 
dulum returns  again  to  its  lowest  position,  but  at  the  same  time  it  regains 
its  previous  velocity.  Thus  during  every  quarter  of  an  oscillation,  the 
energy  of  the  pendulum  changes  from  potential  energy  or  energy  of  posi- 
tion, into  actual  energy  or  energy  of  motion,  or  vice  versa. 

A  more  complex  case  of  the  transformation  of  energy  is  afforded  by  a 
thermo-electric  pile,  the  terminals  of  which  are  connected  by  a  conduct- 
ing wire  :  the  application  of  energy  in  the  form  of  heat  to  one  face  of  the 
pile  gives  rise  to  an  electric  current  in  the  wire,  which,  in  its  turn,  repro- 
duces heat,  or  by  proper  arrangements  can  be  made  to  produce  chemical, 
magnetic,  or  mechanical  effects,  such  as  those  described  below  in  the 
chapters  on  Electricity. 

It  has  also  been  found  that  the  transformations  of  energy  always  take 
place  according  to  fixed  proportions.  For  instance,  when  coal  or  any 
other  combustible  is  burned,  its  chemical  energy,  or  power  of  combining 
with  oxygen  vanishes,  and  heat  or  thermal  energy  is  produced,  and  the 
quantity  of  heat  produced  by  the  combustion  of  a  given  amount  of  coal 
is  fixed  and  invariable.  If  the  combustion  take  place  under  the  boiler  of 
a  steam-engine,  mechanical  work  can  be  obtained  by  the  expenditure  of 
part  of  the  heat  produced,  and  here  again  the  quantitative  relation 
between  the  heat  expended  and  the  work  gained  in  place  of  it  is  perfectly 
constant. 

62.  Conservation  of  Energry. — Another  result  of  great  importance 
which  has  been  arrived  at  by  experiment  is  that  the  total  amount  of  energy 
possessed  by  any  system  of  bodies  is  unaltered  by  any  transformations 
arising  from  the  action  of  one  part  of  the  system  upon  another/  and  can 
only  be  increased  or  diminished  by  effects  produced  on  the  system  by 
external  agents.  In  this  statement  it  is  of  course  understood  that  in 
reckoning  the  sum  of  the  energy  of  various  kinds  which  the  system  may 
possess,  those  amounts  of  the  different  forms  of  energy  which  are  mutually 
convertible  into  each  other  are  taken  as  being  numerically  equal ;  or, 
what  comes  virtually  to  the  same  thing,  the  total  energy  of  the  system  is 
supposed  to  be  reduced — either  actually,  or  by  calculation  from  the  known 


42  On  Matter,  Force,  and  Motion.  [62- 

ratio  of  transformation  of  the  various  forms  of  energy — to  energy  of  seme 
one  kind  ;  then  the  statement  is  equivalent  to  this  :  that  the  total  energy 
of  any  one  form  to  which  the  energy  of  a  given  system  of  bodies  is 
reducible,  is  unalterable  so  long  as  the  system  is  not  acted  on  from  with- 
out. Practically  it  is  always  possible,  in  one  way  or  another,  to  convert 
the  whole  of  the  energy  possessed  by  any  body  or  system  of  bodies 
into  heat,  but  it  cannot  be  all  converted  without  loss  into  any  other  form 
of  energy  ;  hence  the  principle  stated  at  the  beginning  of  this  article  can 
be  enunciated  in  the  closest  conformity  with  the  direct  results  of  experi- 
ment by  saying  that,  so  long  as  any  system  of  bodies  is  not  acted  on 
from  without,  the  total  quantity  of  heat  that  can  be  obtained  from  it  is 
unalterable  by  any  changes  which  may  go  on  within  the  system  itself. 
For  instance,  a  quantity  of  air  compressed  into  the  reservoir  of  an  air-gun 
possesses  energy  which  is  represented  partly  by  the  heat  which  gives  to 
it  its  actual  temperature  above  the  absolute  zero,  and  partly  by  the 
work  which  the  air  can  do  in  expanding.  This  latter  portion  can  be 
converted  into  heat  in  various  ways,  as,  for  example,  by  allowing  the  air  to 
escape  through  a  system  of  capillary  tubes,  so  fine  that  the  air  issues  from 
them  without  any  sensible  velocity  ;  if,  however,  the  expanding  air  be 
employed  to  propel  a  bullet  from  the  gun,  it  produces  considerably  less 
heat  than  in  the  case  previously  supposed,  the  deficiency  being  represented 
for  a  time  by  the  energy  of  the  moving  bullet,  but  reappearing  in  the  form 
of  heat  in  the  friction  of  the  bullet  against  the  air,  and  when  the  motion 
of  the  bullet  is  destroyed,  by  striking  against  an  inelastic  obstacle  at  the 
same  level  -as  the  gun.  But  whatever  the  mode  and  however  numerous 
the  intermediate  steps  by  which  the  energy  of  the  compressed  air  is 
converted  into  heat,  the  total  quantity  of  heat  finally  obtainable  from  it  is 
the  same. 


• 


-63]  Universal  Attraction.  43 


BOOK   II. 

GBAVITATION    AND    MOLECULAR    ATTRACTION. 


CHAPTER   I. 

GRAVITY,  CENTRE  OF  GRAVITY,  THE  BALANCE. 

63.  TTniversal  attraction,  its  laws. —  Universal  attraction  is  a  force 
in  virtue  of  which  the  material  particles  of  all  bodies  tend  incessantly  to 
approach  each  other  ;  it  is  a  mutual  action,  however,  which  all  bodies,  at 
rest  or  in  motion,  exert  upon  one  another,  no  matter  how  great  or  how 
small  the  space  between  them  may  be,  or  whether  this  space  be  occupied 
or  unoccupied  by  other  matter. 

A  vague  hypothesis  of  the  tendency  of  the  matter  of  the  earth  and 
stars  to  a  common  centre  was  adopted  even  by  Democritus  and  Epicurus. 
Kepler  assumed  the  existence  of  a  mutual  attraction  between  the  sun,  the 
earth,  and  the  other  planets.  Bacon,  Galileo,  and  Hooke,  also  recognised 
the  existence  of  universal  attraction.  But  Newton  was  the  first  who 
established  the  law  and  the  universality  of  gravitation. 

Since  Newton's  time  the  attraction  of  matter  by  matter  was  experi- 
mentally established  by  Cavendish.  This  eminent  English  physicist  suc- 
ceeded by  means  of  a  delicate  torsion  balance  (85)  in  rendering  visible 
the  attraction  between  a  large  leaden  and  a  small  copper  ball. 

The  attraction  between  any  two  bodies  is  the  resultant  of  the  attractions 
of  each  molecule  of  the  one  upon  every  molecule  of  the  other  according 
to  the  law  of  Newton,  which  may  be  thus  expressed  :  the  attraction 
between  two  material  particles  is  directly  proportional  to  the  product  of 
their  masses^  and  inversely  proportio?tal  to  the  square  of  their  distances 
asunder.  To  illustrate  this,  we  may  take  the  case  of  two  spheres  which, 
owing  to  their  symmetry,  attract  each  other  just  as  if  their  masses  were 
concentrated  in  their  centres.  If  without  other  alteration  the  mass  of  one 
sphere  were  doubled,  tripled,  etc.,  the  attraction  between  them  would  be 
doubled,  tripled,  etc.  If,  however,  the  mass  of  one  sphere  being  doubled, 
that  of  the  other  were  increased  three  times,  the  distance  between  their 
centres  remaining  the  same,  the  attraction  would  be  increased  six  times. 
Lastly,  if,  without  altering  their  masses,  the  distance  between  their  centres 
were  increased  from  i  to  2,  3,  4,  ...  .  units,  the  attraction  would  be  di- 
minished to  the  4th,  9th,  1 6th,  ....  part  of  its  former  intensity.  In 
short,  if  we  define  the  unit  of  attraction  as  that  which  would  exist  between 


44 


Gravitation  and  Molecular  A  i  tract  ion. 


[61 


two  units  of  mass  whose  distance  asunder  was  the  unit  of  length,  the  at- 
traction of  two  molecules,  having  the  masses  jn  and  m',  at  the  distance  r, 

would  be  expressed  by  — —' 

64.  Terrestrial  grravitation. — The  tendency  of  any  body  to  fall  to- 
wards the  earth  is  due  to  the  mutual  attraction  of  that  body  and  the  earth ; 
or,  to  terrestrial  gravitation,  and  is,  in  fact,  merely  a  particular  case  of 
universal  gravitation. 

At  any  point  of  the  earth's  surface,  the  direction  of  gravity,  that  is  the 
line  which  a  falling  body  describes,  is  called  the  vertical  line.  The  ver- 
tical lines  drawn  at  different  points  of  the  earth's  surface  converge  very 
nearly  to  the  earth's  centre.  For  points  situated  on  the  same  meridian 
the  angle  contained  between  the  vertical  lines  equals  the  difference  between 
the  latitudes  of  those  points. 

The  directions  of  the  earth's  attraction  upon  neighbouring  bodies,  or 
upon  different  molecules  of  one  and  the  same  body,  must,  therefore,  be 
considered  as  parallel,  for  the  two  vertical  lines  form  the  sides  of  a  tri- 
angle whose  vertex  is  near  the  earth's  centre,  about  4,000  miles  distant, 
and  whose  base  is  the  small  distance  between  the  molecules  under  con- 
sideration. 

A  plane  or  Hne  is  said  to  be  horizontal  when  it  is  perpendicular  to  the 
vertical  line. 

The  vertical  line  at  any  point  of  the  globe  is  generally  determined  by 
the  phimb-line  (fig.  29),  which  consists  of  a  weight  at- 
tached to  the  end  of  a  string.  It  is  evident  that  the 
weight  cannot  be  in  equilibrium,  unless  the  direction  of 
the  earth's  attraction  upon  it  passes  through  the  point  of 
support,  and  therefore  coincides  with  that  of  the  string. 
The  horizontal  plane  is  also  determined  with  great 
ease,  since  it  coincides,  as  will  be  afterwards  shown, 
with  the  level  surface  of  every  Hquid  when  in  a  state  of 
equilibrium. 

When  the  mean  figure  of  the  earth  has  been  ap- 
proximately determined,  it  becomes  possible  to  compare 
the  direction  of  the  plumb-line  at  any  place  with  that 
of  the  normal  to  the  mean  figure  at  that  place.  When 
any  difference  in  these  directions  can  be  detected,  it 
constitutes  a  deviation  of  the  plumb-line,  and  is  due  to 
the  attraction  of  some  great  mass  of  matter  in  the  neighbourhood,  such 
as  a  mountain.  Thus,  in  the  case  of  the  mountain  of  Schehallien,  in 
Perthshire,  it  was  found  by  Dr.  Maskelyne  that  the  angle  between  the 
directions  of  two  plumb-lines,  one  at  a  station  to  the  north,  and  the  other 
to  the  south  of  the  mountain,  was  greater  by  w" (y  than  the  angle  between 
the  normals  of  the  mean  surface  of  the  earth  at  those  points  ;  in  other 
words,  each  plumb-line  was  deflected  by  about  d"  towards  the  mountain. 
By  calculating  the  volume  and  mass  of  the  mountain,  it  was  inferred  from 
this  observation  that  the  mean  density  of  the  mountain  was  to  that  of  the 
earth  in  the  ratio  of  5  :  9,  and  that  the  mean  density  of  the  earth  is  about 


Fig.  29. 


-65] 


Centre  of  Gravity. 


Ai 


five  times  that  of  water,— a  result  agreeing  pretty  closely  with  that  deduced 
from  Cavendish's  experiments  referred  to  in  the  last  article. 

65.  Centre  of  gravity,  its  experimental  determination. — Into  what- 
ever position  a  body  may  be  turned  with  respect  to  the  earth,  there  is  a 
certain  point,  invariably  situated  with  respect  to  the  body,  through  which 
the  resultant  of  the  attracting  forces  between  the  earth  and  its  several 
molecules  always  passes.  This  point  is  called  the  cefitre  of  gravity  ;  it 
may  be  within  or  without  the  body,  according  to  the  form  of  the  latter  ; 
its  existence,  however,  is  easily  established  by  the  following  considera- 
tions :  Let  in,  m\  in",  in"'.  .  .  (fig.  30)  be  molecules  of  any  body.  The 
earth's  attraction  upon  these  molecules  will  constitute  a  system  of  parallel 


Fig.  31- 

forces,  having  a  common  vertical  direction,  whose  resultant,  according  to'" 
(36),  will  be  found  by  seeking  first  the  resultant  of  the  forces  which  act 
on  any  two  molecules,  in,  and  in',  then  that  of  this  resultant,  and  a  third 
force  acting  on  in",  and  so  on  until  we  arrive  at  the  final  resultant,  W,  re- 
presenting the  weight  of  the  body,  and  applied  at  a  certain  point,  G.  If 
the  body  be  now  turned  into  the  position  shown  in  fig.  31,  the  molecules 
in.  111',  in".  .  .  .  will  continue  to  be  acted  on- by  the  same  forces  as  before, 
the  resultant  of  the  forces  on  in  and  in'  will  still  pass  through  the  same 
point  o  in  the  line  mm',  the  following  resultant  will  again  pass  through  the 
same  point  0'  in  oin",  and  so  on  up  to  the  final  resultant  P,  which  will  still 
pass  through  the  same  point  G,  which  is  the  centre  of  gravity. 

To  find  the  centre  of  gravity  of  a  body  is  a  purely  geometrical  problem  ; 
in  many  cases,  however,  it  can  be  at  once  determined.  For  instance, 
the  centre  of  gravity  of  a  right  line  of  uniform  density  is  the  point  which 
bisects  its  length  ;  in  the  circle  and  sphere  it  coincides  with  the  geometri- " 
cal  centre  :  in  cylindrical  bars  it  is  the  middle  point  of  the  axis.  The 
centre  of  gravity  of  a  plane  triangle  is  in  the  line  which  joins  any  vertex 
with  the  middle  of  the  opposite  side,  and  at  a  distance  from  the  vertex  equal 
to  two-thirds  of  this  line ;  in  a  cone  or  pyramid  it  is  in  the  line  which 
joins  the  vertex  with  the  centre  of  gravity  of  the  base,  and  at  a  distance 
from  the  vertex  equal  to  three-fourths  of  this  line.  These  rules,  it  must  be 
remembered,  presuppose  that  the  several  bodies  are  of  uniform  density. 

In  order  to  determine  experimentally  the  centre  of  gravity  of  a  body,  it 
is  suspended  by  a  string  in  two  different  positions,  as  shown  in  figs.  32  and 


46 


Gravitation  and  Molecular  A  ttraction. 


[65- 


33  ;  the  point  where  the  directions  AB  and  CD  of  the  string  in  the  two 
experiments  intersect  each  other  is  the  centre  of  gravity  required.  For 
the  resultant  ^of  the  earth's  attraction  being  a  vertical  force  applied  at  the 


Fig   33 


*> 


centre  of  gravity,  the  body  can  only  be  in  equilibrium  when  this  point  lies 
vertically  under  the  point  of  suspension,  that  is  in  the  prolongation  of  the 
suspended  string.  But  the  centre  of  gravity  being  in  AB  as  well  as  in  CD 
must  coincide  with  the  point  of  intersection  of  these  two  lines. 

66.  Equilibrium  of  heavy  bodies. — Since  the  action  of  gravity  upon 
a  body  reduces  itself  to  a  single  vertical  force  applied  at  the  centre  of 
gravity  and  directed  towards  the  earth's  centre,  equilibrium  will  be  estab- 
lished only  when  this  resultant  is  balanced  by  the  resultant  of  other  forces 
and  resistances  acting  on  the  body  at  the  fixed  point  through  which  it 
passes. 

When  only  one  point  of  the  body  is  fixed,  it  will  be  in  equilibrium  if 
the  vertical  line  through  its  centre  of  gravity  passes  through  the  fixed 
point.  If  more  than  one  point  is  supported,  the  body  will  be  in  equili- 
brium if  a  vertical  line  through  the  centre  of  gravity  passes  through  a 
point  within  the  polygon  formed  by  joining  the  points  of  support. 

The  Leaning  Tower  of  Pisa  continues  to  stand  because  the  vertical 
ine  drawn  through  its  centre  of  gravity  passes  within  its  base. 

It  is  easier  to  stand  on  our  feet  than  on  stilts,  because  in  the  latter 
case  the  smallest  motion  is  sufficient  to  cause  the  vertical  line  through  the 
centre  of  gravity  of  our  bodies  to  pass  outside  the  supporting  base,  which 
is  here  reduced  to  a  mere  hne  joining  the  feet  of  the  stilts.  Again,  it  is 
impossible  to  stand  on  one  leg  if  we  keep  one  side  of  the  foot  and  head 
close  to  a  vertical  wall,  because  the  latter  prevents  us  from  throwing  the 
body's  centre  of, gravity  vertically  above  the  supporting  base. 

67.  Bifferent  states  of  equilibrium. — Although  a  body  supported  by 
a  fixed  point  is  in  equilibrium  whenever  its  centre  of  gravity  is  in  the 
vertical  line  through  that  point,  the  fact  that  the  centre  of  gravity  tends 


-68] 


TJie  'Balance. 


47 


incessantly  to  occupy  the  lowest  possible  position  leads  us  to  distinguish 
between  three  states  of  equilibrium — stable^  unstable,  7ieutraL 

A  body  is  said  to  be  in  stable  equilibrium  if  it  tends  to  return  to  its 
first  position  after  the  equilibrium  has  been  slightly  disturbed.  Every 
body  is  in  this  state  when  its  position  is  such  that  the  slightest  alteration 
of  the  same  elevates  its  centre  of  gravity  ;  for  the  centre  of  gravity  will 
descend  again  when  permitted,  and  after  a  few  oscillations  the  body  will 
return  to  its  original  position. 

The  pendulum  of  a  clock  continually  oscillates  about  its  position  of 
stable  equilibrium,  and  an  t.<gz  o^"^  a-  level  table  is 
in  this  state  when  its  long  axis  is  horizontal.  We 
have  another  illustration  in  the  toy  represented  in 
the  adjoining  fig.  34.  A  small  figure  cut  in  ivory 
is  made  to  stand  on  one  foot  at  the  top  of  a  pedes- 
tal by  being  loaded  with  two  leaden  balls,  a,  b, 
placed  sufficiently  low  to  throw  the  centre  of  gravity, 
g,  of  the  whole  compound  body  below  the  foot  of 
the  figure.  After  being  disturbed  the  little  figure 
oscillates  like  a  pendulum,  having  its  point  of  sus- 
pension at  the  toe,  and  its  centre  of  gravity  at  a 
lower  point,  g. 

A  body  is  said  to  be  in  tmstablc  equilibrium, 
when  after  the  slightest  disturbance  it  tends  to  de- 
part still  more  from  its  original  position.  A  body 
is  in  this  state  when  its  centre  of  gravity  is  verti- 
cally above  the  point  of  support,  or  higher  than  it 
would  be  in  any  adjacent  position  of  the  body.  An 
t%<g  standing  on  its  end,  or  a  stick  balanced  upright  on  the  finger  is  in 
this  state. 

Lastly,  if  in  any  adjacent  position  a  body  still  remains  in  equihbrium, 
its  state  of  equilibrium  is  said  to  be  neutral.  In  this  case  an  alteration 
in  the  position  of  the  body  neither  raises  nor  lowers  its  centre  of  gravity. 
A  perfect  sphere  resting  on  a  horizontal  plane  is  in  this  state. 


Fig.  34- 


Fig.  35. 

Fig.  35  represents  three  cones.  A,  B,  C,  placed  respectively  in  stable, 
unstable,  and  neutral  equilibrium  upon  a  horizontal  plane.  The  letter  g 
in  each  shows  the  position  of  the  centre  of  gravity. 

68.  Tlie  balance. — The  balance  is  an  instrument  for  determining  the 
relative  weights  or  masses  of  bodies.     There  are  many  varieties. 

The  ordinary  balance  (fig.  36)   consists  of  a  lever  of  the  first  kind, 


48 


Gravitation  and  MSlecidar  A  ttraction. 


[68- 


called  the  beam  AB,  with  its  fulcrum  in  the  middle  ;  at  the  extremities  of 
the  beam  are  suspended  two  scale  pans,  C  and  D,  one  intended  to  receive 


Fig.  36. 

the  object  to  be  weighed,  and  the  other  the  counterpoise.  The  fulcrum 
consists  of  a  steel  prism,  «,  commonly  called  a  knife  edge,  which  passes 
through  the  beam,  and  rests  with  its  sharp  edge,  or  axis  of  suspensioUj 
upon  two  supports  ;  these  are  formed  of  agate  or  polished  steel,  in  order 
to  diminish  the  friction.  A  needle  or  pointer  is  fixed  to  the  beam,  and 
oscillates  with  it  in  front  of  a  graduated  arc,  a  ;  when  the  beam  is  per- 
fectly horizontal  the  needle  points  to  the  zero  of  the  graduated  arc. 

Since  by  (40)  two  equal  forces  in  a  lever  of  the  first  kind  cannot  be  in 
equilibrium  unless  their  leverages  are  equal,  the  length  of  the  arms  «A 
and  «B  ought  to  remain  equal  during  the  process  of  weighing.  To  secure 
this  the  scales  are  suspended  from  hooks,  whose  curved  parts  have  sharp 
edges,  and  rest  on  similar  edges  at  the  ends  of  the  beam.  In  this  manner 
the  scales  are  supported  on  mere  points,  which  remain  unmoved  during 


70] 


The  Balance. 


49 


the  oscillations  of  the  beam.     This  mode  of  suspension  is  represented  in 

fig.  36. 

69.  Conditions  to  be  satisfied  by  a  balance. — A  good  balance  ought 
to  satisfy  the  following  conditions  : 

i.  The  two  arms  of  the  beam  ought  to  be  precisely  equal,  otherwise, 
according  to  the  principle  of  the  lever,  unequal  weights  will  be  required 
to  produce  equilibrium.  To  test  whether  the  arms  of  the  beam  are  equal, 
weights  are  placed  in  the  two  scales  until  the  beam  becomes  horizontal  ; 
the  contents  of  the  scales  being  then  interchanged,  the  beam  will  remain 
horizontal  if  its  arms  are  equal,  but  if  not,  it  will  descend  on  the  side  of 
the  longer  arm. 

ii.  The  balance  ought  to  be  iu  equilibrium  when  the  scales  are  empty, 
for  otherwise  unequal  weights  must  be  placed  in  the  scales  in  order  to 
produce  equilibrium.  It  must  be  borne  in  mind,  however,  that  the  arms 
are  not  necessarily  equal,  even  if  the  beam  remains  horizontal  when  the 
scales  are  empty  ;  for  this  result  might  also  be  produced  by  giving  to  the 
longer  arm  the  lighter  scale. 

iii.  The  beam  being  horizontal,  its  centre  of  gravity  ought  to  be  in  the 
same  vertical  line  with  the  edge  of  the  fidcrinn,  atid  a  little  beloiv  the 
"latter,  for  otherwise  the  beam  would  not  be  in  stable  equilibrium  (67). 

The  effect  of  changing  the  position  of  the  centre  of  gravity  may  be 
shown  by  means  of  a  beam  (fig,  37),  whose  fulcrum,  being  the  nut  of  a 
screw,  a  can  be  raised  or  lowered  by  turning  the  screw-head,  b. 


Fig.  37 

When  the  fulcrum  is  at  the  top  of  the  groove  c,  in  which  it  slides,  the 
centre  of  gravity  of  the  beam  is  below  its  edge,  and  the  latter  oscillates 
freely  about  a  position  of  stable  equilibrium.  By  gradually  lowering  the 
fulcrum  its  edge  may  be  made  to  pass  through  the  centre  of  gravity  of  the 
beam  when  the  latter  is  in  neutral  equilibrium  :  that  is  to  say,  it  no  longer 
oscillates,  but  remains  in  equilibrium  in  all  positions.  When  the  fulcrum 
is  lowered  still  more,  the  centre  of  gravity  passes  above  its  edge,  the 
beam  is  in  a  state  of  unstable  equilibrium,  and  is  overturned  by  the  least 
displacement. 

70.  Belicacy  of  tbe  balance. — A  balance  is  feaid  to  be  delicate  when 
a  very  small  difference  between  the  weights  in  the  scales  causes  a  percep- 
tible deflection  of  the  pointer. 

Let  A  and  B  (figs.  38  and  39)  be  the  points  from  which  the  scale  pans 
are  suspended,  and  C  the  axis  of  suspension  of  the  beam.  A,  B,  and  C 
are  supposed  to  be  in  the  same  straight  hne,  according  to  the  usual 
arrangement.     Suppose  weights  P  and  O  to  be  in  the  pans  suspended 

D 


50 


Gravitation  and  Molecidar  A  tti^action. 


[70 


from  A  and  B  respectively,  and  let  G  be  the  centre  of  gravity  of  the  beam, 
then  the  beam  will  come  to  rest  in  the  position  shown  in  the  figure  where 
the  line  DCN  is  vertical,  and  ECG  is  the  direction  of  the  pointer.     Ac- 


Fig-  38.  Fig.  35. 

cording  to  the  above  statement  the  greater  the  angle  ECD  for  a  given 
difference  between  P  and  Q  the  greater  is  the  delicacy  of  the  balance. 
Draw  ON  at  right  angles  to  CG. 

Let  W  be  the  weight  of  the  beam,  then  from  the  properties  of  the  lever 
it  follows  that  measuring  moments  with  respect  to  C,  the  moment  of  P 
equals  the  sum  of  the  moments  of  Q  and  W,  a  condition  which  at  once 
leads  to  tlie  relation 

(P-Q)  AC=W.  GN 

Now  it  is  plain  that  for  a  given  value  of  CG  the  angle  GCN  (that  is 
ECD,  which  measures  the  delicacy)  is  greater  as  GN  is  greater  :  and  from 
the  formula  it  is  plain  that  for  a  given  value  of  P  —  Q  we  shall  have  GN 
greater  as  AC  is  greater,  and  as  W  is  less.  Again,  for  a  given  value  of  GN 
the  angle  GCN  is  greater  as  CG  is  less.  Hence  the  means  of  rendering 
a  balance  delicate  are  : — 

i.   To  make  the  arms  of  the  balance  long. 

ii.  To  make  the  weight  of  the  beam  as  small  as  is  consistent  with  its 
rigidity. 

iii.  To  bring  the  centre  of  gravity  of  the  beam  a  very  little  below  the 
point  of  support. 

Moreover,  since  friction  will  always  oppose  the  action  of  the  force  that 
tends  to  preponderate,  the  balance  will  be  rendered  more  delicate  by 
diminishing  friction  :  to  secure  this  advantage  the  edges  from  which  the 
beam  and  scales  are  suspended  are  made  as  sharp  as  possible,  and  the 
supports  on  which  they  rest  are  very  hard.  And  further,  the  pointer  is 
made  long,  since  its  elongation  renders  a  given  deflection  more  perceptible 
by  increasing  the  arc  which  its  end  describes. 

71.  Pbyslcal  and  cbemical  balances. — Fig.  40  represents  one  of 
the  accurate  balances  ordinarily  used  for  chemical  analysis.  Its  sensitive- 
ness is  such  that  when  charged  with  a  kilogramme  (1,000  grms.)  in  each 
scale,  an  excess  of  a  milligramme  (foVo^^  ^^  ^  g^i^O  in  either  scale  pro- 
duces a  very  perceptible  deflection  of  the  index. 

In  order  to  protect  the  balance  from  air-currents,  dust,  and  moisture, 
it  is  always,  even  when  weighing,  surrounded  by  a  glass  case,  whose  front 


-72] 


Method  of  double  Weighing, 


51 


slides  up  and  down,  to  enable  the  operator  to  introduce  the  objects  to  be 
weighed. 

In  order  to  preserve  the  edge  of  the  fulcrum  as  much  as  possible,  the 


Fig.  40. 

whole  beam,  BB,  with  its  fulcrum  K,  can  be  raised  from  the  support  on 
which  the  latter  rests  by  simply  turning  the  button  O  outside  the  case. 

The  horizontality  of  the  beam  is  determined  by  means  of  a  long  index, 
which  points  downwards  to  a  graduated  arc  near  the  foot  of  the  support- 
ing pillar. 

Lastly,  the  button  C  serves  to  alter  the  sensitiveness  of  the  balance  ; 
by  turning  it,  the  centre  of  gravity  of  the  beam  can  be  made  to  approach 
or  recede  from  the  fulcrum  (69). 

72.  method  of  double  weigrhlngr. — Notwithstanding  the  inaccuracy 
of  a  balance,  the  true  weight  of  a  body  may  always  be  determined  by  its 
means.  To  do  so,  the  body  to  be  weighed  is  placed  in  one  scale,  and  shot 
or  sand  poured  into  the  other  until  equihbrium  is  produced  ;  the  body  is 
then  replaced  by  known  weights  until  equilibrium  is  re-established.  The 
sum  of  these  weights  will  necessarily  be  equal  to  the  weight  of  the  body, 
for,  acting  under  precisely  the  same  circumstances,  both  have  produced 
precisely  the  same  effect. 

The  exact  weight  of  a  body  may  also  be  determined  by  placing  it  suc- 
cessively in  the  two  pans  of  a  balance,  and  then  determining  its  true  weight. 

For  having  placed  in  one  pan  the  body  to  be  weighed,  whose  true 
weight  is  x,  and  in  the  other  the  weight  p,  required  to  balance  it,  let  a 
and  b  be  the  arms  of  levers  corresponding  to  x  and  p.  Then  from  the 
principle  of  the  lever  (40)  we  have  ax=pb.  Similarly  if  p^  is  the  weight 
when  the  body  is  placed  in  the  other  pan,  then  bx  =  ap.  Hence  abx^  =  abpp^, 
from  which  x=  i^ppy 


Gravitation  and  Molecular  A  ttraction. 


[73- 


CHAPTER  II. 


LAWS   OF   FALLING   BODIES.      INTENSITY  OF  TERRESTRIAL   GRAVITY. 
THE   PENDULUM. 

73.  Kaws  Of  falling:  bodies. — Since  a  body  falls  to  the  ground  in 
consequence  of  the  earth's  attraction  on  each  of  its 
molecules,  it  follows  that,  everything  else  being  the 
same,  all  bodies,  great  and  small,  light  and  heavy, 
ought  to  fall  with  equal  rapidity,  and  a  lump  of 
sand  without  cohesion  should,  during  its  fall, 
retain  its  original  form  as  perfectly  as  if  it  were 
compact  stone.  The  fact  that  a  stone  falls  more 
rapidly  than  a  feather  is  due  solely  to  the  unequal 
resist3nces  opposed  by  the  air  to  the  descent  ot 
these  bodies ;  in  a  vacuum  all  bodies  fall  with 
equal  rapidity.  To  demonstrate  this  by  experi- 
ment a  glass  tube  about  two  yards  long  (fig.  41) 
may  be  taken,  having  one  of  its  extremities  com- 
pletely closed,  and  a  brass  cock  fixed  to  the  other. 
After  having  introduced  bodies  of  different  weights 
and  densities  (pieces  of  lead,  paper,  feather,  etc.) 
into  the  tube,  the  air  is  withdrawn  from  it  by  an  air 
pump,  and  the  cock  closed.  If  the  tube  be  now 
suddenly  reversed,  all  the  bodies  will  fall  equally 
quickly.  On  introducing  a  little  air  and  again 
inverting  the  tube,  the  lighter  bodies  become 
slightly  retarded,  and  this  retardation  increases 
with  the  quantity  of  air  introduced. 

The  resistance  opposed  by  the  air  to  falling 
bodies  is  especially  remarkable  in  the  case  of 
liquids.  The  Staubbach  in  Switzerland  is  a  good 
illustration ;  an  immense  mass  of  water  is  seen 
falling  over  a  high  precipice,  but  before  reaching 
the  bottom  it  is  shattered  by  the  air  into  the 
finest  mist.  In  a  vacuum,  however,  liquids  fall 
like  solids  without  separation  of  their  molecules. 
The  water  hairwier  illustrates  this  :  the  instru- 
ment consists  of  a  thick  glass  tube  about  a  foot 
long,  half  filled  with  water,  the  air  having  been 
expelled  by  ebullition  previous  to  closing  one  ex- 
tremity with  the  blow-pipe.  When  such  a  tube 
is  suddenly  inverted  the  water  falls  in  one  undi- 
^'S-  41-  vided  mass   against  the   other  extremity  of  the 

tube,  and  produces  a  sharp  dry  sound,  resembling  that  which  accompanies 

the  shock  of  two  solid  bodies. 


-74] 


Atwood's  Machine. 


s! 


From  Newton's  law  (63)  it  follows,  that  when  a  body  falls 
the  force  of  attraction  which  causes  it  to  do  so  increases  as 
jMoaches  the  earth.  Unless  the 
height  from  which  the  body 
falls,  however,  be  very  great,  this 
increase  will  be  altogether  inap- 
preciable, and  the  force  in  ques- 
tion may  be  considered  as  con- 
stant and  continuous.  If  the 
resistance  of  the  air  were  re- 
moved, therefore,  the  motion  of 
all  bodies  falling  to  the  earth 
would  be  uniformly  accelerated, 
and  would  obey  the  laws  already 
explained  (46). 
^     74.    Atwood's     machine. — 

C  Several  instruments  have  been 

|\  invented  for  illustrating  and  ex- 
perimentally verifying  the  laws 
of  falling  bodies.  Galileo,  who 
discovered  these  laws  in  the 
eaHy  part  of  the  seventeenth 
century,  illustrated  them  by 
means  of  bodies  falling  down 
inclined  planes.  The  great  ob- 
ject of  all  such  instruments  is 
to  diminish  the  rapidity  of  the 
fall  of  bodies  without  altering  the 
character  of  their  motion,  for  by 
this  means  their  motion  may 
not  only  be  better  observed,  but 
it  will  be  less  modified  by  the 
resistance  of  the  air. 

The  most  convenient  instru- 
ment of  this  kind  is  that  in- 
vented by  Atwood  at  the  end  of 
the  last  century,  and  represented 
in  fig.  42.  It  consists  of  a  stout 
pillar  of  wood,  about  i\  yards 
high,  at  the  top  of  which  is  a 
brass  pulley,  whose  axle  rests 
and  turns  upon  four  other  wheels, 
called  friction  wheels,  inasmuch  | 
as  they  serve  to  diminish  fric- 
tion. Two  equal  weights,  M 
and  M',  are  attached  to  the 
.  extremities  of  a  fine  silk  thread, 
\  which  passes  round  the  pulley  ; 


to 
the 


the  earth, 
body  ap- 


Fig.  42. 


a  timepiece, 


the  pillar,  is 


54  Gravitation  and  Molecular  A  ttraction.  [74- 

regulated  by  a  seconds  pendulum,  P,  in  the  usual  way — that  is  to  say,  the 
oscillations  of  the  pendulum  are  communicated  to  a  ratchet,  whose  two 
teeth,  as  seen  in  the  figure,  fit  into  those  of  the  ratchet  wheel.  The  axle 
of  this  wheel  gives  motion  to  the  seconds  hand  of  the  dial,  and  also  to  an 
excentric  behind  the  dial,  as  shown  at  E  by  a  separate  figure.  This  ex- 
centric  plays  against  the  extremity  of  a  lever  D,  which  it  pushes  until  the 
latter  no  longer  supports  the  small  plate,  /,  and  thus  the  weight  M,  which 
at  first  rested  on  this  plate,  is  suddenly  exposed  to  the  free  action  of 
gravity.  The  excentric  is  so  constructed  that  the  little  plate  i  falls  pre- 
cisely when  the  hand  of  the  dial  points  to  zero. 

The  weights  M  and  M'  being  equal  hold  each  other  in  equilibrium  ; 
the  weight  M,  however,  is  made  to  descend  slowly  by  putting  a  small  bar 
or  overweight  m  upon  it ;  and  to  measure  the  spaces  which  it  describes, 
the  rod  or  scale,  Q,  is  divided  into  feet  and  inches,  commencing  from  the 
plate  i.  To  complete  the  instrument  there  are  a  number  of  plates,  A,  A', 
C,  C,  and  a  number  of  rings,  B,  B',  which  may  be  fixed  by  screws  at  any 
part  of  the  scale.  The  plates  arrest  the  descending  weight  M,  the  rings 
only  arrest  the  bar  or  overweight  m,  which  was  the  cause  of  motion,  so 
that  after  passing  through  them,  the  weight  M,  in  consequence  of  its 
inertia,  will  move  on  uniformly  with  the  velocity  it  had  acquired  on 
reaching  the  ring.  The  several  parts  of  the  apparatus  being  described,  a 
few  words  will  suffice  to  explain  the  method  of  experimenting. 

Let  the  hand  of  the  dial  be  placed  behind  the  zero  point,  the  lever  D 
adjusted  to  support  the  plate  /,  on  which  the  weight  M  with  its  overweight 
m  rests,  and  the  pendulum  put  in  motion.  As  soon  as  the  hand  of  the 
dial  points  to  zero  the  plate  i  will  fall,  the  weights  M  and  ?7z  will  descend, 
and  by  a  little  attention  and  a  few  trials  it  will  be  easy  to  place  a  plate  A 
so  that  M  may  reach  it  exactly  as  the  dial  indicates  the  expiration  of  one 
second.  To  make  a  second  experiment,  let  the  weights  M  and  in,  the 
plate  i,  and  the  lever  D,  be  placed  as  at  first ;  remove  the  plate  A,  and  in 
its  place  put  a  ring,  B,  so  as  to  arrest  the  overweight  m  just  when  the 
weight  M  would  have  reached  A ;  on  putting  the  pendulum  in  motion 
again  it  will  be  easy,  after  a  few  trials,  to  put  a  plate,  C,  so  that  the  weight 
M  may  fall  upon  it  precisely  when  the  hand  of  the  dial  points  to  two 
seconds.  Since  the  overweight  m  in  this  experiment  was  arrested  by  the 
ring  B  at  the  expiration  of  one  second,  the  space  BC  was  described  by  M 
in  one  second  purely  in  virtue  of  its  own  inertia,  and  consequently,  by 
(32)  BC  will  indicate  the  velocity  of  the  falling  mass  at  the  expiration  of 
one  second. 

Proceeding  in  the  same  manner  as  before,  let  a  third  experiment  be 
made  in  order  to  ascertain  the  point  B'  at  which  the  weight  M  and  fn 
arrive  after  the  lapse  of  two  seconds,  and,  putting  a  ring  at  B',  ascertain 
by  a  fourth  experiment  the  point  C  at  which  M  arrives  alone,  three 
seconds  after  the  descent  commenced  ;  B'C  will  then  express  the 
velocity  acquired  after  a  descent  of  two  seconds.  In  a  similar  manner, 
by  a  fifth  and  sixth  experiment,  we  may  determine  the  space  OB" 
described  in  three  seconds,  and  the  velocity  WC"  acquired  during  those 
three  seconds,  and  so  on  ;  we  shall  find  that  B'C  is  twice,  and  WC" 


-75]  Morhis  Apparatus.  5  5 

three  times  as  great  as  BC — in  other  words,  that  the  velocities  BC, 
B'C,  V>"C,  increase  in  the  same  proportion  as  the  times  (i,  2,  3,  .  .  . 
seconds)  employed  in  their  acquirement.  By  the  definition  (46),  there- 
fore, the  motion  is  uniformly  accelerated.  The  same  experiments  will 
also  serve  to  verify  and  illustrate  the  four  laws  of  uniformly  accelerated 
motion  as  enunciated  in  (46).     For  example,  the  spaces  OB,  OB^,  OB'', 

described  from  a  state  of  rest  in  i,  2,  3,  ...  .  seconds,  will  be 

found  to  be  proportional  to  the  numbers  i,  4,  9,  .  .  .  that  is  to  say,  to 
the  squares  of  those  numbers  of  seconds,  as  stated  in  the  third  law. 

Lastly,  if  the  overweight  m  be  changed,  the  acceleration  or  velocity 
BC  acquired  per  second  will  also  be  changed,  and  we  may  easily  verify 
the  assertion  in  (29),  that  force  is  proportional  to  the  product  df  the  mass 
moved  into  the  acceleration  produced  in  a  given  time.  For  instance, 
assuming  the  pulley  to  be  so  light  that  its  inertia  can  be  neglected,  if  7n 
weighed  half  an  ounce,  and  M  and  M'  each  1 5I  ounces,  the  acceleration 
BC  would  be  found  to  be  six  inches  ;  whilst  if  m  weighed  i  ounce,  and 
M  and  M'  each  63^  ounces,  the  acceleration  BC  would  be  found  to  be 
three  inches. 

Now  in  these  cases  the  forces  producing  motion,  that  is  the  over- 
weights, are  in  the  ratio  of  i  :  2  ;  while  the  products  of  the  masses  and  the 
accelerations  are  in  the  ratio  of  (|  +  I5f  +  I5f)  x  6  to  (i  +  63^  +  63^)  x  3,  that 
is,  they  are  also  in  the  i"atio  of  i  :  2.  Now  the  same  result  is  obtained 
in  whatever  way  the  magnitudes  of  ;;z,  ]\T,  and  M'  are  varied,  and  con- 
sequently in  all  cases  the  ratio  of  the  forces  producing  motion  equals  the 
/atio  of  the  momenta  generated. 
'JS.  Morln's  apparatus. — The  principle  of  this  apparatus,  the  original 
'"^Sdea  of  which  is  due  to  General  Poncelet,  is  to  make  the  body  in  falling 
trace  its  own  path.  Figure  43  gives  a  view  of  the  whole  apparatus,  and 
figure  44  gives  the  details.  The  apparatus  consists  of  a  wooden  frame- 
work, about  7  feet  high,  which  holds  in  a  vertical  position  a  very  light 
wooden  cylinder,  M,  which  can  turn  freely  about  its  axis.  This  cylinder 
is  coated  with  paper  divided  into  squares  by  equidistant  horizontal  and 
vertical  lines.  The  latter  measure  the  path  traversed  by  the  body  falling 
along  the  cylinder,  while  the  horizontal  lines  are  intended  to  divide  the 
duration  of  the  fall  into  equal  parts. 

The  falling  body  is  a  mass  of  iron,  P,  provided  with  a  pencil  which 
is  pressed  against  the  paper  by  a  small  spring.  The  iron  is  guided  in  its 
fall  by  two  light  iron  wires  which  pass  through  guide-holes  on  the  two 
sides.  The  top  of  this  mass  is  provided  with  a  tipper  which  catches 
against  the  end  of  a  bent  lever,  AC.  This  being  pulled  by  the  string  K 
attached  at  A,  the  weight  falls.  If  the  cylinder  M  were  fixed,  the 
pencil  would  trace  a  straight  line  on  it  ;  but  if  the  cylinder  moves  uni- 
formly, the  pencil  traces  the  line  inn,  which  serves  to  deduce  the  law  of 
the  fall. 

The  cylinder  is  rotated  by  means  of  a  weight,  Q,  suspended  to  a  cord 
which  passes  round  the  axle  G.  At  the  end  of  this  is  a  toothed  wheel,  c, 
which  turns  two  endless  screws,  a  and  b,  one  of  which  turns  the  cylinder, 
and  the  other,  two  vanes,  x  and  x\    At  the  other  end  is  a  ratchet  wheel, 


56 


Gravitation  and  Molecular  A  ttraction. 


[75- 


in  which  fits  the  end  of  a  lever,  B  ;  by  pulling  at  a  cord  fixed  to  the  other 
end  of  B,  the  wheel  is  liberated,  the  weight  Q  descends,  and  the  whole 
system  begins  to  turn.  The  motion  is  at  first  accelerated,  but  as  the  air 
offers  a  resistance  to  the  vanes,  which  increases  as  the  rotation  becomes 
more  rapid,  the  resistance  finally  equals  the  acceleration  which  gravity 
tends  to  impart.     From  this  time  the  motion  becomes  uniform.     This  is 


Fig.  43.  Fig.  44. 

the  case  when  the  weight  O  has  traversed  about  three-quarters  its  course  ; 
at  this  moment  the  weight  P  is  detached  by  pulling  the  cord  K,  and  the 
pencil  then  traces  the  curve  vi7i. 

If,  by  means  of  this  curve,  we  examine  the  double  motion  of  the 
pencil  on  the  small  squares  which  divide  the  paper,  we  see  that,  for  dis- 
placements of  I,  2,  3,  ....  in  a  horizontal  direction,  the  displacements 


-76]  Length  of  the  Compound  Pendulum.  57 

are  i,  4,  9  ....  in  a  vertical  direction.  This  shows  that  the  paths  tra- 
versed in  the  direction  of  the  fall  are  directly  as  the  squares  of  the  lines 
in  the  direction  of  the  rotation,  which  verifies  the  second  law  of  falling 
bodies. 

From  the  relation  which  exists  between  the  two  dimensions  of  the  curve 
mn^  it  is  concluded  that  this  curve  is  a  parabola.  ^ 

76.  ]Lengrtli  of  tlie  compound  pendulum. — The  formula  for  the  time 
of  vibration  of  a  simple  pendulum,  and  the  conclusions  deduced  from  it 
(51)  are  also  applicable  to  the  compound  pendulum,  though  in  this  case 
it  will  be  necessary  to  define  accurately  what  is  meant  by  the  length  of 
such  a  pendulum.  A  compound  pendulum  being  formed  of  a  heavy 
rod  terminated  by  a  greater  or  less  mass,  it  follows  that  the  several 
material  points  of  the  whole  system  will  strive  to  perform  their  oscilla- 
tions in  different  times,  their  distances  from  the  axis  of  suspension  being 
different,  and  the  more  distant  points  requiring  a  longer  time  to  complete 
an  oscillation.  From  this,  and  from  the  fact  that  being  points  of  the 
same  body  they  must  oscillate  together,  it  follows  that  the  motion  of  the 
points  near  the  axis  of  suspension  will  be  retarded,  whilst  that  of  the 
more  distant  points  will  be  accelerated,  and  between  the  two  extremities 
there  will  necessarily  be  a  series  of  points  whose  motion  will  be  neither 
accelerated  nor  retarded,  but  which  will  oscillate  precisely  as  if  they 
were  perfectly  free  and  unconnected  with  the  other  points  of  the  system. 
These  points,  being  equidistant  from  the  axis  of  suspension,  constitute  a 
parallel  axis  known  as  the  axis  of  oscillation  ;  and  it  is  to  the  distance 
between  these  two  axes  that  the  term  le?igth  of  the  compound  pendulum 
is  applied  :  we  may  say,  therefore,  that  the  length  of  a  coinpoimd  pendu- 
lum is  that  of  the  simple  pendulum  which  would  describe  its  oscillations 
in  the  same  time. 

Huyghens,  the  celebrated  Dutch  physicist,  discovered  that  the  axes  ot 
suspension  and  oscillation  in  a  mutually  convertible — that  is  to  say,  the 
time  of  oscillation  will  remain  unaltered  when  the  pendulum  is  suspended 
from  its  axis  of  oscillation.  This  remarkable  fact  enables  us  to  determine 
experimentally  the  length  of  a  compound  pendulum.  To  do  so  the  pen- 
dulum is  inverted  and  suspended  from  a  second  and  moveable  axis, 
which,  after  some  trials,  is  placed  so  that  the  inversion  does  not  affect 
the  number  of  oscillations  made  in  a  given  time  ;  the  length  required  is 
then  the  distance  between  the  two  axes,  and  on  giving  to  /  the  value  thus 
determined,  the  formula  of  (51)  for  the  simple  pendulum  becomes  appli- 
cable to  the  compound  pendulum,  whose  oscillations,  in  vacuo,  obey  the 
same  laws. 

The  length  of  the  seconds  pendulum — that  is  to  say,  of  the  pendulum 
which  makes  one  oscillation  in  a  second — varies,  of  course,  with  the  in- 
tensity of  gravity.  The  following  table  gives  its  value  at  the  sea  level 
at  various  places.  The  accelerative  effect  of  gravity  at  these  places, 
according  to  formula  (51),  is  obtained  in  feet  and  metres  by  multiplying 
the  length  of  the  seconds  pendulum,  reduced  to  feet  and  metres,  by  the 
square  of  3-14159. 

D3 


58 


Gravitation  and  Molecular  Attraction. 


[76- 


Length  of 

Acceleration  of  Gravity 

Pendulum 

in 

in  inches. 

feet. 

metres. 

Hammerfest 

.   7o°-4o'N. 

39-1948 

32-2364 

9-8258 

Konigsberg . 

.     54-42 

39-1507 

32-2002 

9-8142 

Greenwich  . 

.     51-29 

39-1398 

32-1912 

9-8115 

Paris  . 

.     48-50 

39-1285 

32-1819 

9-8039 

New  York  . 

.    40-43 

39-1012 

32-1594 

9-8019 

St.  Thomas 

.      0-25 

39-0207 

32-0957 

9-7826 

Cape  of  Good  Hope  33-55  S. 

39-0780 

32-1404 

9-7962 

t 


-S m-S SL 


Consequently,  \g  or  the  space  described  in  the  first  second  of  its  motion 
by  a  body  falHng  in  vacuo  from  a  state  of  rest  (46)  is 

16-0478  feet  or  4-891  metres  at  St.  Thomas, 
16-0956  „  „  4-905  „  at  London,  and 
16-1182     „      ,,4-913       „        at  Hammerfest. 

In  all  calculations  which  are  used  for  the  sake  of  illustration,  we  may 
take  32  feet  and  9-8  metres  as  the  accelerative  effect  due  to  gravity. 

From  observations  of  this  kind,  after  applying  the  necessary  correc- 
tions, and  taking  into  account  the  effect  of  rotation  (79),  the  form  of  the 
earth  can  be  deduced. 

T].  Verification  of  the  laws  of  the 
pendulum. — In  order  to  verify  the  laws 
of  the  simple  pendulum  (51)  we  are  com- 
pelled to  employ  a  compound  one,  whose 
construction  differs  as  little  as  possible 
from  that  of  the  former.  For  this  purpose 
a  small  sphere  of  a  very  dense  substance, 
such  as  lead  or  platinum,  is  suspended 
from  a  fixed  point  by  means  of  a  very  fine 
thread.  A  pendulum  thus  formed  oscil- 
lates almost  likea  simple  pendulum,  whose 
length  is  equal  to  the  distance  of  the 
centre  of  the  sphere  from  the  point  of 
suspension. 

In  order  to  verify  the  isochronism  of 
small  oscillations,  it  is  merely  necessary  to 
count  the  number  of  oscillations  made 
in  equal  times,  as  the  amplitudes  of  these 
oscillations  diminish  from  3  degrees  to  a 
fraction  of  a  degree;  this  number  is  found 
to  be  constant. 

That  the  time  of  vibration  is  propor- 
tional to  the  square  root  of  the  length  is 
verified  by  causing  pendulums,  whose 
lengths  are  as  the  numbers  i,  4,  9,  .  .  .  . 
to  oscillate  simultaneously.  The  corre- 
sponding numbers  of  oscillations  in  a  given  time  are  then  found  to  be 

proportional  to  the  fractions  i  f,  |,  etc which  shows  that  the 

times  of  oscillation  increase  as  the  numbers  1,  2,  3, .  .  .  .  etc. 


Fig-  45- 


-78] 


Application  of  the  Pendulum  to  Clocks. 


59 


By  taking  several  pendulums  of  exactly  equal  length,  B^  C,  D  (fig.  45)^ 
but  with  spheres  of  different  substances,  lead,  copper,  ivory,  it  is  found 
that,  neglecting  the  resistance  of  the  air,  these  pendulums  oscillate  in 
equal  times,  thereby  showing  that  the  accelerative  effect  of  gravity  on  all 
bodies  is  the  same  at  the  same  place. 

By  rheans  of  an  arrangement  resembling  the  above,  Newton  verified 
the  fact  that  the  masses  of  bodies  are  determined  by  the  balance  ;  which, 
it  will  be  remarked,  lies  at  the  foundation  of  the  measure  of  force  (29). 
For  it  will  be  seen  on  comparing  (50)  and  (51)  with  (47)  that  the  law  of  the 
time  of  a  small  oscillation  is  obtained  on  the  supposition  that  the  force  of 
gravity  on  all  bodies  is  represented  by  M^,  in  which  M  is  determined 
by  the  balance.  In  order  to  verify  this,  he  had  made  two  round  equal 
wooden  boxes ;  he  filled  one  with  wood,  and  as  nearly  as  possible  in 
the  centre  of  oscillation  of  the  other  he  placed  an  equal  weight  of  gold. 
He  then  suspended  the  boxes  by  threads  eleven  feet  long,  so  that  they 
formed  pendulums  exactly  equal  so  far  as  weight,  figure,  and  resistance  of 
the  air  were  concerned.  Their  oscillations  were  performed  in  exactly  the 
same  time.  The  same  results  were  obtained  when  other  substances  were 
used,  such  as  silver,  lead,  glass,  sand,  salt,  wood,  water,  corn.  Now  all 
these  bodies  had  equal  weights,  and  if  the  inference  that  therefore  they 
had  equal  masses  had  been  erroneous  by  so  much  as  the  one  thousandth 
part  of  the  whole,  the  experiment  would  have  detected  it. 

78.  Application  of  tlie  pendulum  to  clocks. — The  regulation  of  the 
motion  of  clocks  is  effected  by  means  of  pendulums, 
that  of  watches  by  balance-springs.  Pendulums 
were  first  applied  to  this  purpose  by  Huyghens  in 
1658,  and  in  the  same  year  Hooke  applied  a  spiral 
spring  to  the  balance  of  a  watch.  The  manner  of 
employing  the  pendulum  is  shown  in  fig.  46.  The 
pendulum  rod  passing  between  the  prongs  of  a 
fork  a  communicates  its  motion  to  a  rod  b,  which 
oscillates  on  a  horizontal  axis  0.  To  this  axis  is 
fixed  a  piece  mn  called  an  escapemetit  or  crutch^ 
terminated  by  two  projections  ox  pallets,  which  work 
alternately  with  the  teeth  of  the  escapement  wheel 
R.  This  wheel  being  acted  on  by  the  weight  tends 
to  move  continuously,  let  us  say,  in  the  direction 
indicated  by  the  arrow-head.  Now  if  the  pendulum 
is  at  rest,  the  wheel  is  held  at  rest  by  the  pallet  /«, 
and  with  it  the  whole  of  the  clockwork  and  the 
weight.  If,  however,  the  pendulum  moves  and 
takes  the  position  shown  by  the  dotted  line,  7n  is 
raised,  the  wheel  escapes  from  the  confinement  in 
which  it  was  held  by  the  pallet,  the  weight  de- 
scends, and  causes  the  wheel  to  turn  until  its  motion 
is  arrested  by  the  other  pallet  n  ;  which  in  consequence  of  the  motion  of 
the  pendulum  will  be  brought  into  contact  with  another  tooth  of  the 
escapement  wheel.     In  this  manner  the  descent  of  the  weight  is  alter- 


Fig.  46. 


6o  Gravitation  and  Molecular  A  ttraction.  [78  - 

nately  permitted  and  arrested — or,  in  a  word,  regulated— \y^  the  pen- 
dulum. By  means  of  a  proper  train  of  wheelwork  the  motion  of  the 
escapement  is  communicated  to  the  hands  of  the  clock  ;  and  consequently 
their  motion,  also,  is  regulated  by  the  pendulum. 

The  pendulum  is  also  used  for  measuring  great  velocities.  A  large 
block  of  wood  weighing  from  3  to  5  tons  is  coated  with  iron  ;  against  this 
arrangement,  which  is  known  as  a  ballistic  penduhim,  a  shot  is  fired,  and 
the  deflection  thereby  produced  is  observed.  From  the  laws  of  the 
impact  of  inelastic  bodies,  and  from  those  of  the  pendulum,  the  velocity 
of  the  ball  may  be  calculated  from  the  amount  of  this  deflection. 

79.  Causes  which  modify  the  intensity  of  terrestrial  gravita- 
tion.— The  intensity  of  the  force  of  gravity  at  the  earth's  surface  is 
modified  by  two  causes,  viz.  by  the  form  and  by  the  rotation  of  the 
earth. 

i.  If  the  earth  were  a  sphere  of  uniform  density  the  resultant  of  the 
attractions  which  its  parts  exert  on  an  external  point  would  be  the  same 
as  if  the  whole  of  its  mass  were  collected  at  its  centre,  and  therefore  the 
attraction  at  all  points  of  its  surface  would  be  the  same.  In  consequence 
of  the  flattening  of  the  earth  at  its  poles,  this  is  no  longer  exactly,  but 
only  very  nearly  true  ;  and  the  attraction  on  an  external  point  is  only 
nearly  inversely  as  the  square  of  its  distance  from  the  earth's  centre.  As 
a  further  consequence  of  the  flattening  at  the  poles,  the  distance  from 
the  centre  of  a  point  on  the  surface  decreases  as  we  proceed  from  the 
equator  to  either  pole  ;  but  as  the  distance  decreases  the  attraction  will 
increase,  and  consequently  the  force  of  gravity  increases  as  the  latitude 
increases,  being  least  at  the  equator,  and  greatest  at  the  poles.  This  is 
what  would  be  true  if,  other  things  remaining  the  same,  the  earth  were 
at  rest. 

ii.  In  consequence  of  the  earth's  rotation,  the  force  of  gravity  is 
further  modified.  If  we  imagine  a  body  relatively  at  rest  on  the  equator, 
it  really  shares  the  earth's  rotation,  and  describes,  in  the  course  of  one 
day,  a  circle  whose  centre  and  radius  are  the  centre  and  radius  of  the 
earth.  Now  since  a  body  in  motion  tends  by  reason  of  its  inertia  to 
move  in  a  straight  line,  it  follows  that  to  make  it  move  in  a  circle,  a 
force  must  be  employed  at  each  instant  to  deflect  it  from  the  tangent 
(49).  Consequently,  a  certain  portion  of  the  earth's  attraction  must  be 
employed  in  keeping  the  above  body  on  the  surface  of  the  earth,  and 
only  the  remainder  is  sensible  as  weight  or  accelerating  force.  It 
appears  from  calculation  that  on  the  equator  the  ^s^th  part  of  the  earth's 
attraction  on  any  body  is  thus  employed,  so  that  the  magnitude  of  g  at 
the  equator  is  less  by  the  219th  part  of  what  it  would  be  were  the  earth 
at  rest.  If  the  body,  instead  of  being  on  the  equator,  is  in  any  given 
latitude,  it  will  describe  in  one  day  a  circle  coinciding  with  the  parallel 
of  latitude  on  which  it  is  situated.  Now  when  bodies  describe  in  the 
same  time  circles  of  different  radii,  it  can  be  deduced  from  (49)  that  the 
forces  required  to  keep  them  in  those  circles  are  proportional  to  their 
radii.  Hence  the  force  required  in  the  case  of  a  body  in  any  given 
latitude  is  less  than  that  required  if  the  body  were  on  the  equator,  and  less 


-81]  Molecular  Forces.       '  6l 

as  the  latitude  is  greater,  consequently  were  gravity  diminished  by  the 
whole  amount  of  this  force  the  diminution  would  be  less  the  nearer  the 
body  is  to  either  pole.  But  since  the  force  is  produced  only  by  an  in- 
direct action  of  gravity,  it  appears  that  the  diminution  is  thereby  rendered 
still  less  as  the  latitude  is  greater.  On  the  whole,  therefore,  the  force  of 
gravity  increases  as  we  pass  from  the  equator  to  either  pole,  in  conse- 
quence of  the  rotation  of  the  earth. 

It  will  be  observed  that  both  causes,  viz.  the  flattening  of  the  earth 
;it  the  poles,  and  its  rotation,  concur  in  producing  an  increase  in  the 
nsible  force  of  gravity  as  the  observer  leaves  the  equator  and  approaches 
ither  pole. 


CHAPTER  III. 

MOLECULAR   FORCES. 


80.  Xature  of  molecular  forces. — The  various  phenomena  which 
Ijodies  present  show  that  their  molecules  are  under  the  influence  of  two 
contrary  forces,  one  of  which  tends  to  bring  them  together,  and  the  other 
to  separate  them  from  each  other.  The  first  force,  which  is  called 
molecular  attraction,  varies  in  one  and  the  same  body  with  the  distance 
only.  The  second  force,  which  is  due  to  the  action  of  heat,  varies  with 
the  intensity  of  this  agent,  and  with  the  distance.  It  is  the  mutual  re- 
lation between  these  forces,  the  preponderance  of  the  one  or  the  other, 
which  determines  the  molecular  state  of  a  body  (4), — whether  it  be  solid, 
liquid,  or  gaseous. 

Molecular  attraction  is  only  exerted  at  infinitely  small  distances.  Its 
effect  is  inappreciable  when  the  distance  between  the  molecules  is  appre- 
ciable.    The  laws  which  regulate  this  force  are  not  known. 

According  to  the  manner  in  Avhich  it  is  regarded,  molecular  attraction 
is  designated  by  the  terms  cohesion,  affinity^  or  adhesion. 

81.  Cohesion. — Cohesio7i  is  the  force  which  unites  two  molecules  of 
the  same  nature  ;  for  example,  two  molecules  of  water,  or  two  molecules 
of  iron.  Cohesion  is  strongly  exerted  in  solids,  less  strongly  in  liquids,  and 
scarcely  at  all  in  gases.  Its  intensity  decreases  as  the  temperature 
increases,  because  then  the  repulsive  force  due  to  heat  increases.  Hence 
it  is  that  when  solid  bodies  are  heated  they  first  liquefy,  and  are  ultimately 
converted  into  the  gaseous  state,  provided  that  heat  produces  in  them  no 
chemical  change. 

Cohesion  varies  not  only  with  the  nature  of  bodies,  but  also  with  the 
arrangement  of  their  molecules ;  for  example,  the  difference  between 
tempered  and  untempered  steel  is  due  to  a  difference  in  the  molecular 
arrangement  produced  by  tempering.  It  is  to  the  modifications  which 
this  force  undergoes  that  many  of  the  properties  of  bodies  are  due,  such 
as  tenacity,  hardness,  and  ductility. 

In  large  masses  of  liquids,  the  force  of  gravity  overcomes  that  of  cohe- 
sion. Hence  liquids  acted  upon  by  the  former  force  have  no  special 
shape  ;  they  take  that  of  the  vessel  in  which  they  are  contained.     But  in 


62  Gravitation  and  Molecular  A  ttraction.  [81- 

smaller  masses  cohesion  gets  the  upper  hand,  and  hquids  present  then 
the  spheroidal  form.  This  is  seen  in  the  drops  of  dew  on  the  leaves 
of  plants  ;  it  is  also  seen  when  a  liquid  is  placed  on  a  solid  which  it  does 
not  moisten ;  as,  for  example,  mercury  upon  wood.  The  experiment  may 
also  be  made  with  water,  by  sprinkling  upon  the  surface  of  the  wood 
some  light  powder,  such  as  lycopodium  or  lampblack,  and  then  dropping 
some  water  on  it.  The  following  pretty  experiment  is  an  illustration  of 
the  force  of  cohesion  causing  a  liquid  to  assume  the  spheroidal  form.  A 
saturated  solution  of  sulphate  of  zinc  is  placed  in  a  narrow-necked  bottle, 
and  a  few  drops  of  bisulphide  of  carbon,  coloured  with  iodine,  made  to 
float  on  the  surface.  If  pure  water  be  now  carefully  added,  so  as  to 
rest  on  the  surface  of  the  sulphate  of  zinc  solution,  the  bisulphide  collects 
in  the  form  of  a  flattened  spheroid,  which  presents  the  appearance  of 
blown  coloured  glass,  and  is  larger  than  the  neck  of  the  bottle,  provided  a 
sufficient  quantity  has  been  taken. 

82.  Affinity. — Chemical  affinity  is  the  force  which  is  exerted  between 
molecules  not  of  the  same  kind.  Thus,  in  water,  which  is  composed  of 
oxygen  and  hydrogen,  it  is  affinity  which  unites  these  elements,  but  it  is 
cohesion  which  binds  together  two  molecules  of  water.  In  compound 
bodies  cohesion  and  affinity  operate  simultaneously,  while  in  simple 
bodies  or  elements  cohesion  has  alone  to  be  considered. 

To  affinity  are  due  all  the  phenomena  of  combustion,  and  of  chemical 
combination  and  decomposition. 

The  causes  which  tend  to  weaken  cohesion  are  most  favourable  to 
affinity ;  for  instance,  the  action  of  affinity  between  substances  is  facili- 
tated by  their  division,  and  still  more  by  reducing  them  to  a  liquid  or 
gaseous  state.  It  is  most  powerfully  exerted  by  a  body  in  its  nascent 
state,  that  is,  the  state  in  which  the  body  exists  at  the  moment  it  is 
disengaged  from  a  compound  ;  the  body  is  then  free,  and  ready  to  obey 
the  feeblest  affinity.  An  increase  of  temperature  modifies  affinity  differ- 
ently under  diffierent  circumstances.  In  some  cases,  by  diminishing 
cohesion,  and  increasing  the  distance  between  the  molecules,  heat  pro- 
motes combination.  Sulphur  and  oxygen,  which  at  the  ordinary  tempe- 
rature are  without  action  on  each  other,  combine  to  form  sulphurous 
acid  when  the  temperature  is  raised  :  in  other  cases  heat  tends  to  decom- 
pose compounds  by  imparting  to  their  elements  an  unequal  expansi- 
iDility.  Thus  it  is  that  many  metallic  oxides,  as  for  example  those  of 
silver  and  mercury,  are  decomposed,  by  the  action  of  heat,  into  gas  and 
metal. 

83.  Adbesion. — The  molecular  attraction  exerted  between  bodies  in 
contact  is  called  adhesioti. 

i.  Adhesion  takes  place  between  solids.  If  two  leaden  bullets  are  cut 
with  a  penknife  so  as  to  form  two  equal  and  brightly  polished  surfaces, 
and  the  two  faces  are  pressed  and  turned  against  each  other  until  they 
are  in  the  closest  contact,  they  adhere  so  strongly  as  to  require  a  force 
of  more  than  100  grammes  to  separate  them.  .The  same  experiment 
may  be  made  with  two  equal  pieces  of  glass,  which  are  polished  and 
made  perfectly  plane.     When  they  are  pressed  one  against  the  other,  the 


-85]  Properties  peculiar  to  Solids.  63 

adhesion  is  so  powerful  that  they  cannot  be  separated  without  breaking. 
As  the  experiment  succeeds  in  vacuo,  it  cannot  be  due  to  atmospheric 
pressure,  but  must  be  attributed  to  a  reciprocal  action  between  the  two 
surfaces.  The  attraction  also  increases  as  the  contact  is  prolonged,  and 
is  greater  in  proportion  as  the  contact  is  closer. 

In  the  operation  of  gluing,  the  pores  and  crevices  of  the  fresh  surfaces 
being  filled  with  liquid  glue,  so  that  there  is  no  empty  space  on  drying, 
wood  and  glue  form  one  compact  whole.  In  some  cases  the  adhesion  of 
the  cement  is  so  powerful  that  the  mass  breaks  more  readily  at  other 
places  than  at  the  cemented  parts. 

ii.  Adhesion  also  takes  place  between  solids  and  liquids.  If  we  dip  a 
glass  rod  into  water,  on  withdrawing  it  a  drop  will  be  found  to  collect  at 
its  lower  extremity,  and  remain  suspended  there.  As  the  weight  of  the 
drop  tends  to  detach  it,  there  must  necessarily  be  some  force  superior  to 
this  weight  which  maintains  it  there  :  this  force  is  the  force  of  adhesion. 

iii.  The  force  of  adhesion  operates,  lastly,  between  solids  and  gases. 
If  a  glass  or  metal  plate  be  immersed  in  water,  bubbles  will  be  found  to 
appear  on  the  surface.  As  air  cannot  penetrate  into  the  pores  of  the  plate, 
the  bubbles  could  not  arise  from  the  air  which  had  been  expelled.  It  is 
solely  due  to  the  layer  of  air  which  covered  the  plate,  and  moistened  it  like 
a  liquid.  In  many  cases  when  gases  are  separated  in  the  nascent  state 
on  the  surface  of  metals — as  in  electrolysis — the  layer  of  gas  which  covers 
the  plate  has  such  a  density  that  it  is  susceptible  of  very  energetic  chemi- 
cal actions. 

^^  ^  CHAPTER  W. 

PROPERTIES  PECULIAR  TO   SOLIDS. 

84.  Various  special  properties. — After  having  described  the  princi- 
pal properties  common  to  solids,  liquids,  and  gases,  we  shall  discuss  the 
properties  peculiar  to  solids.  They  are,  elasticity  of  traction,  elasticity 
oftorsioti,  elasticity  of  flexure,  teftacity,  ductility,  and  hardness. 

85.  Elasticity  of  traction. — Elasticity,  as  a  general  property  of 
matter,  has  been  already  mentioned  (17),  but  simply  in  reference  to  the 
elasticity  developed  by  pressure  ;  in  solids  it  may  also  be  called  into  play 
by  traction,  by  torsion,  and  by  flexure.  The  definitions  there  given  re- 
quire some  extension.  In  ordinary  life  we  consider  those  bodies  as  highly 
elastic  which,  like  caoutchouc,  undergo  considerable  change  on  the  appli- 
cation of  only  a  small  force.  Yet  the  force  of  elasticity  is  greatest  in  many 
bodies,  such  as  iron,  which  do  not  seem  to  be  very  elastic.  For  hy  force 
of  elasticity  is  understood  the  force  with  which  the  displaced  particles 
tend  to  revert  to  their  original  position,  and  which  force  is  equivalent  to 
that  which  has  brought  about  the  change.  Considered  from  this  point  of 
view,  gases  have  the  least  force  of  elasticity  ;  that  of  liquids  is  con- 
siderably greater,  and  is,  indeed,  greater  than  that  of  many  solids.  Thus, 
the  force  of  elasticity  of  mercury  is  greater  than  that  of  caoutchouc,  glass, 


64 


Gravitation  and  Molecular  A  ttr action. 


[85- 


wood,  and  stone.     It  is,  however,  less  than  that  of  the  other  metals  with 
the  exception  of  lead. 

This  seems  discordant  with  ordinary  ideas  about  elasticity  ;  but  it 
must  be  remembered  that  those  bodies  which  by  the  exertion  of  a  small 
force,  undergo  a  considerable  change,  generally  have  also  the  property  of 
undergoing  this  change  without  losing  the  property  of  reverting  completely 
to  their  original  state.  They  have  a  wide  limit  of  elasticity.  Those 
bodies  which  require  great  force  to  effect  a  change  are  also  for  the  most 
part,  those  on  which  the  exertion  of  a  force  produces  a  permanent  altera- 
tion ;  when  the  force  is  no  longer  exerted,  they  do  not  completely  revert 
to  their  original  state. 

In  order  to  study  the  laws  of  the  elasticity  of  traction,  Savart  used  the 

apparatus  represented  in  fig.  47. 
It  consists  of  a  wooden  support 
from  which  are  suspended  the 
rods  or  wires  taken  for  experi- 
ment. At  the  lower  extremity 
there  is  a  scale  pan,  and  on 
the  wire  two  points,  A  and  B, 
are  marked,  the  distance  between 
which  is  measured  by  means  of 
the  cathetojneter,  before  the 
weights  are  added. 

The  cathetorneter  consists  of 
a  strong  brass  support,  K, 
divided  into  millimetres,  and 
which  can  be  adjusted  in  a 
vertical  position  by  means  of 
levelling  screws  and  the  plumb 
line.  A  small  telescope,  exactly 
at  right  angles  to  the  scale,  can 
be  moved  up  and  down,  and  is 
provided  with  a  vernier  which 
measures  fiftieths  of  a  millimetre. 
By  fixing  the  telescope  succes- 
sively on  the  two  points  A  and 
B,  as  represented  in  the  figure, 
the  distance  between  these 
points  is  obtained  on  the  gradu- 


Fig.  47- 


ated  scale.  Placing  then  weights  in  the  pan,  and  measuring  again  the 
distance  from  A  to  B,  the  elongation  is  obtained. 

By  experiments  of  this  kind  it  has  been  ascertained  that  for  elasticity 
effraction  or  pressure-- 

The  alteration  in  length,  within  the  limits  of  elasticity,  is  in  propor- 
tion to  the  length  and  to  the  load  actifig  on  the  body,  a?id  is  inversely  as 
the  section. 

It  depends,  moreover,  on  the  specific  elasticity,  that  is,  on  the  material 
of  the  bodv.    If  this  coefficient  be  denoted  by  E,  and  if  the  length,  section. 


-86]  Elasticity  of  Torsion.  65 

and  load  are  respectively  designated  by  /,  j,  and  P,  then  for  the  alteration 
in  length  e^  we  have 

s 

The  following  are   the   best  values   for  some  of  the  principal  sub- 
stances : — 


Steel  . 

.     21000 

Silver 

.     7400 

W)?might  Iron     , 
Copps^r 

.     19000 

Lead    . 

.     1800 

.     1 2400 

Wood 

.     1 100 

Brass  .'  .      . 

9000 

Whalebone  . 

.       700 

Zinc    .    \  . 

.       8700 

Glass 

90 

Thus,  to  d^ouble  the  length  of  a  wrought  iron  wire  a  square  millimetre 
in  section,  woii^d  (if  this  were  possible)  require  a  weight  of  19,000  kilo- 
grammes ;  but  i^>,weight  of  1 5  kilogrammes  produces  a  permanent  altera- 
tion in  length  of  x|Wth,  and  this  is  the  limit  of  elasticity.  Whalebone,  on 
the  contrary,  has  otiN  a  modulus  of  700,  and  experiences  a  permanent 
change  by  a  weight  of \kilogrammes  ;  its  limit  is,  therefore,  much  greater 
than  that  of  iron.     Steershas  a  high  modulus,  along  with  a  wide  limit. 

If  in  the  above  expresshm  the  sectional  area  be  a  square  miUimetre, 
and  P  be  one  kilogramme,  thi 

e  =  E/,  fr^  which  E  =  ^, 

which  expresses  by  what  fraction  the  length  of  a  bar  a  square  millimetre 
in  section  is  altered  by  a  load  of  a  ki^gramme.  This  is  called  the 
coefficient  of  elasticity ;    it  is   a  very  smalP^raction,  and  it  is  therefore 

desirable  to  use  its  reciprocal,  that  is  the  fractrism  _  as  the   modulus  of 

elasticity  ;  or  the  weight  in  kilogrammes  which  a]^lied  to  a  bar  would 
elongate  it  by  its  own  length,  assuming  it  to  be  peJsfectly  elastic.  This 
cannot  be  observed,  for  no  body  is  perfectly  elastic,  but^it  may  be  calcu- 
lated from  any  accurate  observations  by  means  of  the  above  formula. 

Both  calculation  and  experiment  show  that  when  bodies  are  lengthened 
by  traction  their  volume  increases.  ' 

From  numerous  experiments  on  the  elasticity  of  iron,  copper,  and 
brass,  made  by  Kohlrausch,  it  follows  that  the  modulus  of  elasticity 
diminishes  as  the  temperature  rises. 

86.  Elasticity  of  torsion. — The  laws  of  the  torsion  of  wires^were 
determined  by  Coulomb,  by  means  of  an  apparatus  called  the  tof^ioti 
balance  (fig.  48).  It  consists  of  a  metal  wire,  clasped  at  its  upper  extremity 
in  a  support.  A,  and  holding  at  the  other  extremity  a  metallic  sphere,  B, 
to  which  is  affixed  an  index,  C.  Immediately  below  this  there  is  a 
graduated  circle,  CD.  If  the  needle  is  turned  from  its  position  of  equi- 
librium through  a  certain  angle  which  is  the  aiigle  of  torsion,  the  force 
necessary  to  produce  this  effect  is  called  the  force  of  torsion.  When, 
after  this  deflection,  the  sphere  is  left  to  itself,  the  reaction  of  torsion 


66 


Gravitation  and  Molecular  Attraction. 


[86- 


produces  its  effect,  the  wire  untwists  itself,  and  the  sphere  rotates  about 
its  vertical  axis  with  increasing  rapidity  until  it  reaches  its  position  ot 
equilibrium.  It  does  not,  however,  rest  there  ;  in  virtue  of  its  inertia  it 
passes  this  position,  and  the  wire  undergoes  a  torsion  in  the  opposite 
direction.  The  equilibrium  being  again  destroyed,  the  wire  again  tends 
to  untwist  itself,  the  same  alterations  are 
again  produced,  and  the  needle  does  not  rest 
at  zero  of  the  scale  until  after  a  certain 
number  of  oscillations  about  this  point  have 
been  completed, 
,___^^  By  means  of  this  apparatus  Coulomb  found 
Tltat  when  the  amplitude  of  the  oscillations 
is  within  certain  limits,  the  oscillations  are 
subject  to  the  following  laws  : — 

I.  The  oscillatio7is  are  very  nearly  iso- 
chronous. 

II.  For  the  same  wire,  the  angle  of  torsiori 
is  proportional  to  the  inoment  of  the  force  of 
torsion. 

III.  With  the  same  force  of  torsion,  and 
with  wires  of  the  same  diameter,  the  angles 
of  torsion  are  proportional  to  the  lengths  of 
the  wires.  \ 

IV.  The  same  force  of  torsion  beingHpplied 
to  wires  of  the  same  length,  the  angles  of  tor- 
sion are  inversely  proportional  to  the  fourth 
powers  of  the  diaineters.  \ 

Wertheim  has  examined  the  elasticity  of  torsion  in  the  case  of  stoiit 
rods  by  means  of  a  different  apparatus,  and  finds  that  it  is  also  subject  to\ 
these  laws.     He  has  further  found  that,  all  dimensions  being  the  same,  \ 
different  substances  undergo  different  degrees  of  torsion,  and  each  sub- 
stance has  its  own  coefficient  of  torsion,  which  is  denoted  by  — . 


Fig.  48. 


The  laws  of  torsion  may  be  enunciated  in  the  formula  w  =  - 


II 
Tr* 


which  w  is  the  angle  of  torsion,  F  the  moment  of  the  force  of  torsion, 
/  the  length  of  the  wire,  r  its  diameter,  and  -  the  specific  torsion- 
coefficient. 

87.  Elasticity  of  flexure. — A  solid,  when  cut  into  a  thin  plate,  and 
fixed  at  one  of  its  extremities,  after  having  been  more  or  less  bent,  strives 
to  return  to  its  original  position  when  left  to  itself.  This  property  is  the 
elasticity  of  flexure  and  is  very  distinct  in  steel,  caoutchouc,  wood,  and 
paper. 

If  a  rectangular  bar  be  clamped  at  one  end  and  loaded  at  the  other, 
the  flexure  e  is  represented  by  the  formula 

P/ 
^     t?hhn' 


-88]  Tenacity.  67 

where  P  is  the  load,  /  the  length  of  the  bar,  b  its  breadth,  h  its  vertical 
height,  and  in  the  modulus  of  elasticity. 

The  elasticity  of  flexure  is  applied  in  a  vast  variety  of  instances,  for 
example,  in  bows,  watch  springs,  carriage  springs ;  in  spring  balances  it 
is  used  to  determine  weights,  in  dynamometers  to  determine  the  force 
of  agents  in  prime  movers ;  and,  as  existing  in  wool,  hair,  and  feathers,  it 
is  applied  to  domestic  uses  in  cushions  and  mattresses. 

Whatever  be  the  kind  of  elasticity,  there  is,  as  has  been  already  said, 
a  limit  to  it — that  is,  there  is  a  molecular  displacement,  beyond  which 
bodies  are  broken,  or  at  any  rate  do  not  regain  their  primitive  form. 
This  limit  is  affected  by  various  causes.  The  elasticity  of  many  metals 
is  increased  by  hardening,  whether  by  cold,  by  means  of  the  draw-plate, 
by  rolling,  or  iDy  hammering.  Some  substances,  such  as  steel,  cast  iron, 
and  glass,  become  both  harder  and  more  elastic  by  tempering  (91). 

Elasticity,  on  the  other  hand,  is  diminished  by  annealing,  which  con- 
sists in  raising  the  body  to  a  temperature  lower  than  that  necessary  for 
tempering,  and  allowing  it  to  copl  slowly.  It  is  by  this  means  that  the 
elasticity  of  springs  may  be  regulated  at  pleasure.  Glass,  when  it  is 
heated,  undergoes  a  true  tempering^ in  being  rapidly  cooled,  and  hence,  in 
order  to  lessen  the  fragility  of  glass  oibjects,  they  are  reheated  in  a  furnace, 
and  are  carefully  allowed  to  cool  slow^,  so  that  the  particles  have  time  to 
assume  their  most  stable  position, 

88.  Tenacity. — Tenacity  is  the  resi^nce  which  bodies  oppose  to 
traction.  It  is  determined  in  different  bodies  by  forming  them  into 
cylindrical  or  prismatic  wires,  and  ascertainn^  the  weight  necessary  to 
break  them. 

Tenacity  is  directly  proportional  to  the  b7'eaking^eight,  and  inversely 
proportional  to  the  area  of  a  transverse  secihm  of  the  wire. 

Tenacity  diminishes  with  the  duration  of  the  tracHon.  A  small  force 
continuously  applied  for  a  long  time  will  often  break  a\^ire,  which  would 
not  at  once  be  broken  by  a  larger  weight. 

Not  only  does  tenacity  vary  with  different  substance\  but  it  also 
varies  with  the  form  of  the  body.  Thus,  with  the  same  sectional  area,  a 
cylinder  has  greater  tenacity  than  a  prism.  The  quantity  of  matter  being 
the  same,  a  hollow  cylinder  has  greater  tenacity  than  asoHd  one}  and  the 
tenacity  of  this  hollow  cylinder  is  greatest  when  the  external  radius  is  to 
the  internal  one  in  the  ratio  of  1 1  to  5. 

The  shape  has  also  the  same  influence  on  the  resistance  to  crushing, 
as  it  has  on  the  resistance  to  traction.  A  hollow  cylinder  with  the  samei 
mass,  and  the  same  weight,  offers  a  greater  resistance  than  a  solid  cyHn- 
der.  Thus  it  is  that  the  bones  of  animals,  the  feathers  of  birds,  the  stems 
of  com  and  other  plants,  offer  greater  resistance  than  if  they  were  solid, 
the  mass  remaining  the  same. 

Tenacity,  like  elasticity,  is  different  in  different  directions  in  bodies. 
In  wood,  for  example,  both  the  tenacity  and  the  elasticity  are  greater  in 
the  direction  of  the  fibres  than  in  a  transverse  direction.  And  this  differ- 
ence obtains  in  general  in  all  bodies,  the  texture  of  which  is  not  the  same 
in  all  directions. 


68 


Gravitation  and  Molecular  A  ttr action. 


[88- 


The  following  table 
having  a  sectional  area 

Antimony,  cast 
Bismuth,  „ 
Lead, 

„    drawn 
Tin,       „ 

„    cast     . 
Zinc,  annealed  . 

„     drawn 
Gold,  annealed . 

„      drawn 
Silver,  annealed 

„      drawn 
Platinum,  annealed 
„        drawn 


gives  the  breaking  weight  in  pounds  for  wires 
of  a  square  millimetre  : — 

Copper,  annealed        .         .       69*52 


1-47 

2*13 

4-86 

5-19 

6-6o 

9-15 

31-68 

34-58 

24-20 

6 1 -60 

36-08 

63-80 

58-85 

77-00 


„         drawn     . 
Iron,  annealed     . 

„     drawn 
Cast  steel,  drawn 


90*20 
[IO-55 

[40*71 
[84-36 


Wood  in  the  direction 

of  the  fibres. 

Mahogany  . 

ii*o 

Oak     ...         . 

15*4 

Beech 

.         17*6 

Fir      ...         . 

19*8 

Ash     ...         . 

26*4 

Box     .         .         .         . 

30-8 

In  this  table  the  bodies  are  supposed  to  be  at  the  ordinary  temperature. 
At  a  higher  temperature  the  tenacity  rapidly  decreases.  M.  Seguin,  sen., 
who  has  recently  made  some  experiments  on  this  point  with  iron  and 
copper,  has  obtained  the  following  values  for  the  tenacity,  in  pounds,  of 
millimetre  wire  at  different  temperatures  : — 

Iron         .         .     at  10°,  132*0;  at  370°,  118-8  ;  at  500°,  77-0  ; 


Copper   . 


46-2 


[6-9 


o. 


89.  Ductility. — Ductility  is  the  property  in  virtue  of  which  a  great 
number  of  bodies  change  their  forms  by  the  action  of  traction  or  pres- 
sure. 

With  certain  bodies,  such  as  clay,  wax,  etc.,  the  application  of  a  very 
little  force  is  sufficient  to  produce  a  change  ;  with  others,  such  as  the 
resins  and  glass,  the  aid  of  heat  is  needed,  while  with  the  metals,  more 
powerful  agents  must  be  used,  such  as  percussion,  the  draw-plate,  or  the 
rolling-mill. 

Malleability  is  that  modification  of  ductility  which  is  exhibited  by 
hammering.  The  most  malleable  metal  is  gold,  which  has  been  beaten 
into  leaves  about  the  gooW^^  ^^  ^"^  m^  thick. 

The  most  ductile  metal  is  platinum.  Wollaston  obtained  a  wire  of  it 
0-00003  of  an  inch  in  diameter.  This  he  effected  by  covering  with  silver 
a  platinum  wire  0-0 1  of  an  inch  in  diameter,  so  as  to  obtain  a  cylinder 
0-2  inch  in  diameter  only,  the  axis  of  which  was  of  platinum.  This  was 
then  drawn  out  in  the  form  of  wire  as  fine  as  possible  ;  the  two  metals 
were  equally  extended.  When  this  wire  was  afterwards  treated  with 
dilute  nitric  acid  the  silver  was  dissolved,  and  the  platinum  wire  left 
intact.  The  wire  was  so  fine  that  1,060  yards  only  weighed  0-75  of  a 
grain. 

90.  Hardness. — Hardness  is  the  resistance  which  bodies  offer  to  being 
scratched  or  worn  by  others.  It  is  only  a  relative  property,  for  a  body 
which  is  hard  in  reference  to  one  body  may  be  soft  in  reference  to  others. 


-91]  Hardness.  69 

The  relative  hardness  of  two  bodies  is  ascertained  by  trying  which  of 
them  will  scratch  the  other.  Diamond  is  the  hardest  of  all  bodies,  for  it 
scratches  all,  and  is  not  scratched  by  any.  The  hardness  of  a  body  is 
expressed  by  referring  it  to  a  scale  of  hardness  :  that  usually  adopted  is — 

1.  Talc  5.  Apatite  8.  Topaz 

2.  Rock  salt  6.  Felspar  9.  Corundum 

3.  Calcspar  7.  Quartz  10.  Diamond 

4.  Fluorspar 

Thus  the  hardness  of  a  body  which  would  scratch  felspar,  but  would  be 
scratched  by  quartz,  would  be  expressed  by  the  number  6'5. 

The  pure  metals  are  softer  than  their  alloys.  Hence  it  is  that  for 
jewellery  and  coinage  gold  and  silver  are  alloyed  with  copper  to  increase 
their  hardness. 

The  hardness  of  a  body  has  no  relation  to  its  resistance  to  compression. 
Glass  and  diamond  are  much  harder  than  wood,  but  the  latter  offers  far 
greater  resistance  to  the  blow  of  a  hammer.  Hard  bodies  are  often  used 
for  polishing  powders  ;  for  example,  emery,  pumice,  and  tripoli.  Diamond, 
being  the  hardest  of  all  bodies,  can  only  be  ground  by  means  of  its  own 
powder. 

91.  Temper. — By  sudden  cooling  after  they  have  been  raised  to  a  high 
temperature,  many  bodies  acquire  great  hardness.  This  operation  is  called 
tempering.  All  cutting  instruments  are  made  of  tempered  steel.  There 
are,  however,  some  few  bodies  upon  which  tempering  produces  quite  a 
contrary  effect.  An  alloy  of  one  part  of  tin  and  four  parts  of  copper, 
called  taintajn  metal^  is  ductile  and  malleable  when  rapidly  cooled,  buf 
hard  and  brittle  as  glass  when  cooled  slowly. 


\  \ 


70  On  Liquids.  [92- 


BOOK    III. 

ON   LIQUIDS. 

CHAPTER   I. 

HYDROSTATICS. 

92.  Object  of  Hydrostatics. — The  science  of  hydrostatics  treats  of  the 
conditions  of  the  equiHbrium  of  liquids,  and  of  the  pressures  they  exert, 
whether  within  their  own  mass  or  on  the  sides  of  the  vessels  in  which  they 
are  contained. 

The  science  which  treats  of  the  motion  of  liquids  is  hydrodynamics, 
and  the  application  of  the  principles  of  this  science  to  conducting  and 
raising  water  in  pipes  is  known  by  the  name  of  hydraulics. 

93.  General  characters  of  liquids. — It  has  been  already  seen  (4) 
that  liquids  are  bodies  whose  molecules  are  displaced  by  the  slightest 
force.  Their  fluidity,  however,  is  not  perfect,  there  is  always  a  sufficient 
adherence  between  their  molecules  to  produce  a  greater  or  less  viscosity. 

Gases  also  possess  fluidity,  but  in  a  higher  degree  than  liquids.  The 
distinction  between  the  two  forms  of  matter  \$,  that  liquids  are  almost  in- 
compressible and  are  comparatively  inexpansible,  while  gases  are  eminently 
compressible  and  expand  spontaneously. 

The  fluidity  of  liquids  is  seen  in  the  readiness  with  which  they  take 
all  sorts  of  shapes.  Their  compressibility  is  established  by  the  following 
experiment. 

94.  Compressibility  of  liquids. — From  the  experiment  of  the  Floren- 
tine Academicians  (13),  liquids  were  for  a  long  time  regarded  as  being 
completely  incompressible.  Since  then,  researches  have  been  made  on 
this  subject  by  various  physicists,  which  have  shown  that  liquids  are 
really  compressible. 

The  apparatus  used  for  rneasuring  the  compressibility  of  liquids  has 
been  named  the  piezometer  {-KitX^hi,  I  compress,  fihpov,  measure).  That 
shown  in  fig.  49  is  the  form  invented  by  Oersted  as  improved  by  MM. 
Despretz  and  Saigey  ;  it  consists  of  a  strong  glass  cylinder,  with  very 
thick  sides  and  an  internal  diameter  of  about  3^-  inches.  The  base  of 
the  cylinder  is  firmly  cemented  into  a  wooden  foot,  and  on  its  upper  part 
is  fitted  a  metallic  cylinder  closed  by  a  cap  which  can  be  unscrewed.  In 
this  cap  there  is  a  funnel,  R,  for  introducing  water  into  the  cylinder,  and 
a  small  barrel  hermetically  closed  by  a  piston  which  is  moved  by  a 
screw,  P. 


94] 


Compressibility  of  Liquids. 


n 


In  the  inside  of  the  apparatus  there  is  a  glass  vessel,  A,  containing  the 
liquid  to  be  compressed.  The  upper  part  of  this  vessel  terminates  in  a 
capillary  tube,  which  dips  under  mercury,  O. 
This  tube  has  been  previously  divided  into 
parts  of  equal  capacity,  and  it  has  been 
determined  how  many  of  these  parts  the 
vessel  A  contains.  The  latter  is  ascertained 
by  finding  the  weight,  P,  of  the  mercury 
which  the  reservoir.  A,  contains,  and  the 
weight,  p,  of  the  mercury  contained  in  a 
certain  number  of  divisions,  ??,  of  the  capil- 
lary tube.  If  N  be  the  number  of  divisions 
of  the  small  tube  contained  in  the  whole  re- 

N     P 
servoir,  we  have  —  =  — ,  from  which  the  value 
n     p 

of  N  is  obtained.  There  is  further  a  ma- 
nometer. This  is  a  glass  tube,  B,  containing 
air,  closed  at  one  end,  and  the  lower  ex- 
tremity of  which  dips  under  mercury. 
When  there  is  no  pressure  on  the  water  in 
the  cylinder,  the  tube  B  is  completely  full  of 
air  ;  but  when  the  water  within  the  cylinder 
is  compressed  by  means  of  the  screw  P, 
the  pressure  is  transmitted  to  the  mercury, 
which  rises  in  the  tube,  compressing  the  air 
which  it  contains.  A  graduated  scale  fixed 
on  the  side  of  the  tube  shows  the  reduction 
of  volume,  and  this  reduction  of  volume  in-  Fis-  49- 

dicates  the  pressure  exerted  on  the  liquid  in  the  cylinder,  as  will  be  seen 
in  speaking  of  the  manometer. 

In  making  the  experiment,  the  vessel  A  is  filled  with  the  liquid  to  be 
compressed,  and  the  end  dipped  under  the  mercury.  By  means  of  the 
funnel  R  the  cylinder  is  entirely  filled  with  water.  The  screw  P  being 
then  turned  the  piston  moves  downwards,  and  the  pressure  exerted  upon 
the  water  is  transmitted  to  the  mercury  and  the  air ;  in  consequence  of 
which  the  mercury  rises  in  the  tube  B,  and  also  in  the  capillary  tube. 
The  ascent  of  mercury  in  the  capillary  tube  shows  that  the  liquid  in  the 
vessel  A  has  diminished  in  volume,  and  gives  the  amount  of  its  compres- 
sion, for  the  capacity  of  the  whole  vessel  A  in  terms  of  the  graduated 
divisions  on  the  capillary  tube  has  been  previously  determined. 

In  his  first  experiments.  Oersted  assumed  that  the  capacity  of  the 
vessel  A  remained  the  same,  its  sides  being  compressed  both  internally 
and  externally  by  the  liquid.  But  mathematical  analysis  proves  that  this 
capacity  diminishes  in  consequence  of  the  external  and  internal  pressures. 
Colladon  and  Sturm  have  made  some  experiments  allowing  for  this  change 
of  capacity,  and  have  found  that  for  a  pressure  equal  to  that  of  the  atmo- 
sphere, mercury  experiences  a  compression  of  0*000005  parts  of  its  original 
volume ;  water  a  compression  of  o'oooo5,  and  ether  a  compression  of 


72  On  Liquids.  [94- 

o-<X)Oi33  parts  of  its  original  bulk.  The  compressibility  of  sea  water 
is  only  about  0*000044  :  it  is  not  materially  denser  even  at  great  depths  ; 
thus  at  the  depth  of  a  mile  its  density  would  only  be  about  jlo^h  the 
greater. 

For  water  and  nierairy  it  was  also  found  that  within  certain  limits  the 
decrease  of  volume  is  proportional  to  the  pressure. 

Whatever  be  the  pressure  to  which  a  liquid  has  been  subjected,  ex- 
periment shows  that  as  soon  as  the  pressure  is  removed  the  liquid  regains 
its  original  volume,  from  which  it  is  concluded  that  liquids  are  pe?'fectly 
elastic. 

95.  Equality  of  pressures,  Pascal's  law. — By  considering  liquids  as 
perfectly  fluid,  and  assuming  them  to  be  uninfluenced  by  the  action  of 
gravity,  the  following  law  has  been  established.  It  is  often  called  Pascal's 
law,  for  it  was  first  enunciated  by  him. 

Pressure  exerted  anywhere  7ipon  a  mass  of  liquid  is  transmitted  un- 
dijninished  in  ail  directions,  and  acts  with  the  same  force  on  all  eqiial 
surfaces,  and  in  a  direction  at  7'ight  angles  to  those  surfaces. 

To  get  a  clearer  idea  of  the  truth  of  this  principle,  let  us  conceive  a 
vessel  of  any  given  form  in  the  sides  of  which  are  placed  various  cylin- 
drical apertures,  all  of  the  same  size,  and  closed 
«JL  by  moveable  pistons.      Let  us,  further,  imagine 

lir"  this  vessel  to  be  filled  with  liquid  and  withdrawn 

•^Hri  from  the  action  of  gravity  ;  the  pistons  will,  ob- 

E    ^J^gL^^  -D  viously,  have  no  tendency  to  move.     If  now  upon 

/^^^^^fei_^^\     the  piston  A  (fig.  50),  which  has  a  surface  a,  a 
^5^^^^^^^^^^^     weight  of  P  pounds  be  placed,  it  will  be  pressed 

^^^^L- ^^^^       inwards,  and  the  pressure  will  be  transmitted  to 

^^^^^^^M^^^      the  internal  faces  of  each  of  the  pistons,  B,  C,  D, 

'^^^^S^^^^^^y^    and  E,  which  will  each  be  forced  outwards  by  a 

^^^^^^^^^^^     pressure  P,  their  surfaces  being  equal  to  that  of 

the  first  piston.     Since  each  of  the  pistons  un- 

'^'  ^^  dergoes  a  pressure  P,  equal  to  that  on  A,  let  us 

suppose  two  of  the  pistons  united  so  as  to  constitute  a  surface  ia,  it  will 

have  to  support  a  pressure  2 P.     Similarly,  if  the  piston  were  equal  to  3^:, 

it  would  experience  a  pressure  of  3P  :  and  if  its  area  were  100  or  1,000 

times  that  of  «,  it  would  sustain  a  pressure  of  100  or  1,000  times  P.     In 

other  words,  the  pressure  on  any  part  of  the  internal  walls  of  the  vessel 

would  be  proportional  to  the  surface. 

The  principle  of  the  equality  of  pressure  is  assumed  as  a  consequence 
of  the  constitution  of  fluids.  By  the  following  experiment  it  can  be  shown 
that  pressure  is  transmitted  in  all  directions,  although  it  cannot  be  shown 
that  it  is  equally  transmitted.  A  cyHnder  provided  with  a  piston  is  fitted 
'  into  a  hollow  sphere  (fig.  51),  in  which  small  cylindrical  jets  are  placed 
perpendicular  to  the  sides.  The  sphere  and  the  cylinder  being  both  filled 
with  water,  when  the  piston  is  moved  the  liquid  spouts  forth  from  all  the 
orifices,  and  not  merely  from  that  which  is  opposite  to  the  piston. 

The  reason  why  a  satisfactory  quantitative  experimental  demonstration 
of  the  principle  of  the  equality  of  pressure  cannot  be  given  is.  that  the 


-96]  Pressure  produced  in  Liquids  by  Gravity. 


73 


influence  of  the  weight  of  the  liquid  and  of  the  friction  of  the  pistons 
cannot  be  ehminated. 

Yet  an  approximate  verification  may  be  effected  by  the  experiment 
represented  in  fig.  52.     Two  cyhnders  of  different  diameters  are  joined 


■I 


II 


xss&sssssssss^ 


Fig.  52. 


Fig.  51. 

by  a  tube  and  filled  with  water.  On  the  surface  of  the  liquid  are  two 
pistons  P  and  p,  which  hermetically  close  the  cylinders,  but  move  with 
friction.  Let  the  area  of  the  large 
piston  be,  for  instance,  thirty  times 
that  of  the  smaller  one.  That  being 
assumed,  let  a  weight,  say  of  two 
pounds,  be  placed  upon  the  small 
piston,  this  pressure  will  be  trans- 
mitted to  the  water  and  to  the  large 
piston,  and  as  this  pressure  amounts 
to  two  pounds  on  each  portion  of  its 
surface  equal  to  that  of  the  small 
piston^  the  large  piston  must  support 
an  upward  pressure  thirty  times  as 
much,  or  of  sixty  pounds.  If  now  this  weight  be  placed  upon  the  large 
piston,  both  will  remain  in  equilibrium ;  but  if  the  weight  is  greater  or 
less,  this  is  no  longer  the  case.     If  S  and  s  are  the  areas  of  the  large  and 

P     S* 
small  piston  respectively,  and  P  and/  the  corresponding  loads,  then,  -r  =  - ' 

p     s 

whence  P=^. 
s 

It  is  important  to  observe  that  in  speaking  of  the  transmission  of  pres- 
sures to  the  sides  of  the  containing  vessel,  these  pressures  must  always 
be  supposed  to  be  perpendicular  to  the  sides  ;  for  any  oblique  pressure 
may  be  decomposed  into  two  others,  one  at  right  angles  to  the  side,  and 
the  other  acting  parallel  with  the  side ;  but  as  the  latter  has  no  action  on 
the  side,  the  perpendicular  one  is  the  only  one  to  be  considered. 

PRESSURE  PRODUCED  IN  LIQUIDS  BY  GRAVITY. 

96.  Vertical  downward  pressure,  its  laws. — Any  given  liquid  being 
in  a  state  of  rest  in  a  vessel,  if  we  suppose  it  to  be  divided  into  horizontal 
layers  of  the  same  density,  it  is  evident  that  each  layer  supports  the 
weight  of  those  above  it.     Gravity,  therefore,  produces  internal  pressures 

£ 


v.. 


74 


On  Liquids. 


[96 


in  the  mass  of  a  liquid  which  vary  at  different  points.     These  pressures 
are  submitted  to  the  following  general  laws  :— 

I.  The  pressure  in  each  layer  is  proportional  to  the  depth. 

II.  With  different  liquids  and  the  same  depth ^  the  pressure  is  propor- 
tional to  the  density  of  the  liquid. 

III.  The  pressure  is  the  same  at  all  points  of  the  same  horizontal  layer. 
The  first  two  laws  are  self-evident ;  the  third  necessarily  follows  from 

the  first  and  from  Pascal's  principle. 

97.  Vertical  upward  pressure. — The  pressure  which  the  upper 
layers  of  a  liquid  exert  on  the  lower  layers  causes  them  to  exert  an  equal 
reaction  in  an  upward  direction,  a  necessary  consequence  of  the  principle 
of  transmission  of  pressure  in  all  directions.  This  upward  pressure  is 
termed  the  buoyancy  of  liquids  ;  it  is  very  sensible  when  the  hand  is 
plunged  into  a  liquid,  more  especially  one  of  great  density,  like  mercury. 
The  following  experiment  (fig.  53)  serves  to  exhibit  the  upward 
pressure  of  liquids.  A  large  open  glass  tube 
A,  one  end  of  which  is  ground,  is  fitted  with 
a  ground  glass  disc,  O,  or  still  better,  with  a 
thin  card  or  piece  of  mica,  the  weight  of  which 
may  be  neglected.  To  the  disc  is  fitted  a 
string,  C,  by  which  it  can  be  held  against  the 
bottom  of  the  tube.  The  whole  is  then  im- 
mersed in  water,  and  now  the  disc  does  not  fall, 
although  no  longer  held  by  the  string  ;  it  is 
consequently  kept  in  its  position  by  the  upward 
pressure  of  the  water.  If  water  be  now  slowly 
poured  into  the  tube,  the  disc  will  only  sink 
when  the  height  of  the  water  inside  the  tube  is 
equal  to  the  height  outside.  It  follows  thence 
that  the  upward  pressure  on  the  disc  is  equal  to 
the  pressure  of  a  column  of  water,  the  base  of  which  is  the  internal  sec- 
tion of  the  tube  A,  and  the  height,  the  distance  from  the  disc  to  the  outer 
surface  of  the  liquid.  Hence  the  upward  pressure  of  liquids  at  any  point 
is  governed  by  the  same  laws  as  the  downward  pressure. 

98.  Pressure  is  independent  of  the  shape  of  the  vessel. — The 
pressure  exerted  by  a  liquid,  in  virtue  of  its  weight,  on  any  portion  of  the 
liquid,  or  on  the  sides  of  the  vessel  in  which  it  is  contained,  depends  on 
the  depth  and  density  of  the  liquid,  but  is  independent  of  the  shape  of 
the  vessel  and  of  the  quantity  of  the  liquid. 

This  principle,  which  follows  from  the  law  of  the  equality  of  pressure, 
may  be  experimentally  demonstrated  by  many  forms  of  apparatus.  The 
following  is  the  one  most  frequently  used,  and  is  due  to  Haldat.  It 
consists  of  a  bent  tube,  ABC  (fig.  54),  at  one  end  of  which,  A,  is  fitted  a 
stop-cock,  in  which  can  be  screwed  two  vessels,  M  and  P,  of  the  same 
height,  but  different  in  shape  and  capacity,  the  first  being  conical,  and 
the  other  nearly  cylindrical.  Mercury  is  poured  into  the  tube,  ABC, 
until  its  level  nearly  reaches  A.  The  vessel  M  is  then  screwed  on  and 
filled  with  water.     The  pressure  of  the  water  acting  on  the  mercury 


Fig-  53- 


-98] 


Pressure  produced  in  L  iquids  by  Gravity. 


75 


causes  it  to  rise  in  the  tube  C,  and  its  height  may  be  marked  by  means  of 
a  little  collar,  a,  which  slides  up  and  down  the  tube.  The  level  of  the 
water  in  M  is  also  marked  by  means  of  the  movable  rod  o.  When  this 
is  done,  M  is  emptied  by  means  of  the  stop-cock,  unscrewed  and  re- 
placed by  P.  When  water  is  now  poured  in  this,  the  mercury,  which 
had  resumed  its  original  level  in  the  tube  ABC,  again  rises  in  C,  and 
when  the  water  in  P  has  the  same  height  as  it  had  in  M,  which  is  indi- 


Fig.  54- 

cated  by  the  rod  <?,  the  mercury  will  have  risen  to  the  height  it  had  betore, 
which  is  marked  by  the  collar  a.  Hence  the  pressure  on  the  mercury  in 
both  cases  is  the  same.  This  pressure  is  therefore  independent  of  the 
shape  of  the  vessels,  and,  consequently,  also  of  the  quantity  of  liquid. 
The  base  of  the  vessel  is  obviously  the  same  in  both  cases  ;  it  is  the  sur- 
face of  the  mercury  in  the  interior  of  the  tube  A. 

Another  mode  of  demonstrating  this  principle  is  by  means  of  an 
apparatus  devised  by  Masson.  In  this  (fig.  55)  the  pressure  of  the  water 
contained  in  the  vessel  M  is  not  exerted  upon  the  column  of  mercury,  as. 
in  that  of  Haldat,  but  on  a  small  disc  or  stop  «,  which  closes  a  tubulure 
<:,  on  which  is  screwed  the  vessel  M.  The  disc  is  not  fixed  to  the  tubulure, 
but  is  sustained  by  a  thread  attached  to  the  end  of  a  scale-beam.  At  the 
other  end  is  a  pan  in  which  weights  can  be  placed  until  they  counter- 
balance the  pressure  exerted  by  the  water  on  the  stop.  The  vessel  M 
being  emptied  is  unscrewed,  and  replaced  by  the  narrow  tube  O.  This 
being  filled  to  the  same  height  as  the  large  vessel,  which  is  observed  by 
means  of  the  mark  0^  it  will  be  observed  that  to  keep  the  disc  in  its  place 
just  the  same  weight  must  be  placed  in  the  pan  as  before,  which  leads, 
therefore,  to  the  same  conclusion  as  does  Haldat's  experiment.     The 


76 


On  Liquids. 


[98- 


same  result  is  obtained  if,  instead  of  the  vertical  tube  P,  the  oblique  tube 
Q  be  screwed  to  the  tubulure. 


Fig.  55. 


From  a  consideration  of  these  principles  it  will  be  readily  seen  that 
a  very  small  quantity  of  water  can  produce  considerable  pressures.  Let 
us  imagine  any  vessel,  a  cask,  for  example,  filled  with  water  and  with  a 
long  narrow  tube  tightly  fitted  into  the  side.  If  water  is  poured  into  the 
tube,  there  will  be  a  pressure  on  the  bottom  of  the  cask  equal  to  the 
weight  of  a  column  of  water  whose  base  is  the  bottom  itself,  and  whose 
height  is  equal  to  that  of  the  water  in  the  tube.  The  pressure  may  be 
made  as  great  as  we  please  ;  by  means  of  a  narrow  thread  of  water  forty 
feet  high,  Pascal  succeeded  in  bursting  a  very  solidly  constructed  cask. 

The  toy  known  as  the  hydrostatic  bellows  depends  on  the  same  prin- 
ciple, and  we  shall  presently  see  a  most  important  application  of  it  in  the 
hydraulic  press. 

From  the  principle  just  laid  down,  the  pressures  produced  at  the 
bottom  of  the  sea  may  be  calculated.  It  will  be  presently  demonstrated 
that  the  pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  sea- 
water  about  thirty-three  feet  high.  At  sea  the  lead  has  frequently  de- 
scended to  a  depth  of  thirteen  thousand  feet  ;at  the  bottom  of  some  seas, 
therefore,  there  must  be  a  pressure  of  four  hundred  atmospheres, 

99.  Pressure  on  the  sides  of  vessels. — Since  the  pressure  caused  by 
gravity  in  the  mass  of  a  liquid  is  transmitted  in  every  direction,  accord- 
ing to  the  general  law  of  the  transmission  of  fluid  pressure,  it  follows  that 
at  every  point  of  the  side  of  any  vessel  a  pressure  is  exerted,  at  right 
angles  to  the  side,  which  we  will  suppose  to  be  plane.     The  resultant  of 


-100]  ^Hydrostatic  Paradox.  77 

all  these  pressures  is  the  total  pressure  on  the  sides.  But  since  these 
pressures  increase  in  proportion  to  the  depth,  and  also  in  proportion  to 
the  horizontal  extent  of  their  side,  their  resultant  can  only  be  obtained  by 
calculation,  which  shows  that  the  total  pressure  on  any  given  portion  of 
the  side  is  equal  to  the  weight  of  a  column  of  liquid,  which  has  this  por- 
tion of  the  side  for  its  base,  and  whose  height  is  the  vertical  distance  from 
the  centre  of  gravity  of  the  portion  to  the  surface  of  the  liquid.  If  the  side 
of  a  vessel  is  a  curved  surface  the  same  rule  gives  the  pressure  on  the 
surface,  but  the  total  pressure  is  no  longer  the  resultant  of  the  fluid 
pressures. 

The  point  in  the  side  supposed  plane,  at  which  the  resultant  of  all  the 
pressure  is  applied,  is  called  the  centre  of  pressure,  and  is  always  below  the 
centre  of  gravity  of  the  side.  For  if  the  pressures  exerted  at  different 
parts  of  the  plane  side  were  equal,  the  point  of  application  of  their  resul- 
tant, the  centre  of  pressure,  would  obviously  coincide  with  the  centre  of 
gravity  of  the  side.  But  since  the  pressure  increases  with  the  depth,  the 
centre  of  pressure  is  necessarily  below  the  centre  of  gravity.  This  point 
is  determined  by  calculation,  which  leads  to  the  following  results  : — 

i.  With  a  rectangular  side  whose  upper  edge  is  level  with  the  water,  the 
centre  of  pressure  is  at  two-thirds  of  the  line  which  joins  the  middle  of  the 
horizontal  sides  measured  from  the  top. 

ii.  With  a  triangular  side  whose  base  is  horizontal,  and  coincident 
with  the  level  of  the  water,  the  centre  of  pressure  is  at  the  middle  of  the 
line  which  joins  the  vertex  of  the  triangle  with  the  middle  of  the  base. 

iii.  With  a  triangular  side  whose  vertex  is  level  with  the  water,  the 
centre  of  pressure  is  in  the  line  joining  the  vertex  and  the  middle  of  the 
base,  and  at  three-fourths  of  the  distance  of  the  latter  from  the  vertex. 

100.  Hydrostatic  paradox. — We  have  already  seen  that  the  pressure 
on  the  bottom  of  a  vessel  depends  neither  on  the  form  of  the  vessel  nor 
on  the  quantity  of  the  liquid,  but  simply  on  the 
height  of  the  liquid  above  the  bottom.     But  the  ^g'^iiiill 

pressure  thus  exerted  must  not  be  confounded  with  fe 

the  pressure  which  the  vessel  itself  exerts  on  the  A 

body  which  supports  it.     The  latter  is  always  equal  j  ^ 

to   the  combined  weight  of   the  liquid  and  the  L 

vessel  in  which  it  is  contained,  while  the  former  a 

may  be  either  smaller  or  greater  than  this  weight,  m 

according  to  the  form  of  the  vessel.     This  fact  is  J^ 

usually  termed  the  hydrostatic  paradox,  because  at      3)  ^t 
first  sight  it  appears  paradoxical.  i|l    ^ 

CD  (fig,  56)  is  a  vessel  composed  of  two  cylin-  >i^!       '^"^        MM 
drical  parts  of  unequal  diameters,  and  filled  with    /l^^j^,,,,,,,,,!,,!^^!^ 
water  to  a.     From  what  has  been  said  before,  the  pj      ^ 

bottom    of   the    vessel    CD    supports    the    same 

pressure  as  if  its  diameter  were  everywhere  the  same  as  that  of  its  lower 
part  ;  and  it  would  at  first  sight  seem  that  the  scale  MN  of  the  balance, 
in  which  the  vessel  CD  is  placed,  ought  to  show  the  same  weight  as  if 
there  had  been  placed  in  it  a  cylindrical  vessel  having  the  same  height  of 
water,  and  having  the  diameter  of  the  part  D.     But  the  pressure  exerted 


'jS  On  Liquids.         ,  [100- 

on  the  bottom  of  the  vessel  is  not  all  transmitted  to  the  scale  M  N  ;  for  the 
iipzva7-d  pressure  upon  the  surface  no  of  the  vessel  is  precisely  equal  to 
the  weight  of  the  extra  quantity  of  water  which  a  cylindrical  vessel  would 
contain,  and  balances  an  equal  portion  of  the  downward  pressure  on  m. 
Consequently,  the  pressure  on  the  plate  M  N  is  simply  equal  to  the  weight 
of  the  vessel  CD  and  of  the  water  which  it  contains. 


CONDITIONS  OF  THE   EQUILIBRIUM    OF   LIQUIDS. 

loi.  Equilibrium  of  a  liquid  in  a  sing^le  vessel. — In  order  that 
a  liquid  may  remain  at  rest  in  a  vessel  of  any  given  form,  it  must  satisfy 
the  two  following  conditions  : — 

I.  Its  surface  mnst  be,  everywhere,  perpendicular  to  the  7'esultant  of  the 
forces  which. act  on  the  molecules  of  the  liquid. 

II.  Every  molecule  of  the  mass  of  the  liquid  must  be  subject  in  every 
di7'ectioji  to  equal  and  contrary  pressures. 

The  second  condition  is  self-evident ;  for  if,  in  two  opposite  directions, 
the  pressures  exerted  on  any  given  molecule  were  not  equal  and  contrary, 
the  molecule  would  be  moved  in  the  direction  of  the  greater  pressure,  and 
there  would  be  no  equilibrium.  Thus  the  second  condition  follows  from 
the  principle  of  the  equality  of  pressures,  and  from  the  reaction  which  all 
pressure  causes  on  the  mass  of  hquids. 

To  prove  the  first  condition,  let  us  suppose  that  mp  is  the  resultant  of 
all  the  forces  acting  upon  any  molecule  m  on  the  surface  (fig.  57),  and 
that  this  surface  is  inclined  in  reference  to  the  force  mp.     The  latter  can 
consequently  be  decomposed  into  two  forces, 
mq  and  mf;  the  one  perpendicular  to  the  sur- 
face of  the  liquid  and  the  other  to  the  direction 
;;//.     Now  the  first  force,  mq,  would  be   de- 
stroyed by  the  resistance  of  the  liquid,  while  the 
second  would  move  the  molecule  in  the  direction 
Fig.  57.  nif  which  shows  that  equilibrium  is  impossible. 

It  gravity  be  the  force  acting  on  the  liquid,  the  direction  mp  is  verti- 
cal ;  hence,  if  the  liquid  is  contained  in  a  basin  or  vessel  of  small  extent, 
the  surface  ought  to  be  plane  and  horizontal  (64),  because  then  the  direc- 
tion of  gravity  is  the  same  in  every  point.  But  the  case  is  different  with 
liquid  surfaces  of  greater  extent,  like  the  ocean.  The  surface  will  be  per- 
pendicular to  the  direction  of  gravity  :  but  as  this  changes  from  one  point 
to  another,  and  always  tends  towards  a  point  near  the  centre  of  the  earth,  . 
it  follows  that  the  direction  of  the  surface  of  the  ocean  will  change  also, 
and  assume  a  nearly  spherical  form. 

102.  Equilibrium  of  tbe  same  liquid  in  several  communicatingT 
vessels. — When  several  vessels  of  any  given  form  communicate  with 
each  other,  there  will  be  equilibrium  when  the  liquid  in'each  vessel  satis- 
fies the  two  preceding  conditions  (loi),  and  further,  when  the  surfaces  of 
the  liquids  in  all  the  vessels  are  in  the  same  horizontal  plane. 

In  the  vessels  ABCD  (fig.  58),  which  communicate  with  each  other, 


-104]         Conditions  of  the  Equilibrium  of  Liquids. 


79 


Fig.  58. 


let  us  consider  any  transverse  section  of  the  tube  7nn  ;  the  liquid  can  only 
remain  in  equilibrium  as  long  as  the  pressures  which  this  section  sup- 
ports from  ;«  in  the  direction  of  n, 
and  from  71  in  the  direction  of  ;«. 
are  equal  and  opposite.  Now  it 
has  been  already  proved  that  these 
pressures  are  respectively  equal  to 
the  weight  of  a  column  of  water, 
whose  base  is  the  supposed  section, 
and  whose  height  is  the  distance 
from  the  centre  of  gravity  of  this 
section  to  the  surface  of  the  liquid. 
If  we  conceive,  then,  a  horizontal 
plane,  Jnn,  drawn  through  the  centre 
of  gravity  of  ttiis  section,  it  will  be 
seen  that  there  will  only  be  equi  ^ 
librium  as  long  as  the  height  of  the 
liquid  above  this  plane  is  the  same 
in  each  vessel,  which  demonstrates  the  principle  enunciated. 

103.  Eciuilibrium  of  superposed  liquids In  order  that  there  should 

be  equilibrium  when  several  heterogeneous  liquids  are  superposed  in  the 
same  vessel,  each  of  them  must  satisfy  the  conditions  necessary  for  a 
single  liquid  (loi) ;  and  further,  there  will  be  stable  eqiiilibriuin  onlywhev 
the  liquids  ai^e  arranged  in  the  order  of  their  decreasing  densities  from  the 
bottom  upwards. 

The  last  condition  is  experimentally  demonstrated  by  means  of  the 
phial  of  four  elements.  It  consists  of  a  long  narrow  bottle  containing 
mercury,  water  saturated  with  carbonate  of  potass,  alcohol  coloured  red, 
and  petroleum.  When  the  phial  is  shaken  the  liquids  mix,  but  when  it 
is  allowed  to  rest  they  separate  ;  the  mercury  sinks  to  the  bottom,  then 
comes  the  water,  then  the  alcohol,  and  then  the  petroleum.  This  is  the 
order  of  the  decreasing  densities  of  the  bodies.  The  water  is  saturated 
with  carbonate  of  potass  to  prevent  its  mixing  with  the  alcohol. 

This  separation  of  the  liquids  is  due  to  the  same  cause  as  that  which 
enables  solid  bodies  to  float  on  the  surface  of  a  liquid  of  greater  density 
than  their  own.  It  is  also'  from  this  principle  that  fresh  Avater,  at  the 
mouths  of  rivers,  floats  for  a  long  time  on  the  denser  salt  water  of  the 
sea ;  and  it  is  for  the  same  reason  that  cream,  which  is  lighter  than  milk, 
rises  to  the  surface. 

104.  Equilibrium  of  two  different  liquids  in  communicatingr 
vessels. — When  two  liquids  of  different  densities,  which  do  not  mix,  are 
contained  in  two  communicating  vessels,  they  will  be  in  equilibrium  when, 
in  addition  to  the  preceding  principles,  they  are  subject  to  the  following  : 
that  the  heights  above  tJie  Jiorizontal  surface  of  contact  of  two  columns  of 
liquid  in  equilibrium  are  in  tJie  inverse  ratio  of  their  densities. 

To  show  this  experimentally,  mercury  is  poured  into  a  bent  glass  tube, 
mn,  fixed  against  an  upright  wooden  support  (fig.  59),  and  then  water  is 
poured  into  one  of  the  legs,  AB.     The  column  of  water,  AB,  pressing  on 


8o 


On  Liquids. 


[104- 


rtie  mercury  at  B,  lowers  its  level  in  the  leg  AB,  and  raises  it  in  the  other 
by  a  quantity,  CD  ;  so  that  if,  when  equilibrium  is  established,  we  imagine 

a  horizontal  plane,  BC,  to  pass  through  B, 
the  column  of  water  in  AB  will  balance 
the  column  of  mercury  CD.  If  the  heights 
of  these  two  columns  are  then  measured, 
by  means  of  the_  scales,  it  will  be  found 
that  the  height  of  the  column  of  water  is 
about  13^  times  that  of  the  height  of  the 
column  of  mercury.  We  shall  presently 
see  that  the  density  of  mercury  is  about 
13I  times  that  of  water,  from  which  it 
follows  that  the  heights  are  inversely  as 
the  densities. 

It  may  be  added,  that  the  equilibrium 
cannot  exist  unless  there  is  a  sufficient 
quantity  of  the  heavier  liquid  for  part  of 
it  to  remain  in  both  legs  of  the  tube. 

The  preceding  principle  may  be  de- 
duced by  a  very  simple  calculation.  Let 
d  and  df  be  the  densities  of  water  and  mercury,  and  h  and  h'  their  respec- 
tive heights,  and  let  g  be  the  force  of  gravity.  The  pressure  on  B  will  be 
proportional  to  the  density  of  the  liquid,  to  its  height,  and  to  the  force  of 
gravity  ;  on  the  whole,  therefore,  to  the  product  dhg.  Similarly,  the 
pressure  at  C  will  be  proportional  to  d'h'g.  But  in  order  to  produce 
equilibrium,  dhg  must  be  equal  to  d'h'g,  or  dh  =  d'h\  This  is  nothing 
more  than  an  algebraical  expression  of  the  above  principle  ;  for  since  the 
two  products  must  always  be  equal,  d'  must  be  as  many  times  greater  than 
d,  as  h'  is  less  than  h. 

In  this  manner  the  density  of  a  liquid  may  be  determined.  Suppose 
one  of  the  branches  contained  water  and  the  other  oil,  and  their  heights 
were,  respectively  15  inches  for  the  oil,  and  14  inches  for  .the  water.  The 
density  of  water  being  taken  as  unity,  and  that  of  oil  being  called  x,  we 
shall  have 

14 
I5x;i-=i4xi;  whence  x  =  —  =  0-933. 

15 


Fig.  59- 


APPLICATIONS  OF  THE   PRECEDING   HYDROSTATIC  PRINCIPLES. 

105. — Hydraulic  press. — The  law  of  the  equality  of  pressure  has 
received  a  most  important  application  in  the  hydraulic  press,  a  machine 
by  which  enormous  pressures  may  be  produced.  Its  principle  is  due  to 
Pascal,  but  it  was  first  constructed  by  Bramah  in  1 796. 

It  consists  of  a  cylinder,  B,  with  very  strong  thick  sides  (fig.  60),  in 
which  there  is  a  cast  iron  ram,  P,  working  water  tight  in  the  collar  of  the 
cylinder.  On  the  ram  P  there  is  a  cast  iron  plate  on  which  the  substance 
to  be  pressed  is  placed.  Four  strong  columns  serve  to  support  and  fix  a 
second  plate,  Q. 


-105] 


Hydratdic  Press. 


8i 


By  means  of  a  leaden  pipe,  K,  the  cylinder,  B,  which  is  filled  with 
water,  communicates  with  a  small  force  pump.  A,  which  works  by  means 
of  a  lever,  M.     When  the  piston  of  this  pump  p  ascends,  a  vacuum  is 


Fig.  60. 

produced  and  the  water  rises  in  the  tube  a,  at  the  end  of  which  there  is  a 
rose,  to  prevent  the  entrance  of  foreign  matters.  When  the  piston  p 
descends,  it  drives  the  water  into  the  cylinder  by  the  tube  K. 


Fig.  61. 

Fig.  61  represents  a  section,  on  a  larger  scale,  of  the  system  of  valves 
necessary  in  working  the  apparatus.     The  valve  o,  below  the  piston  p 

E3 


82  On  Liquids.  [105- 

opens  when  the  piston  rises,  and  closes  when  it  descends.  The  valve  <?, 
during  this  descent,  is  opened  by  the  pressure  of  the  water  which  passes 
by  the  pipe  K.  The  valve  /is  a  safety  valve^  held  by  a  weight  which 
acts  on  it  by  means  of  a  lever.  By  weighting  the  latter  to  a  greater  or 
less  extent  the  pressure  can  be  regulated,  for  as  soon  as  there  is  an 
upward  pressure  greater  than  that  of  the  weight  upon  it,  it  opens  and 
water  escapes.  A  screw  r  serves  to  relieve  the  pressure,  for  when  it 
is  opened  it  affords  a  passage  "for  the  efflux  of  the  water  in  the  cylin- 
der B. 

A  most  important  part  is  the  leather  collar,  ;/,  the  invention  of  which 
by   Bramah  removed   the   difficulties   which   had  been   experienced   in 

making  the  large  ram  work  water-tight  when 
submitted  to  great  pressures.  It  consists  of 
a  circular  piece  of  stout  leather,  fig.  62, 
saturated  with  oil  so  as  to  be  impervious  to 
water,  in  the  centre  of  which  a  circular  hole 
is  cut.  This  piece  is  bent,  so  that  a  section 
of  it  represents  a  reversed  U,  and  is  fitted 
Fig-  62.  into  a  groove  n  made  in  the  neck  of  the 

cylinder.  This  collar  being  concave  downwards,  in  proportion  as  the 
pressure  increases  it  fits  the  more  tightly  against  the  ram  P  on  one  side 
and  the  neck  of  the  cylinder  on  the  other,  and  quite  prevents  any  escape 
of  water. 

The  pressure  which  can  be  obtained  by  this  press  depends  on  the 
relation  of  the  piston  P  to  that  of  the  piston  p.  If  the  former  has  a 
transverse  section  fifty  or  a  hundred  times  as  large  as  the  latter,  the  up- 
ward pressure  on  the  large  piston  will  be  fifty  or  a  hundred  times  that 
exerted  upon  the  small  one.  By  means  of  the  lever  M  an  additional 
advantage  is  obtained.  It  the  distance  from  the  fulcrum  to  the  point 
where  the  power  is  applied  is  five  times  the  distance  from  the  fulcrum  to 
the  piston  /,  the  pressure  on  p  will  be  five  times  the  power.  Thus,  if  a 
man  acts  on  M  with  a  force  of  sixty  pounds,  the  force  transmitted  by  the 
piston/  will  be  300  pounds,  and  the  force  which  tends  to  raise  the  piston 
P  will  be  30,000  pounds,  supposing  the  section  of  P  is  a  hundred  times 
that  of  p. 

The  hydraulic  press  is  used  in  all  cases  in  which  great  pressures  are 
required.  It  is  used  in  pressing  cloth  and  paper,  in  extracting  the  juice 
of  beetroot,  in  compressing  hay  and  cotton,  in  expressing  oil  from  seeds, 
and  in  bending  iron  plates  ;  it  also  serves  to  test  the  strength  of  cannon, 
of  steam  boilers,  and  of  chain  cables.  The  parts  composing  the  tubular 
bridge  which  spans  the  Menai  Straits  were  raised  by  means  of  an  hydrau- 
lic press.  The  cylinder  of  this  machine,  the  largest  which  has  ever  been 
constructed,  was  nine  feet  long  and  twenty-two  inches  in  internal  diameter; 
it  was  capable  of  raising  a  weight  of  two  thousand  tons. 

106.  "Water  level. — The  water  level  is  an  application  of  the  conditions 
of  equilibrium  m  communicating  vessels.  It  consists  of  a  metal  tube 
bent  at  both  ends,  in  which  are  fitted  glass  tubes  D  and  E  (fig.  63).  It 
is  placed  on  a  tripod,  and  water  poured  in   until  it  rises  in  both  legs. 


-107] 


Spirit  Level. 


83 


When  the  Hquid  is  at  rest,  the  level  of  the  water  in  both   tubes  is  the 
same — that  is,  they  are  both  in  the  same  horizontal  plane. 

This  instrument  is  used  in  levelling,  or  ascertaining  how  much  one 
point  is  higher  than  another.  If,  for  example,  it  is  desired  to  find  the 
difference  between  the  heights  of  B  and  A,  a  levelling-staff  is  fixed  on 


Fig.  £3- 


the  latter  place.  This  staff  consists  of  a  rule  formed  of  two  sliding 
pieces  of  wood,  and  supporting  a  piece  of  tin  plate  M,  in  the  centre  of 
which  there  is  a  mark.  This  staff  being  held  vertically  at  A,  an  observer 
looks  at  it  through  the  level  along  the  surfaces  D  and  E,  and  directs  the 
holder  to  raise  or  lower  the  slide  until  the  mark  is  in  the  prolongation 
of  the  line  DE.  The  height  AM  is  then  measured,  and  subtracting  it 
from  the  height  of  the  level,  the  height  of  the  point  A  above  B  is 
obtained. 

107.  Spirit  level. — The  spirit  level  is  both  more  delicate  and  more 
accurate  than  the  water  level.     It  consists  of  a  glass  tube,  AB  (fig.  64) 

Fig.  64. 


nr 


Fig.  65. 


very  slightly  curved;  that  is,  the  tube,  instead  of  being  a  true  cylinder  as 
it  seems  to  be,  is  in  fact  slightly  curved  in  such  a  manner  that  its  axis  is 
an  arc  or  a  circle  of  very  large  radius  ;  it  is  filled  with  spirit  with  the  ex- 
ception of  a  bubble  of  air,  which  tends  to  occupy  the  highest  part.  The 
tube  is  placed  in  a  brass  case,  CD  (fig.  65),  which  is  so  arranged  that 
when  it  is  in  a  perfectly  horizontal  position  the  bubble  of  air  is  exactly 
between  the  two  points  marked  in  the  case- 


*« 


84 


Oil  Liquids. 


[107 


To  take  levels  with  this  apparatus,  it  is  fixed  on  a  telescope,  which  can 
consequently  be  placed  in  a  horizontal  position, 

1 08.  Artesian  wells.— All  natural  collections  of  water  exemplify  the 
tendency  of  water  to  find  its  level.  Thus,  a  group  of  lakes,  such  as  the 
great  lakes  of  North  America,  may  be  regarded  as  a  number  of  vessels  in 
communication,  and  consequently  the  waters  tend  to  maintain  the  same 
level  in  all.  This,  too,  is  the  same  with  the  source  of  a  river  and  the  sea 
and  as  the  latter  is  on  the  lower  level,  the  river  continually  flows  down 
to  the  sea  along  its  bed,  which  is,  in  fact,  the  means  of  communication 
between  the  two. 

Perhaps  the  most  striking  instance  of  this  class  of  natural  phenomena 
is  that  of  artesian  wells.  These  wells  derive  their  name  from  the  pro- 
vince of  Artois,  where  it  has  long  been  customary  to  dig  them,  and  from 
whence  their  use  in  other  parts  of  France  and  Europe  were  derived.  It 
seems,  however,  that  at  a  very  remote  period  wells  of  the  same  kind  were 
dug  in  China  and  Egypt. 


Fig.  66. 


To  understand  the  theory  of  these  wells,  it  must  be  premised  that  the 
strata  composing  the  earth's  crust  are  of  two  kinds  :  the  one  permeable 
to  water,  such  as  sand,  gravel,  etc  ;  the  others  impermeable,  such  as 
clay.  Let  us  suppose,  then,  a  geographical  basin  of  greater  or  less  ex- 
tent, in  which  the  two  imperrrwsable  layers  AB,  CD  (fig.  66),  enclose 
between  them  a  permeable  layea:  KK.  The  rain-water  falling  on  the  part 
of  this  layer  which  comes  to  the  surface,  which  is  called  the  outcrop,  will 
filter  through  it,  and  following  the  natural  fall  of  the  ground  will  collect 
in  the  hollow  of  the  basin,  whence  it  cannot  escape  owing  to  the  imperme- 
able strata  above  and  below  it.  If  now  a  vertical  hole  I  be  sunk  down 
to  the  water-bearing  stratum^  the  water  striving  to  regain  its  level  will 
spout  out  to  a  height  which  depends  on  the  difference  between  the  levels 
of  the  outcrop  and  of  the  point  at  which  the  perforation  is  made. 

The  waters  which  feed  artesian  wplls  often  come  from  a  distance  of 
sixty  or  seventy  miles.  The  depth  varies  in  different  places.  The  well 
at  Crenelle  is  1,800  feet  deep ;  it  gives  656  gallons  of  water  in  a  minute, 
and  is  one  of  the  deepest  and  most  abundant  which  have  been  made.  The 


-109] 


Pressure  on  a  Body  immersed  in  Liquid. 


85 


temperature  of  the  water  is  27°  C.  It  follows  from  the  law  of  the  in- 
crease of  temperature  with  the  increasing  depth  below  the  surface  of  the 
ground,  that,  if  this  well  were  210  feet  deeper,  the  water  would  have  all 
the  year  round  a  temperature  of  32°  C,  that  is,  the  ordinary  temperature 
of  baths. 


BODIES   IMMERSED   IN   LIQUIDS. 

109.  Pressure    supported   by   a   body    immersed   in  a   liquid.— 

When  a  solid  is  immersed  in  a  liquid,  every  portion  of  its  surface  is  sub- 
mitted to  a  perpendicular  pressure  which  increases  with  the  depth.  If 
we  imagine  all  these  pressures  decomposed  into  horizontal  and  vertical 
pressures,  the  first  set  are  in  equilibrium.  The  vertical  pressures  are  ob- 
viously unequal,  and  will  tend  to  move  the  body  upwards. 

Let  us  imagine  a  cube  immersed  in  a  mass  of  water  (fig.  67),  and  that 
four  of  its  edges  are  vertical.  The  pressures 
upon  the  four  vertical  faces  being,  clearly,  in 
equilibrium,  we  need  only  consider  the  pressures 
exerted  on  the  horizontal  faces  A  and  B.  The 
first  is  pressed  downwards  by  a  column  of  water, 
whose  base  is  the  face  A,  and  whose  height  is  AD, 
the  lower  face  B  is  pressed  upwards  by  the  weight 
of  a  column  of  water  whose  base  is  the  face  itself, 
and  whose  height  is  BD  (96.)  The  cube,  therefore, 
is  urged  upwards  by  a  force  equal  to  the  difference 
between  these  two  pressures,  which  latter  is  mani- 
festly equal  to  the  weight  of  a  column  of  water 
having  the  same  base  and  the  same  height  as  this 
cube.  Consequently  y  this  upward  pressure  is  equal 
to  the  weight  of  the  volume  of  water  displaced  by 
the  immersed  body. 

We  shall  readily  see  from  the  following  reasoning  that  every  body 
immersed  in  a  hquid  is  pressed  upwards  by  a  force  equal  to  the  weight 
of  the  displaced  Hquid.  In  a  liquid  at  rest,  let  us  suppose  a  portion  of 
it  of  any  given  shape,  regular  or  irregular,  to  become  solidified,  without 
either  increase  or  decrease  of  volume.  The  liquid  thus  solidified  will 
remain  at  rest,  and  therefore  must  be  acted  upon  by  a  force  equal  to  its 
weight,  and  acting  vertically  upwards  through  its  centre  of  gravity  ;  for 
otherwise  motion  would  ensue.  If  in  the  place  of  the  solidified  water  we 
imagine  a  solid  of  another  substance  of  exactly  the  same  volume  and 
shape,  it  will  necessarily  receive  the  same  pressures  from  the  surrounding 
liquid  as  the  solidified  portion  did  ;  hence,  hke  the  latter,  it  will  sustain 
the  pressure  of  a  force  acting  vertically  upwards  through  the  centre  of 
gravity  of  the  displaced  liquid,  and  equal  to  the  weight  of  the  displaced 
liquid.  If,  as  almost  invariably  happens,  the  liquid  is  of  uniform  density, 
the  centre  of  gravity  of  the  displaced  liquid  means  the  centre  of  gravity 
of  the  immersed  part  of  the  body  supposed  to  be  ofunifor?n  density.  This 
distinction   is  sometimes  of  importance  ;   for  example,  if  a   sphere   is 


Fig.  67. 


86 


On  Liquids. 


[109- 


composed  of  a  hemisphere  of  iron  and  another  of  wood,  its  centre  of 
gravity  would  not  coincide  with  its  geometrical  centre  ;  but  if  it  were 
placed  under  water,  the  centre  of  gravity  of  the  displaced  water  would  be 
at  the  geometrical  centre,  that  is,  will  have  the  same  position  as  the 
centre  of  gravity  of  the  sphere  if  of  uniform  density. 

no.  Principle  ef  iLrcbimedes. — The  preceding  principles  prove  that 
every  body  immersed  in  a  liquid  is  submitted  to  the  action  of  two  forces  ; 
gravity  which  tends  to  lower  it,  and  the  buoyancy  of  the  liquid  which 
tends  to  raise  it  with  a  force  equal  to  the  weight  of  the  liquid  displaced. 


Fig.  68 

The  weight  of  the  body  is  either  totally  or  partially  overcome  by  this 
buoyancy,  from  which  it  is  concluded  that  a  body  immersed  in  a  liquid 
loses  a  part  of  its  weight  equal  to  the  weight  of  the  displaced  liquid. 

This  principle,  which  is  the  basis  of  the  theory  of  immersed  and  float- 
ing bodies,  is  called  the  principle  of  Archimedes,  after  the  discoverer.  It 
may  be  shown  experimentally  by  means  of  the  hydrostatic  balafice  (fig.  68). 
This  is  an  ordinary  balance,  each  pan  of  which  is  provided  with  a  hook  ; 
the  beam  can  be  raised  by  means  of  a  toothed  rack,  which  is  worked  by 
a  little  pinion,  C.  A  catch,  D,  holds  the  rack  when  it  has  been  raised. 
The  beam  being  raised,  a  hollow  copper  cylinder,  A,  is  suspended  to  one 


-112] 


Eqiiilibrmm  of  Floating  Bodies. 


87 


of  the  pans,  and  below  this  a  sohd  cyHnder,  B,  whose  volume  is  exactly* 
equal  to  the  capacity  of  the  first  cylinder  ;  lastly,  an  equipoise  is  placed  in 
the  other  pan.  If  now  the  hollow  cylinder  be  filled  with  water  the  equili- 
brium is  disturbed  ;  but  if  at  the  same  time  the  beam  is  lowered  so  that 
the  solid  cylinder  B  becomes  immersed  in  a  vessel  of  water  placed  be- 
neath it,  the  equilibrium  will  be  restored.  By  being  immersed  in  water 
the  cylinder  B  loses  a  portion  of  its  weight  equal  to  that  of  the  water  in 
the  cylinder  A.  Now  as  the  capacity  of  the  cylinder  A  is  exactly  equal' to 
the  volume  of  the  cylinder  B,  the  principle  which  has  been  before  laid 
down  is  proved. 

111.  Determination  of  tbe  volume  of  a  body. — The  principle  of 
Archimedes  furnishes  a  method  for  obtaining  the  volume  of  a  body  of  any 
shape,  provided  it  is  not  soluble  in  water.  The  body  is  suspended  by  a 
fine  thread  to  the  hydrostatic  balance,  and  is  weighed  first  in  the  air,  and 
then  in  distilled  water  at  4°  C.  The  loss  of  weight  is  the  weight  of  the 
displaced  water,  from  which  the  volume  of  the  displaced  water  is  readily 
calculated.  But  this  volume  is  manifestly  that  of  the  body  itself.  Suppose, 
for  example,  1 55  grammes  is  the  loss  of  weight.  This  is  consequently  the 
weight  of  the  displaced  water.  Now  it  is  known  that  a  gramme  is  the 
weight  of  a  cubic  centimetre  of  water  at  4°;  consequently,  the  volume  of 
the  body  immersed  is  155  cubic  centimetres. 

1 1 2.  Equilibrium  of  floating:  bodies. — A  body  when  floating  is  acted 
on  by  two  forces,  namely,  its  weight,  which  acts  vertically  downwards 
through  its  centre  of  gravity,  and  the  resultant  of  the  fluid  pressures, 
which  (104)  acts  vertically  upwards  through  the  centre  of  gravity  of  the 
fluid  displaced  ;  but  if  the  body  is  at  rest  these  two  forces  must  be  equal 


Fig.  69.  '  Fig.  70.  Fis-  71- 

and  act  in  opposite  directions  ;  whence  follow  the  conditions  of  equilibrium, 
namely  : — 

i.  The  floating  body  jnust  displace  a  vqlume  of  liquid  whose  weight 
equals  that  of  the  body. 

ii.  The  ce7itre  of  gravity  of  the  floating  body  must  be  in  the  same  vertical 
line  with  that  of  the  fluid  displaced. 

Thus  in  fig.  69,  if  C  is  the  centre  of  gravity  of  the  body  and  G  that  of 
the  displaced  fluid,  the  line  GC  must  be  vertical,  since  when  it  is  so  the 
weight  of  the  body  and  the  fluid  pressure  will  act  in  opposite  directions 
along  the  same  line,  and  will  be  in  equilibrium  if  equal.     It  is  convenient 


88  On  Liquids.  [112- 

with  reference  to  the  subject  of  the  present  article,  to  speak  of  the  Une 
CG  produced  as  the  axis  of  the  body. 

Next  let  it  be  enquired  whether  the  equilibrium  be  stable  or  unstable. 
Suppose  the  body  to  be  turned  through  a  small  angle  (fig.  70)  so  that 
the  axis  takes  a  position  inclined  to  the  vertical.  The  centre  of  gravity 
of  the  displaced  fluid  will  no  longer  be  G,  but  some  other  point  G^  And 
since  the  fluid  pressure  acts  vertically  upwards  through  G',  its  direction 
will  cut  the  axis  in  some  point  M^,  which  will  generally  have  different 
positions  according  as  the  inclination  of  the  axis  to  the  vertical  is  greater 
or  smaller.  If  the  angle  is  indefinitely  small,  M'  will  have  a  definite 
position  M,  which  always  admits  of  determination,  and  is  called  the 
inetacentre. 

If  we  suppose  M  to  be  above  C,  an  inspection  of  fig,  71  will  show  that 
when  the  body  has  received  an  indefinitely  small  displacement  the  weight 
of  the  body  W  and  the  resultant  of  the  fluid  pressures  R  tends  to  bring 
the  body  back  to  its  original  position,  that  is,  in  this  case  the  equilibrium 
is  stable  (67).  If,  on  the  contrary,  M  is  below  C,  the  forces  tend  to  cause 
the  axis  to  deviate  farther  from  the  vertical,  and  the  equilibrium  is  un- 
stable.    Hence  the  rule, 

iii.  The  eqicilibrium  of  a  floating  body  is  stable  or  unstable  accoj'dingas 
the  metacentre  is  above  or  below  the  centre  of  gravity. 

The  determination  of  the  metacentre  can  rarely  be  affected  except  by 
means  of  a  somewhat  difficult  mathematical  process.  When,  however, 
the  form  of  the  immersed  part  of  a  body  is  spherical  it  can  be  readily 
determined,  for  since  the  fluid  pressure  at  each  point  converges  to  the 
centre,  and  continues  to  do  so  when  the  body  is  slightly  displaced,  their 
resultant  must  in  all  cases  pass  through  the  centre,  which  is  therefore  the 
metacentre.  To  illustrate  this  :  let  a  spherical  body  float  on  the  surface  of 
a  liquid  (fig.  72),  then  its  centre  of  gravity  and 
the  metacentre  both  coinciding  with  the  geome- 
trical centre  C  its  equilibrium  is  neutral  (67)  ; 
now  suppose  a  small  heavy  body  to  be  fastened 
at  P,  the  summit  of  the  vertical  diameter.  The 
centre  of  gravity  will  now  be  at  some  point 
G  above  C.  Consequently,  the  equilibrium  is 
unstable,  and  the  sphere,  left  to  itself,  will 
instantly  turn  over  and  will  rest  when  P  is  the 
lower  end  of  a  vertical  diameter. 

On  investigating  the  position  of  the  meta- 
centre of  a  cylinder,  it  is  found  that  when  the  ratio  of  the  radius  to  the 
height  is  greater  than  a  certain  quantity,  the  position  of  stable  equilibrium 
is  that  in  which  the  axis  is  vertical ;  but  if  it  be  less  than  that  quantity, 
the  equilibrium  is  stable  when  the  axis  is  horizontal.  For  this  reason  the 
stump  of  a  tree  floats  lengthwise,  but  a  thin  disc  of  wood  floats  flat  on 
the  water. 

Hence,  also,  if  .it  is  required  to  make  a  cylinder  of  moderate  length 
float  with  its  axis  vertical,  it  is  necessary  to  load  it  at  the  lower  end.  By 
so  doing  its  centre  of  gravity  is  brought  below  the  metacentre. 


U6] 


Specific  Gravity. 


89 


The  determination  of  the  metacentre  and  of  the  centre  of  gravity  is  of 
great  importance  in  the  stowage  of  vessels,  for  on  their  relative  positions 
the  stability  depends. 

1 1 3.  Cartesian  diver. — The  different  effects  of  suspension,  immersion, 
and  floating  are  reproduced  by  means  of  a  well-known  hydrostatic  toy, 
the  Cartesian  diver  (fig.  73).  It  consists  of  a  glass  cylinder  nearly  full  of 
water,  on  the  top  of  which  a  brass  cap,  provided  with  a  piston,  is  herme- 
tically fitted.  In  the  liquid  there  is  a  little  porcelain  figure  attached  to 
a  hollow  glass  ball  a^  which  contains  air  and  water,  and  floats  on  the 
surface.  In  the  lower  part  of  this  ball  there  is  a  little  hole  by  which 
water  can  enter  or  escape,  according  as  the  air  in  the  interior  is  more  or 
less  compressed.  The  quantity  of  water  in  the  globe  is  such  that  very 
little  more  is  required  to  make  it  sink.  If  the  piston  be  slightly  lowered, 
the  air  is  compressed,  and  this  pressure  is  transmitted  to  the  water  of 
the  vessel  and  the  air  in  the  bulb.  The  conse- 
quence is,  that  a  small  quantity  of  water  pene- 
trates into  the  bulb,  which  therefore  becomes 
heavier  and  sinks.  If  the  pressure  is  reheved, 
the  air  in  the  bulb  expands,  expels  the  excess  of 
water  which  had  entered  it,  and  the  apparatus 
being  now  lighter,  rises  to  the  surface.  The  ex- 
periment may  also  be  made,  by  replacing  the 
brass  cap  and  piston  by  a  cover  of  sheet  india 
rubber,  which  is  tightly  tied  over  the  mouth  : 
when  this  is  pressed  by  the  hand  the  same  effects 
are  produced. 

114.  Swimmingr  bladder  of  fishes. — Most 
fishes  have  an  air-bladder  below  the  spine,  which 
is  called  the  swimming  bladder.  The  fish  can 
compress  or  dilate  this  at  pleasure  by  means  of  a 
muscular  effort,  and  produce  the  same  effects  as 
those  just  described — that  is,  it  can  either  rise 
or  sink  in  water. 

1 1 5.  Swimmingr.— The  human  body  is  lighter, 
on  the  whole,  than  an  equal  volume  of  water  ; 
it  consequently  floats  on  the  surface  and  still 
better  in  sea-water,  which  is  heavier  than  fresh 
water.  The  difficulty  in  swimming  consists  not 
so  much  in  floating,  as  in  keeping  the  head  above 
water,  so  as  to  breathe  freely.  In  man  the  head  is  heavier  than  the  lower 
parts,  and  consequently  tends  to  sink,  and  hence  swimming  is  an  art 
which  requires  to  be  learned.  With  quadrupeds,  on  the  contrary,  the 
head  being  less  heavy  than  the  posterior  parts  of  the  body,  remains  above 
water  without  any  effort,  and  these  animals  therefore  swim  naturally. 


Fig-  73- 


SPECIFIC  GRAVITY— HYDROMETERS. 

116.    Determination   of  specific  grravities. — It   has   been   already 
(explained  (24)  that  the  specific  gravity  of  a  body,  whether  solid  or  liquid, 


90 


Oji  Liquids. 


[116- 


is  the  number  which  expresses  the  relation  of  the  weight  of  a  given  volume 
of  this  body,  to  the  weight  of  the  same  volume  of  distilled  water  at  a 
temperature  of  4°.  In  order,  therefore,  to  calculate  the  specific  gravity  of 
a  body,  it  is  sufficient  to  determine  its  weight  and  that  of  an  equal  volume 
of  water,  and  then  to  divide  the  first  weight  by  the  second:  the  quotient 
is  the  specific  gravity  of  the  body. 

Three  methods  are  commonly  used  in  determining  the  specific  gravities 
of  solids  and  liquids.  These  are,  ist,  the  method  of  the  hydrostatic 
balance  ;  2nd,  that  of  the  hydrometer ;  and  3rd,  the  specific  gravity  flask. 
All  three,  however,  depend  on  the  same  principle,  that  of  first  ascertain- 
ing the  weight  of  a  body,  and  then  that  of  an  equal  volume  of  water. 
We  shall  first  apply  these  methods  to  determining  the  specific  gravity  of 
solids,  and  then  to  the  specific  gravity  of  liquids. 

117.  Specific  gravity  of  solids. — i.  Hydrostatic  balance.  To  obtain 
the  specific  gravity  of  a  solid  by  the  hydrostatic  balance  (fig.  68),  it  is 
first  weighed  in  the  air,  and  is  then  suspended  to 
the  hook  of  the  balance  and  weighed  in  water  (fig. 
74).  The  loss  of  weight  which  it  experiences  is, 
according  to  Archimedes'  principle,  the  weight  of 
a  volume  of  water  equal  to  its  own  volume  ;  con- 
sequently, dividing  the  weight  in  air  by  the  loss  of 
weight  in  water,  the  quotient  is  the  specific  gravity 
required.  If  P  is  the  weight  of  the  body  in  air,  P' 
its  weight  in  water,  and  D  its  specific  gravity, 
P  —  P'  being  the  weight  of  the  displaced  water,  we 

P 
have   D  =  'u~—V'' 

It  may  be  observed  that  though  the  weighing  is 
performed  in  air,  yet,  strictly  speaking,  the  quantity 
required  is  the  weight  of  the  body  m  vacuo,  and 
when  great  accuracy  is  required,  it  is  necessary  to. 
apply  to  the  observed  weights  a  correction  for  the 
weights  of  the  unequal  volumes  of  air  displaced  by 
the  substance,  and  the  weights  in  the  other  scale 
pan.  It  may  also  be  remarked  that  the  water  in  which  bodies  are  weighed 
is,  strictly  speaking,  distilled  water  at  a  standard  temperature. 

ii.  Nicholson's  hydi'ometer.—TMxs  apparatus  consists  of  a  hollow 
metallic  cylinder  B  (fig.  75),  to  which  is  fixed  a  cone  C,  loaded  with  lead. 
The  object  of  the  latter  is  to  bring  the  centre  of  gravity  below  the  meta- 
centre,  so  that  the  cylinder  may  float  with  its  axis  vertical.  At  the  top  is 
a  stem,  terminated  by  a  pan,  in  which  is  placed  the  substance  whose 
specific  gravity  is  to  be  determined.  On  the  stem  a  standard  point,  ^,  is 
marked. 

The  apparatus  stands  partly  out  of  the  water,  and  the  first  step  is  to 
ascertain  the  weight  which  must  be  placed  in  the  pan  in  order  to  make 
the  hydromet-er  sink  to  the  standard  point  o.  Let  this  weight  be  125 
grains,  and  let  sulphur  be  the  substance  whose  specific  gravity  is  to  be 
determined.     The  weights  are  then  removed  from  the  pan,  and  replaced 


J^'iff-  74- 


-118] 


Specific  Gravity  Flask, 


91 


Fig-  75- 


by  a  piece  of  sulphur  which  weighs  less  than  125  grains,  and  weights 

added  until  the  hydrometer  is  again  depressed 

to  the  standard,  0.     If,  for  instance,  it  has  been 

necessar}'  to  add  55  grains,  the  weight  of  the 

sulphur  is  evidently  the  difference  between  125 

and  55  grains,  that  is,  70  grains.     Having  thus 

determined  the  weight  of  the  sulphur  in  air,  it  is 

now  only  necessary  to  ascertain  the  weight  of 

an    equal  volume  of  water.      To  do  this,  the 

piece  of  sulphur  is  placed  in  the  lower  pan  C  at 

7/2,  as   represented  in  the  figure.      The  whole 

weight  is  not  changed,  nevertheless  the  hydro- 
meter  no   longer   sinks    to  the   standard  ;   the 

sulphur,   by   immersion,   has  lost  a  part  of  its 

weight   equal  to   that   of  the  water  displaced. 

Weights  are  added  to  the  upper  pan  until  the 

hydrometer  sinks  again  to  the  standard.     This 

weight,  34-4  grains,  for  example,  represents  the 

weight  of  the  volume  of  water  displaced  ;  that 

is,  of  the  volume  of  water  equal  to  the  volume   ^ 

of  the  sulphur.     It  is  only  necessary,  therefore, 

to  divide  70  grains,  the  weight  in  air,  by  34-4 

grains,  and  the  quotient  2*03  is  the  specific  gravity. 

If  the  body  in  question  is  lighter  than  water  it  tends  to  rise  to  the 

surface,  and  will  not  remain  on  the  lower  pan  C.    To  obviate  this,  a  small 

moveable  cage  of  fine  wire  is  adjusted  so  as  to  prevent 

the  ascent  of  the  body.     The    experiment   is   in   other 

respects  the  same. 

118.  Specific  gravity  flask. — When  the  specific 
gravity  of  a  substance  in  a  state  of  powder  is  required,  it 
can  be  found  most  conveniently  by  means  of  the  specific 
gravity  flask.  This  instrument  is  a  small  flask,  with  a 
large  neck  fitted  with  a  carefully  ground  glass  stopper 
(fig.  76).  The  stopper  is  perforated  along  its  axis,  and 
the  bore  is  continued  by  means  of  a  thin  tube  which  ex- 
pands into  a  tube  of  greater  diameter,  as  shown  in  the 
figure.  On  the  thin  tube  is  a  mark  a^  and  at  each  weigh- 
ing the  flask  is  filled  with  water  exactly  to  the  mark.  This 
is  done  by  filling  the  flask  when  wholly  under  water,  and 
putting  in  the  stopper  while  it  is  immersed.  The  flask  and  the  tube  are 
then  completely  filled,  and  the  quantity  of  water  in  excess  is  removed  by 
blotting  paper.  To  find  the  specific  gravity  proceed  as  follows  :  Having 
weighed  the  powder,  place  it  in  one  of  the  scale  pans,  and  with  it  the  flask 
filled  exactly  to  a  and  carefully  dried.  Then  balance  it  by  placing  small 
shot,  or  sand,  in  the  other  pan.  Next,  remove  the  flask  and  pour  the 
powder  into  it,  and,  as  before,  fill  it  up  with  water  to  the  mark  a.  On 
replacing  the  flask  in  the  scale  pan  it  will  no  longer  balance  the  shot, 
since  the  powder  has  displaced  a  volume  of  water  equal  to  its  own  volume. 


Fig.  76. 


92 


On  Liquids. 


[118- 


Place  weights  in  the  scale  pan  along  with  the  flask  until  they  balance  the 
shot.  These  weights  give  the  weight  of  the  water  displaced.  Then  the 
weight  of  the  powder,  and  the  weight  of  an  equal  bulk  of  water  being 
known,  its  specific  gravity  is  determined  as  before. 

It  is  important  in  this  determination  to  remove  the  layer  of  air  which 
adheres  to  the  powder,  and  unduly  increases  the  quantity  of  water  expelled. 
This  is  effected  by  placing  the  bottle  under  the  receiver  of  an  air  pump,  and 
exhausting.  The  same  result  is  obtained  by  boihng  the  water  in  which 
the  powder  is  placed. 

-  119.  Bodies  soluble  in  water. — If  the  body,  whose  specific  gravity  is 
to  be  determined  by  any  of  these  methods,  is  soluble  in  water,  the  deter- 
mination is  made  in  some  liquid  in  which  it  is  not  soluble,  such  as  oil, 
turpentine,  or  naphtha,  the  specific  gravity  of  which  is  known.  The 
specific  gravity  is  obtained  by  multiplying  the  number  obtained  in  this 
experiment  by  the  specific  gravity  of  the  liquid  used  for  the  determi- 
nation. 

Suppose,  for  example,  a  determination  of  the  specific  gravity  of  potassium 
has  been  made  in  naphtha.  For  equal  volumes,  P  represents  the  weight  of 
the  potassium,  P^  that  of  the  naphtha,  and  Y"  that  of  water;  consequently, 

P 

_-  will  be  the  specific  gravity  of  the  substance  in  reference  to  naphtha,  and 

p/ 

—.  the  specific  gravity  of  the  naphtha  in  reference  to  water.     The  product 

p 

of  these  two  fractions  —  is  the  specific  gravity  of  the  substance  compared 

with  water. 

In  determining  the  specific  gravity  of  porous  substances,  they  are 
varnished  before  being  immersed,  in  water,  which  renders  them  impervious 
to  moisture  without  altering  their  volume. 


Specific  gravity  of  solids  at 

zero  as  compared  with  distilled  'i 

i/ater  at  4°  C. 

Platinum,  rolled   . 

.  22-069 

Statuary  marble  . 

.     2-837 

„         cast       . 

.  20-337 

Aluminium  . 

.     2 -680 

Gold,  stamped 

.   19-362 

Rock  crystal 

•     2-653 

„     cast     . 

.   19-258 

St.  Gobin  glass   . 

.     2-488 

Lead,  cast    . 

.   11-352 

China  porcelain  . 

.         .     2-385 

Silver,  cast  . 

.   10-474 

Sevres  porcelain . 

.     2-146 

Bismuth,  cast 

.     9-822 

Native  sulphur    . 

.     2-033 

Copper,  drawn  wire 

.     8-878 

Ivory  . 

.     1-917 

„       cast. 

.     8-788 

Anthracite  . 

.     1-800 

Brass    .... 

.     8-383 

Compact  coal      . 

.     1*329 

Steel,  not  hammered    . 

.     7-8i6 

Amber 

.     1-078 

Iron,  bar 

.     7788 

Melting  Ice 

.     0-930 

„     cast      . 

.    7-207 

Beech . 

.     0-852 

Tin,  cast 

.    7-291 

Oak    . 

.     0-845 

Zinc,  cast      .         .         . 

.    6-861 

Elm    . 

.     o-8oo 

Antimony,  cast     . 

.    6-712 

Yellow  Pine 

.     0-657 

Diamonds     .         .        3-531 

to  3-501 

Common  poplar . 

.     0-389 

Flint  glass    . 

.     3-329 

Cork    . 

.     0-240 

-121] 


Specific  Gravity  of  Liquids. 


93 


120.  Specific  g:ravity  of  liquids. — i.  Method  of  the  hydrostatic  balance. 
From  the  pan  of  the  hydrostatic  balance  a  body  is  suspended,  on  which 
the  hquid  whose  specific  gravity  is  to  be  determined  exerts  no  chemical 
action  ;  for  example,  a  ball  of  platinum.  This  is  then  successively 
weighed  in  air,  in  distilled  water,  and  in  the  liquid.  The  loss  of  weight  of 
the  body  in  these  two  liquids  is  noted.  They  represent  respectively  the 
weights  of  equal  volumes  of  water  and  of  the  given  liquid,  and  consequently 
it  is  only  necessary  to  divide  the  second  of  them  by  the  first  to  obtain  the 
required  specific  gravity. 

Let  P  be  the  weight  of  the  platinum  ball  in  air,  P'  its  weight  in  water, 
Y"  its  weight. in  the  given  liquid,   and  let   D   be  the  specific  gravity 


displaced 
is    P-P^ 


by  the    platinum    is 
from   which   we  get 


sought.       The    weight  of   the    water 
P  — P'  and  that  of  the  second   liquid 
P  — P^'' 

P-P' 

ii.  Fahrenheit's  hydrometer. — This    instrument   (fig.    jy)    resembles 
Nicholson's  hydrometer,  but  it  is  made  of  glass,  so  as  to  be  used  in  all 
liquids.     At  its  lower  extremity,  instead  of  a  pan,  it 
is  loaded  with  a  small  bulb  containing  mercury.    There 
is  a  standard  mark  on  the  stem. 

The  weight  of  the  instrument  is  first  accurately 
determined  "in  air ;  it  is  then  placed  in  water,  and 
weights  added  to  the  scale  pan  until  the  mark  on  the 
stem  is  level  with  the  water.  It  follows  from  the  first 
principle  of  the  equilibrium  of  floating  bodies,  that  the 
weight  of  the  hydrometer,  together  with  the  weight  in 
the  scale  pan,  is  equal  to  the  weight  of  the  volume  of 
the  displaced  water.  In  the  same  manner,  the  weight 
of  an  equal  volume  of  the  given  liquid  is  determined, 
and  the  specific  gravity  is  found  by  dividing  the  latter 
weight  by  the  former. 

Neither  Fahrenheit's  nor  Nicholson's  hydrometers 
give  such  accurate  results  as  the  hydrostatic  balance. 

iii.  Specific  gravity  flask. — This  has  been  already 
described.  In  determining  the  specific  gravity  of  a  Hquid,  the  flask  is  first 
weighed  empty,  and  then  successively,  full  of  water,  and  of  the  given 
liquid.  If  the  weight  of  the  flask  be  substracted  from  the  two  weights 
thus  obtained,  the  result  represents  the  weights  of  equal  volumes  of  the 
liquid  and  of  water,  from  which  the  specific  gravity  is  obtained  by  division. 

121.  On  tbe  observation  of  temperature  in  ascertaining-  specific 
cavities. — As  the  volume  of  a  body  increases  with  the  temperature,  and 
as  this  increase  varies  with  different  substances,  the  specific  gravity  of 
any  given  body  is  not  exactly  the  same  at  different  temperatures  ;  and 
consequently,  a  certain  fixed  temperature  is  chosen  for  those  determina- 
tions. That  of  water,  for  example,  has  been  made  at  4°  C,  for  at  this 
point  it  has  the  greatest  density.  The  specific  gravities  of  other  bodies 
are  assumed  to  be  taken  at  zero;  but  as  this  is  not  always  possible, 
certain  corrections  must  be  made,  which  we  shall  consider  in  the  Book 
on  Heat. 


Fig.  77. 


94 


Oil  Liquids. 


[121- 


Specijic  gravilies  of  liquids  at  zero,  compared  with  that  of  water  at  4°C. 

as  unity. 


Mercury 
Bromine 
Sulphuric  acid 
Chloroform  . 
Nitric  acid    . 
Bisulphide  of  carboji 
Hydrochloric  acid 
Blood  . 
Milk     . 


.  13*598  Sea-water  ....  1-026 
.  2-960  Distilled  water  at  4°  C.  .  i-ooo 
.     1-841  „  „      ato°C.        .     o'999 

.  1*525  Claret.  ....  0-994 
1*420  Olive  oil  .  .  .  .  0-915 
.  1*293  Oil  of  turpentine .  .  .  0*870 
.  1*240  Naphtha  ....  0-847 
.     1*060    Absolute  alcohol .        .        .     0-803 

.     1-032     Ether 0-723 

122.  irse  of  tables  of  specific  gravity. — Tables  of  specific  gravity 
admit  of  numerous  applications.  In  mineralogy  the  specific  gravity  of  a 
mineral  is  often  a  highly  distinctive  character.  By  means  of  tables  of 
specific  gravities  the  weight  of  a  body  may  be  calculated  when  its  volume 
is  known,  and  conversely  the  volume  when  its  weight  is  known. 

With  a  view  to  explaining  the  last-mentioned  use  of  these  tables,  it 
will  be  well  to  premise  a  statement  of  the  connection  existing  between 
the  British  units  of  length,  capacity,  and  weight.  It  will  manifestly  be 
sufficient  for  this  purpose  to  define  that  which' exists  between  the  yard, 
gallon,  and  pound  avoirdupois,  since  other  measures  stand  to  these  in 
well-known  relations.  T\\^  yard,  consisting  of  36  inches,  may +)e  regarded 
as  the  primary  unit.  Though  it  is  essentially  an  arbitrary  standard,  it  is 
determined  by  this,  that  the  simple  pendulum  which  makes  one  oscilla- 
tion, in  a  mean  second  at  London  on  the  sea  level,  is  39*1398  inches  long. 
T'hQgallo7i  contains  277-274  cubic  inches.  A  gallon  of  distilled  water  at 
the  standard  temperature  weighs  10  pounds  avoirdupois  or  70,000  grains 
troy  ;  or,  which  comes  to  the  same  thing,  one  cubic  inch  of  water  weighs 
252-5  grains. 

On  the  French  system  the  fnetre  is  a  primary  unit,  and  is  so  chosen 
that  10,000,000  metres  are  the  length  of  a  quadrant  of  the  meridian  from 
either  pole  to  the  equator.  The  metre  contains  10  decimett'es,  or  100 
centitJietres,  OY  \,ooo  millimetres,  its  length  equals  1-0936  yards.  The 
unit  of  the  measure  of  capacity  is  the  litre  or  cubic  decimetre.  The  unit 
of  weight  is  the  gratnme,  which  is  the  weight  of  a  cubic  centimetre  of 
distilled  water  at  4°  C.  The  kilogramme  contains  1,000  grammes,  or  is 
the  weight  of  a  decimetre  of  distilled  water  at  4°  C.  The  grainme  equals 
1 5 '443  grains. 

If  V  is  the  number  of  cubic  centimetres  (or  decimetres)  in  a  certain 
quantity  of  distilled  water  at  4°  C,  and  P  its  weight  in  grammes  (or  kilo- 
grammes), it  is  plain  that  P  =  V.  Now  consider  a  substance  whose  speci- 
fic gravity  is  D,  every  cubic  centimetre  of  this  substance  will  weigh  as 
much  as  D  cubic  centimetres  of  water,  and  therefore  V  centimetres  of 
this  substance  will  weigh  as  much  as  DV  centimetres  of  water.  Hence 
if  P  is  the  weight  of  the  substance  in  grammes  we  have  P  =  DV.  If, 
however,  V  is  the  volume  i-n  cubic  inches,  and  P  the  weight  in  grains,  we 
shall  have  P  =  252*5  DV. 

As  an  example,  we  may 'calculate  the  internal  diameter  of  a  glass  tube. 


-124]      Hydrometers,  Alcoholometers,  Salimeters,  &€. 


95 


Mercury  is  introduced,  and  the  length  and  we'ght  of  the  column  at  4°  C. 
are  accurately  determined.  As  the  column  is  cylindrical,  we  have  V  = 
Tcr-l,  where  r  is  the  radius,  and  /  the  length  of  the  column  in  centimetres. 
Hence  if  D  is  the  specific  gravity  of  mercury,  and  P  the  weight  of  the 
column  in  grammes,  we  have  P  =  Trr^lD,  and  therefore 


y- 


■D/ 

If  r  and  /  are  in  inches  and  P  in  grains,  we  shall  have  P  =  252*57rr'^/D, 
and  therefore 


V. 


;52'57rD/ 

In  a  similar  manner  the  diameter  of  very  fine  metallic  wires  can  be 
calculated. 

123.  Hydrometers  with  variable  volume.— The  hydrometers  of 
N  icholson  and  Fahrenheit  are  called  hydrometers  of  constant  volume,  but 
variable  weight,  because  they  are  always  immersed  to  the  same  extent, 
but  carry  different  weights.  There  are  also  hydro- 
meters of  variable  volume  but  of  constant  weight. 
These  instruments,  known  under  the  different  names 
of  acidometer ,  alcoholometer,  lactometer,  and  saccha- 
rometer,  are  not  used  to  determine  the  specific 
gravity  of  the  liquids,  but  to  show  whether  the  acids, 
alcohols,  solutions  of  sugar,  etc.,  under  investigation, 
are  more  or  less  concentrated. 

124.  Beaume's  hydrometer. — This,  which  was 
the  first  of  these  instruments,  may  serve  as  a  type  of 
them.  It  consists  of  a  glass  tube  (fig.  78)  loaded  at 
its  lower  end  with  mercury,  and  with  a  bulb  blown  in 
the  middle.  The  stem,  the  external  diameter  of 
which  is  as  regular  as  possible,  is  hollow,  and  the 
scale  is  marked  upon  it. 

The  graduation  of  the  instrument  differs  according 
as  the  liquid,  for  which  it  is  to  be  used,  is  heavier  or 
lighter  than  water.  In  the  first  case,  it  is  so  constructed  that  it  sinks  in 
water  nearly  to  the  top  of  the  stem,  to  a  point  A,  which  is  marked  zero. 
A  solution  of  fifteen  parts  of  salt  in  eighty-five  parts  of  water  is  made, 
and  the  instrument  immersed  in  it.  It  sinks  to  a  certain  point  on  the 
stem,  B,  which  is  marked  15  ;  the  distance  between  A  and  B  is  divided 
into  15  equa  parts,  and  the  graduation  continued  to  the  bottom  of  the 
stem.  Sometimes  the  graduation  is  on  a  piece  of  paper  in  the  interior  of 
the  stem. 

The  hydrometer  thus  graduated  only  serves  for  liquids  of  a  greater 
specific  gravity  than  water,  such  as  acids  and  saline  solutions.  For 
liquids  lighter  than  water  a  different  plan  must  be  adopted.  Beaume  > 
took  for  zero  the  point  to  which  the  apparatus  sank  in  a  solution  of  10 
parts  of  salt  in  90  of  water,  and  for  10°  he  took  the  level  in  distilled 
water.  This  distance  he  divided  into  10°,  and  continued  the  division  to 
the  top  of  the  scale. 


F5g.  78. 


96  On  Liq?nds.  [124- 

The  graduation  of  these  hydrometers  is  entirely  conventional,  and  they 
give  neither  the  densities  of  the  liquids,  nor  the  quantities  dissolved.  But 
they  are  very  useful  in  making  mixtures  or  solutions  in  given  propor- 
tions, the  results  they  give  being  sufficiently  near  in  the  majority  of 
cases.  For  instance,  it  is  found  that  a  well-made  syrup  marks  35°  on 
Beaume's  hydrometer,  from  which  a  manufacturer  can  readily  judge 
whether  a  syrup  which  is  being  evaporated  has  reached  the  proper  degree 
of  concentration. 

125.  Gay-]bussac's  alcobolometer. — This  instrument  is  used  to 
determine  the  strength  of  spirituous  liquors ;  that  is,  the  proportion  of 
pure  alcohol  which  they  contain.  It  differs  from  Beaume's  hydrometer 
in  the  graduation. 

Mixtures  of  absolute  alcohol  and  distilled  water  are  made,  containing 
5,  10,  20,  30,  etc.,  per  cent,  of  the  former.  The  alcoholometer  is  so  con- 
structed that,  when  placed  in  pure  distilled  water,  the  bottom  of  its 
stem  is  level  with  the  water,  and  this  point  is  zero.  It  is  next  placed 
in  absolute  alcohol,  which  marks  100°,  and  then  successively  in  mixtures 
of  different  strengths,  containing  10,  20,  30,  etc.,  per  cent.  The  divisions 
thus  obtained  are  not  exactly  equal,  but  their  difference  is  not  great,  and 
they  are  subdivided  into  ten  divisions,  each  of  which  marks  one  per  cent, 
of  absolute  alcohol  in  a  liquid.  Thus  a  brandy  in  which  the  alcoholo- 
meter stood  at  48°,  would  contain  48  per  cent,  of  absolute  alcohol,  and  the 
rest  would  be  water. 

All  these  determinations  are  made  at  15°  C,  and  for  that  temperature 
only  are  the  indications  correct.  For,  other  things  being  the  same,  if  the 
temperature  rises  the  liquid  expands,  and  the  alcoholometer  will  sink, 
and  the  contrary,  if  the  temperature  falls.  To  obviate  this  error,  Gay- 
Lussac  constructed  a  table  which  for  each  percentage  of  alcohol  gives 
the  reading  of  the  instrument  for  each  degree  of  temperature  from  0°  up 
to  30°.  When  the  exact  analysis  of  an  alcoholic  mixture  is  to  be  made,  the 
temperature  of  the  Hquid  is  first  determined,  and  then  the  point  to  which 
the  alcoholometer  sinks  in  it.  The  number  in  the  table  corresponding  to 
these  data  indicates  the  percentage  of  alcohol.  From  its  giving  the  per- 
centage of  alcohol,  this  is  often  called  the  ce7itesimal  alcoholometer. 

1 26.  Salimeters. — Salimeters,  or  instruments  for  indicating  the  per- 
centage of  salt  contained  in  a  solution,  are  made  on  the  principle  of 
the  centesimal  alcoholometer.  They  are  graduated  by  immersing  them 
in  pure  water,  which  gives  the  zero,  and  then  solutions  containing 
different  percentages,  5,  10,  20,  etc.,  of  the  salt,  and  marking  on  the 
scale  the  corresponding  points.  These  instruments  are  so  far  objection- 
able, that  every  salt  requires  a  special  instrument.  Thus  one  gradu- 
ated for  common  salt  would  give  totally  false  indications  in  a  solution  of 
nitre. 

Lactometers  and  vino7neters  are  similar  instruments,  and  are  used  for 
measuring  the  quantity  of  water  which  is  introduced  into  milk  or  wine  for 
the  purpose  of  adulteration.  But  their  use  is  limited,  because  the  density 
of  these  liquids  is  very  variable,  even  when  they  are  perfectly  natural, 
and  an  apparent  fraud  may  be  really  due  to  a  bad  natural  quantity  of  wine 


-128] 


Densimeter. 


97 


or  milk.     Urinometers^  which  are  of  extensive  use  in  medicine,  are  based 
on  the  same  principle. 

127.  Densimeter. — The  densimeter  is  an  ap- 
paratus for  indicating  the  specific  gravity  of  a 
liquid.  Gay-Lussac's  densimeter  has  the  same 
construction  as  Baume's  hydrometer,  but  is  gra- 
duated in  a  different  manner.  Rosseau's  densi- 
meter (fig.  79)  is  of  great  use  in  many  scientific 
investigations,  in  determining  the  specific  gravity  of 
a  small  quantity  of  a  liquid.  It  has  the  same  form 
as  Beaume's  hydrometer,  but  on  the  upper  part 
of  the  stem  there  is  a  small  tube  AC,  in  which  is 
placed  the  substance  to  be  determined.  A  mark  A 
on  the  side  of  the  tube  indicates  a  measure  of  a 
cubic  centimetre. 

The  instrument  is  so  constructed  that  when  AC 
is  empty  it  sinks  in^iistilled  water  to  a  point,  B,  just 
at  the  bottom  of  the  stenj.  It  is  then  filled  with 
distilled  water  to  the  height  measured  on  the  tube  AC, 
which  indicates  a  cubic  centimetre,  and  the  point  to  which  it  now  sinks  is 
20°.  The  interval  between  o  and  20  is  divided  into  20  equal  parts,  and 
this  graduation  is  continued  to  the  top  of  the  scale.  As  this  is  of  uniform 
bore  each  division  corresponds  to  ^  gramme  or  0*05. 

To  obtain  the  density  of  any  Hquid,  bile  for  example,  the  tube  is  filled 
with  it  up  to  the  mark  A ;  if  the  densimeter  sinks  to  20^  divisions,  its 
weight  is  0*05  +  20*5  =  1-025  5  that  is  to  say,  that  with  equal  volumes  the 
weight  of  water  being  i,  that  of  bile  is  1*025.  The  specific  gravity  of 
bile  is  therefore  i'025. 


Fig.  79. 


^¥^  ^i^ 


:af 

CAPILLARITY,  ENDOSMOSE,   EFFUSION,   ABSORPTION,    AND    IMBIBITION. 

128.  Capillary  ptaenomena. — When  solid  bodies  are  placed  in  con- 
tact with  liquids,  a  class  of  phenomeha  is  produced  called  capillary 
phenomena,  because  they  are  best  seen  In  tubes  whose  diameters  are 
comparable  with  the  diameter  of  a  hair.  Thfse  phenomena  are  treated 
of  in  physics  under  the  head  of  capillarity  orxapillary  attractio?i  :  the 
latter  expression  is  also  applied  to  the  force  which  produces  the  pheno- 
mena. \ 

The  phenomena  of  capillarit>'  are  very  various,  but  may  all  be  referred 
to  the  mutual  attraction  of  the  liquid  molecules  for  each  other,  and  to 
the  attraction  between  these  molecules  and  solid  bodies.  The  following 
are  some  of  these  phenomena  : — 

When  a  body  is  placed  in  a  liquid  which  wets  it,  for  example,  a  glass 
rod  in  water,  the  liquid,  as  if  not  subject  to  the  laws  of  gravitation,  is 
raised  upwards  against  the  sides  of  the  solid,  and  its  surface^j  instead  of 


98 


On  Liquids, 


[128- 


being  horizontal,  becomes  slightly  concave  (fig.  80).  If,  on  the  contrary, 
the  solid  is  one  which  is  not  moistened  by  the  liquid,  as  glass  by  mercury, 
the  liquid  is  depressed  against  the  sides  of  the  solid,  and  assumes  a  convex 
shape,  as  represented  in  fig.  81.  The  surface  of  the  liquid  exhibits  the 
same  concavity  or  convexity  against  the  sides  of  a  vessel  in  which  it  is 
contained,  according  as  the  sides  are  or  are  not  moistened  by  the  liquid. 


Fig  80.  Fig.  81 


Fig.  82. 


Fig.  83. 


These  phenomena  are  much  more  apparent  when  a  tube  of  small  dia- 
meter is  placed  in  a  liquid.  And  according  as  the  tubes  are  or  are  not 
moistened  by  the  liquid,  an  ascent  or  a  depression  of  the  liquid  is  produced, 
which  is  greater  in  proportion  as  the  diameter  is  less  (figs.  82  and  83). 

When  the  tubes  are  moistened  by  the  hquid,  its  surface  assumes  the 
form  of  a  concave  hemispherical  segment,  called  the  concave  meniscus 
(fig.  82) ;  when  the  tubes  are  not  moistened,  there  is  convex  meniscus 
(fig.  83). 

129.  ]Laws  of  tbe  ascent  and  depression  in  capillary  tubes. — 
Gay-Lussac  has  shown  experimentally  that  the  elevation  and  depression 
of  liquids  in  capillary  tubes  are  governed  by  the  three  following  laws  : — 

I.  When  a  capillary  tube  is  placed  in  a  liquid,  the  liquid  is  raised  or 
depressed  according  as  it  does  or  does  not  moisteii  the  tube. 

II.  For  the  same  liquid  the  elevation  varies  inversely  as  the  diameter 
of  the  tube,  when  the  diameter  does  not  exceed  two  millimetres. 

III.  The  elevation  varies  with  the  nature  of  the  liquid,  and  with  the 
temperature,  but  is  indepetidetit  of  the  natui'e  and  thickness  of  the  tube. 

These  laws  hold  good  in  vacuo  as  well  as  in  air. 

When  liquids  are  in  tubes  which  they  do  not  moisten,  the  depression 
is  in  the  inverse  ratio  of  the  diameter  of  the  tubes  ;  but  for  tubes  of  the 
same  diameter  the  depression  depends  on  the  substance  of  the  tubes. 
For  instance,  in  an  iron  tube  i  millimetre  in  diameter,  the  depression  of 
mercury  is  1-226  millimetre ;  but  in  a  platinum  tube  of  the  same  diameter 
the  depression  is  0*655  niillimetre.  Moreover,  the  depression  depends  on 
the  height  of  the  convex  meniscus  of  the  mercury,  and  this  height  varies 
for  the  same  tube,  according  as  the  meniscus  is  formed  during  an  ascend- 
ing or  descending  motion  of  the  mercurial  column  in  the  tube.  These 
results  undergo  modification  if  the  mercury  is  impure. 

1 30.  iiscent  and  depression  betixreen  parallel  or  inclined  surfaces. 
— When  two  bodies  of  any  given  shape  are  dipped  in  water,  analogous 
capillary  phenomena  are  produced,  provided  the  bodies  are  sufficiently 
near.     If,  for  example,  two  parallel  glass  plates  are  immersed  in  water 


-  \ 


o- 


-132] 


Capillarity. 


99 


at  a  very  small  distance  from  each  other,  water  will  rise  between  the  two 
plates  in  the  inverse  ratio  of  the  distance  which  separates  them.  The 
height  of  the  ascent  for  any  given  distance  is  half  what  it  would  be  in  a 
tube  whose  diameter  is  equal  to  the  distance  between  the  plates. 

If  the  parallel  plates  are  immersed  in  mercury,  a  corresponding  de- 
pression is  produced,  subject  to  the  same  laws. 

If  two  glass  plates  AB  and  AC  with  their  planes  vertical  and  inclined 
to,  one  another  at  a  small  angle,  as  represented  in  fig.  84,  have  their  ends 
dipped  into  a  liquid  which  wets  them,  the  liquid  will  rise  between  them. 
The  elevation  will  be  greatest  at  the  line  of  contact  of  plates  and  from 
thence  gradually  less,  the  surface  taking  the  form  of  an  equilateral  hyper- 
bola, wh'bse  asymptotes  are  respectively  the  line  of  intersection  of  the 
plates,  ana^he  line  in  which  the  plates  cut  the  horizontal  surface  of  the 
water.  \ 


V     V    f 


V 


Fig.  84. 


Fig.  85. 


Fig.  86. 


If  a  drop  of  water  be  placed  within  a  conical  glass  tube  whose  angle 
is  small  and  axis  horizontal,  it  will  have  a  concave  meniscus  at  each  end 
(fig.  85),  and  will  tend  to  move  towards  the  vertex.  But  if  the  drop  be  of 
mercury  it  will  have  a  convex  meniscus  at  each  end  (fig.  86)  and  will  tend 
to  move  from  the  vertex. 

131.  Attraction  and  repulsion  produced  by  capillarity. — The 
attractions  and  repulsions  observed  between  bodies  floating  on  the  surface 
of  liquids  are  due  to  capillarity,  and  are  subject  to  the  following  laws  : — 

i.  When  two  floating  balls  both  moistened  by  the  liquid,  for  example, 
cork  upon  water,  are  so  near  that  the  liquid  surface  between  them  is  not 
level,  an  attraction  takes  place. 

ii.  The  same  effect  is  produced  when  neither  of  the  balls  is  moistened, 
as  is  the  case  with  balls  of  wax  on  water. 

iii.  Lastly,  if  one  of  the  balls  is  moistened  and  the  other  not,  as  a  ball 
of  cork  and  a  ball  of  wax  in  water,  they  repel  each  other  if  the  curved 
surfaces  of  the  liquid  in  their  respective  neighbourhoods  intersect. 

As  all  these  capillary  phenomena  depend  on  the  concave  or  convex 
curvature  which  the  liquid  assumes  in  contact  with  the  solid,  a  short  ex- 
planation of  the  cause  which  determines  the  form  of  this  curvature  is 
necessary. 

1 32.  Cause  of  tbe  curvature  of  liquid  surfaces  in  contact  with 
solids.— The  form  of  the  surface  of  a  liquid  in   contact  with   a  solid 


lOO 


On  Liquids. 


[132 


depends  on  the  relation  between  the  attraction  of  the  solid  for  the  liquid, 
and  of  the  mutual  attraction  between  the  molecules  of  the  liquid. 

Let  7)1  be  a  liquid  molecule  (fig.  87)  in  contact  with  a  solid.  This 
molecule  is  acted  upon  by  three  forces  ;  by  gravity,  which  attracts  it  in  the 
direction  of  the  vertical  ni9  ;  by  the  attraction  of  the  liquid  F,  which  acts 
in  the  direction  inY  \  and  by  the  attraction  of  the  plate  ;z,  which  is  exerted 
in  the  direction  mn.  According  to  the  relative  intensities  of  these  forces, 
their  resultant  can  take  three  positions  : — 


Fig.  87 


i.  The  resultant  is  in  the  direction  of  the  vertical  ;;zR  (fig.  87).  In  this 
case  the  surface  in  is  plane  and  horizontal  :  for,  from  the  condition  of  the 
equihbrium  of  liquids,  the  surface  must  be  perpendicular  to  the  force 
which  acts  upon  the  molecules. 

ii.  If  the  force  n  increases  or  F  diminishes,  the  resultant  R  is  within 
the  angle  mnV  (fig.  88) ;  in  this  case  the  surface  takes  a  direction  perpen- 
dicular to  ;;2R,  and  becomes  concave. 

iii.  If  the  force  F  increases,  or  n  diminishes,  the  resultant  R  takes  the 
direction  ?/zR  (fig.  89)  within  the  angle  PwF,  and  the  surface  becoming 
perpendicular  to  this  direction  is  convex. 

133.  Influence  of  tbe  curvature  on  capillary  phenomena. — The 
elevation  or  depression  of  a  liquid  in  a  capillary  tube  depends  on  the 
concavity  or  convexity  of  the  meniscus.  In  a  concave  meniscus,  abed 
(fig.  90),  the  liquid  molecules  are  sustained  in  equilibrium  by  the  forces 
acting  on  them,  and  they  exercise  no  downward  pressure  on  the  inferior 


Fig.  90.  Fig.  91. 

layers.  On  the  contrary,  in  virtue  of  the  molecular  attraction,  they  act 
on  the  nearest  inferior  layers,  from  which  it  follows  that  the  pressure  on 
any  layer,  mn^  in  the  interior  of  the  tube,  is  less  than  if  there  were  no 
meniscus.  The  consequence  is,  that  the  liquid  ought  to  rise  in  the  tube 
until  the  internal  pressure  on  the  layer  w«,  is  equal  to  the  pressure,  op^ 
which  acts  externally  on  a  point,  p^  of  the  same  layer. 


-134]  VariouTVttptUary  Phenomena.  loi 


Where  the  meniscus  is  convex  (fig.  90)  equilibrium  exists  in  virtue  of 
the  molecular  forces  acting  on  the  liquid  ;  but  as  the  molecules  which 
would  occupy  the  same  space  ghik,  if  there  were  no  molecular  action,  do 
not  exist,  they  exercise  no  attraction  on  the  lower  layers.  Consequently, 
the  pressure  on  any  layer  ;;z;/,  in  the  interior  of  the  tube,  is  greater  than 
if  the  space  ghik  were  filled,  for  the  molecular  forces  are  more  powerful 
than  gravity.  The  liquid  ought,  therefore,  to  sink  in  the  tube  until  the 
internal  pressure  on  a  layer,  inn,  is  equal  to  the  external  pressure  on  any 
point,  p,  of  this  layer. 

134.  Various  capillary  phenomena. — The  following  facts  are  among 
the  many  which  are  caused  by  capillarity  : — 

When  a  capillary  tube  is  immersed  in  a  liquid  which  moistens  it,  and 
is  then  carefully  removed,  the  column  of  liquid  in  the  tube  is  seen  to  be 
longer  than  while  the  tube  was  immersed  in  the  liquid.  This  arises  from 
the  fact  that  a  drop  adheres  to  the  lower  extremity  of  the  tube  and  forms 
a  concave  meniscus,  which  concurs  with  that  of  the  upper  meniscus  to 
form  a  longer  column  (128). 

For  the  same  reason  a  liquid  does  not  overflow  in  a  capillary  tube, 
although  the  latter  may  be  shorter  than  the  hquid  column  which  would 
otherwise  be  formed  in  it.  For  when  the  liquid  reaches  the  top  of  the 
tube,  its  upper  surface,  though  previously  concave,  becomes  convex, 
and  as  the  downward  pressure  becomes  greater  than  if  the  surface  were 
plane,  the  ascending  motion  ceases. 

A  drop  of  mercury  on  a  table  has  a  spherical  shape,  which,  like  that  of 
the  heavenly  bodies,  is  due  to  attraction.  The  globule  of  mercury  behaves 
as  if  its  molecules  had  no  weight,  since  it  remains  spherical.  That  is,  the 
molecular  attraction  is  far  greater  than  the  weight,  which  only  alters  the 
shape  of  the  globule  if  the  quantity  of  mercury  is  much  greater  ;  it  theil 
flattens,  but  always  retains  at  its  edge  the  convex  form  which  attraction 
imparts  to  it. 

Insects  can  often  move  on  the  surface  of  water  without  sinking.  This 
is  a  capillary  phenomenon  caused  by  the  fact,  that  as  their  feet  are  not 
wetted  by  the  water,  a  depression  is  produced  which  keeps  them  up  in 
spite  of  their  weight.  Similarly  a  sewing  needle  gently  placed  on  water, 
does  not  sink,  because  its  surface  being  covered  with  an  oily  layer,  does 
not  become  wetted.  But  if  washed  in  alcohol,  or  in  potash,  it  at  once 
sinks  to  the  bottom. 

It  is  from  capillarity  that  oil  ascends  in  the  wicks  of  lamps,  that  water 
rises  in  wood,  sponge,  bibulous  paper,  sugar,  sand,  and  in  all  bodies  which 
possess  pores  of  a  perceptible  size.  Capillarity  is,  moreover,  the  cause  of 
the  following  phenomenon  : — When  a  porous  substance,  such  as  gypsum, 
or  chalk,  or  even  earth,  is  placed  in  a  porous  vessel  of  unbaked  porcelain, 
and  the  whole  is  dipped  in  water,  the  water  penetrates  into  the  pores, 
and  the  air  is  driven  inwards,  so  that  it  is  under  four  or  five  times  its 
usual  pressure  and  density. 

Jamin  has  proved  this  by  cementing  a  manometer  into  blocks  of  chalk, 
gyp-um,  etc.,  and  he  has  made  it  probable  that  a  pressure  of  this  kind, 
exerted  upon  the  roots,  promotes  the  ascent  of  sap  in  plants. 


102 


On  Liquids. 


[136- 


ENDOSMOSE,   EFFUSION,   ABSORPTION,  AND   IMBIBITION. 

135.  Endosmose  and  exosmose. — When  two  different  liquids  are 
separated  by  a  thin  porous  partition,  either  inorganic  or  organic,  a  current 
sets  in  from  each  hquid  to  the  other  ;  to  these  currents  the  names  etidos- 
niose  and  exosmose  are  respectively  given.  These  terms  which  signify 
impulse  from  within  and  impulse  frojfi  without,  were  originally  intro- 
duced by  M.  Dutrochet,  who  first  drew  attention  to  these  phenomena. 

They  may  be  well  illustrated  by  means  of 
the  endosmoitieter.      This    consists    of    a 
long  tube,  at  the  end  of  which  a  mem- 
A  branous  bag  is  firmly  bound  (fig.  92).    The 

S  bag  is  then  filled  with  a  strong  syrup,  or 

^  fespiaiiaaji  ^  some  other  solution  denser  than  water, 

I  '  such  as  milk  or  albumen,  and  is  immersed 

in  water.  The  liquid  is  found  gradually 
to  rise  in  the  tube,  to  a  height  which  may 
attain  several  inches  :  at  the  same  time, 
the  level  of  the  liquid  in  which  the  endos- 
mometer  is  immersed  becomes  lower.  It 
follows,  therefore,  that  some  of  the  exter- 
nal liquid  has  passed  through  the  mem- 
brane and  has  mixed  with  the  internal 
liquid.  The  external  liquid  moreover  is 
found  to  contain  some  of  the  internal 
liquid.  Hence  two  currents  have  been 
produced  in  opposite  directions.  The 
flow  of  the  liquid  towards  that  which  in- 
i  creases  in  volume  is  endosmose,  and  the 
'^^  current  in  the  opposite  direction  is  exos- 
mose. If  water  is  placed  in  the  bag,  and 
Fig.  92.  immersed  in  the  syrup,  endosmose  is  pro- 

duced from  the  water  towards  the  syrup, 
and  the  liquid  in  the  interior  diminishes  in  volume  while  the  level  of  the 
exterior  is  raised. 

The  height  of  the  ascent  in  the  endosmometer  varies  with  different 
liquids.  Of  all  vegetable  substances,  sugar  is  that  which,  for  the  same 
density,  has  the  greatest  power  of  endosmose,  while  albumen  has  the 
highest  power  of  all  animal  substances.  In  general,  it  may  be  said  that 
endosmose  takes  place  towards  the  denser  liquid.  Alcohol  and  ether 
form  an  exception  to  this  ;  they  behave  like  liquids  which  are  denser 
than  water.  With  acids,  according  as  they  are  more  or  less  dilute,  the 
endosmose  is  from  the  water  towards  the  acid,  or  from  the  acid  towards 
water. 

According  to  Dutrochet,  it  is  necessary  for  the  production  of  endos- 
mose :  i.  that  the  liquids  be  different  but  capable  of  mixing,  as  alcohol 
and  water ;  there  is  no  endosmose,  for  instance,  with  water  and  oil  : 


-136]  Diffusion  of  Liquids.  103 

ii,  that  the  liquids  be  of  different  densities  ;  and  iii.  that  the  membrane 
must  be  permeable  to  at  least  one  of  the  substances. 

The  current  through  thin  inorganic  plates  is  feeble,  but  continuous, 
while  organic  membranes  are  rapidly  decomposed,  and  endosmose  then 
ceases. 

The  well-known  fact  that  dilute  alcohol  kept  in  a  porous  vessel  be- 
comes concentrated,  depends  on  endosmose.  If  a  mixture  of  alcohol  and 
water  be  kept  for  some  time  in  a  bladder,  the  volume  diminishes,  but  it 
becomes  much  more  concentrated.  The  reason,  doubtless,  is  that  the 
bladder  permits  the  endosmose  of  water  rather  than  that  of  alcohol. 

Dutrochet's  method  is  not  adapted  for  quantitative  measurements,  for 
it  does  not  take  into  account  the  hydrostatic  pressure  produced  by  the 
column.  Jolly  has  examined  the  endosmose  of  various  liquids  by 
weighing  the  bodies  diffused.  He  calls  the  endosmotic  equivalent  of  a 
substance  the  number  which  expresses  how  many  parts  by  weight  of 
water  pass  through  the  bladder  in  exchange  for  one  part  by  weight  of  the 
substance.  The  following  are  some  of  the  endosmotic  equivalents  which 
he  determined  : — 


Chloride  of  sodium 

.       4-3 

Caustic  potass     . 

.     215-0 

Sulphate  of  magnesium 

.     T17 

Sulphuric  acid    . 

0-4 

copper 

.       9'5 

Alcohol 

4-2 

Sugar     .... 

.       7-1 

He  also  found  that  the  endosmotic  equivalent  increases  with  the  tempera- 
ture ;  and  that  the  quantities  of  substances  which  pass  in  equal  times 
through  the  bladder  are  proportional  to  the  strength  of  the  solution. 

136.  Diffusion  of  liquids. — If  oil  be  poured  on  water  no  tendency  to 
intermix  is  observed,  and  even  if  the  two  hquids  be  violently  agitated 
together,  on  allowing  them  to  stand,  two  separate  layers  are  formed. 
With  alcohol  and  water  the  case  is  different ;  if  alcohol,  which  is  specifi- 
cally lighter,  be  poured  upon  water,  the  liquids  gradually  intermix,  they 
diffuse  into  one  another. 

The  laws  of  this  diffusion,  in  which  no  porous  diaphragm  intervenes, 
have  been  completely  investigated  by  Graham.  The  method,  by  which 
his  latest  experiments  were  made,  was  the  following  : — In  a  glass  vessel, 
containing  about  700  cubic  centimetres  of  distilled  water,  about  100  cubic 
centimetres  of  the  solution  to  be  examined  were  carefully  added  by  means 
of  a  capillary  tube  so  as  to  form  a  layer  on  the  bottom.  After  a  certain 
interval  of  time,  successive  layers  were  carefully  drawn  off  by  a  syphon, 
and  their  contents  examined. 

The  general  results  of  these  investigations  may  be  thus  stated  : — 

i.  When  solutions  of  the  same  substance,  but  of  different  strengths,  are 
taken,  the  quantities  diffused  in  equal  times  are  proportional  to  the 
strengths  of  the  solutions. 

ii.  In  the  case  of  solutions  containing  equal  weights  of  different  sub- 
stances, the  quantities  diffused  vary  with  the  nature  of  the  substances. 
Saline  substances  may  be  divided  into  a  number  of  equidiffusive  groups^ 


104  On  Liquids.  [136- 

the  rates  of  diffusion  of  each  group  being  connected  with  the  others  by  a 
simple  numerical  relation. 

iii.  The  quantity  diffused  varies  with  the  temperature.  Thus,  taking 
the  rate  of  diffusion  of  hydrochloric  acid  at  1 5°  C.  as  unity  ;  at  49°  C.  it  is 
2-i8. 

iv.  If  two  substances  which  do  not  combine  be  mixed  in  solution,  they 
may  be  partially  separated  by  diffusion,  the  more  diffusive  one  passing 
out  most  rapidly.  In  some  cases  chemical  decomposition  even  may  be 
effected  by  diffusion.  Thus  bisulphate  of  potassium  is  decomposed  into 
free  sulphuric  acid  and  neutral  sulphate  of  potassium. 

V.  If  liquids  be  dilute  a  substance  will  diffuse  into  water,  containing 
another  substance  dissolved  as  into  pure  water ;  but  the  rate  is  materially 
reduced  if  a  portion  of  the  diffusing  substance  be  already  present. 

The  following  table  gives  the  approximate  times  of  equal  diffusion  : — 

Hydrochloric  acid  .  .  .  I'o  Sulphate  of  magnesium  .  7*0 
Chloride  of  sodium  .  .  2*3  Albumen  .  .  .  .  49-0 
Sugar 7-0      Caramel         ....     98-0 

It  will  be  seen  from  the  above  table  that  the  difference  between  the 
rates  of  diffusion  is  very  great.  Thus,  sulphate  of  magnesium,  one  of  the 
least  diffusible  saline  substances,  diffuses  7  times  as  rapidly  as  albumen 
and  14  times  as  rapidly  as  caramel.  These  last  substances,  like  hydrated 
silicic  acid,  starch,  dextrine,  gum,  etc.,  constitute  a  class  of  substances 
which  are  characterised  by  their  incapacity  for  taking  the  crystalline  form 
and  by  the  mucilaginous  character  of  their  hydrates.  Considering  gela- 
tine as  the  type  of  this  class,  Graham  has  proposed  to  call  them  colloids 
(k-o\Xt/,  glue),  in  contradistinction  to  the  far  more  easily  diffusible  aystal- 
loid  substances. 

Graham  has  proposed  a  method  of  separating  bodies  based  on  their 
unequal  diffusibility,  which  he  calls  dialysis.  His  dialyser  consists  of  a 
ring  of  gutta  percha  over  which  is  stretched  while  wet  a  sheet  of  parch- 
ment paper,  forming  thus  a  vessel  about  two  inches  high  and  ten  inches 
in  diameter,  the  bottom  of  which  is  of  parchment  paper.  After  pouring 
in  the  mixed  solution  to  be  dialysed,  the  whole  is  floated  on  a  vessel 
containing  a  very  large  quantity  of  water.  In  the  course  of  one  or  two 
days  a  more  or  less  complete  separation  will  have  been  effected.  Thus  a 
solution  of  arsenious  acid  mixed  with  various  kinds  of  food  readily  diffuses 
out. 

The  process  has  received  important  applications  to  laboratory  and 
pharmaceutical  purposes. 

For  further  information  on  this  subject  the  student  is  referred  to  a  very 
complete  article  on  the  diffusion  of  Hquids  in  the  third  volume  of  Watts's 
*  Dictionary  of  Chemistry.' 

137.  Endosmose  of  grases. — The  phenomena  of  endosmose  are  seen 
in  a  high  degree  in  the  case  of  gases.  When  two  different  gases  are  se- 
parated by  a  porous  diaphragm,  an  exchange  takes  place  between  them, 
and  ultimately  the  composition  of  the  gas  on  both  sides  of  the  diaphragm 
is  the  same ;  but  the  rapidity  with  which  different  gases  diffuse  into  each 
other  under  these  circumstances  varies  considerably.     The  laws  regu- 


-138] 


Effusion  and  Transpiration  of  Gases. 


105 


lating  this  phenomenon  have  been  investigated  by  Graham.  Numerous 
experiments  illustrate  it,  two  of  the  most  interesting  of  which  are  the  fol- 
lowing : — 

A  glass  cylinder  closed  at  one  end  is  filled  with  carbonic  acid  gas,  its 
open  end  tied  over  with  a  bladder,  and  the  whole  placed  under  a  jar  of 
hydrogen.  Diffusion  takes  place  between  them  through  the  porous  dia- 
phragm, and  after  the  lapse  of  a  certain  time  hydrogen  has  passed  throiigh 
the  bladder  into  the  cylindrical  vessel  in  much  greater  quantity  than  the 
carbonic  acid  which  has  passed  out,  so  that  the  bladder  becomes  very 


Fig.  93- 


Fig.  94. 


much  distended  outwards  (fig.  93).  If  the  cylinder  be  filled  with  hydro- 
gen and  the  bell-jar  with  carbonic  acid,  the  reverse  phenomenon  will  be 
produced — the  bladder  will  be  distended  inwards  (fig.  94). 

A  tube  about  12  inches  long,  closed  at  one  end  by  a  plug  of  dry  plaster 
of  Paris,  is  filled  with  dry  hydrogen,  and  its  open  end  then  immersed  in 
a  mercury  bath.  Endosmose  of  the  hydrogen  towards  the  air  takes  place 
so  rapidly  that  a  partial  vacuum  is  produced,  and  mercury  rises  in  the 
tube  to  a  height  of  several  inches  (fig.  95).  If  several  such  tubes  are 
filled  with  different  gases,  and  allowed  to  diffuse  into  the  air  in  a  similar 
manner,  in  the  same  time,  different  quantities  of  the  various  gases  will 
diffuse,  and  Graham  found  that  the  law  regulating 
these  diffusions  is,  that  the  force  of  difftcsion  is  in- 
versely as  the  square  roots  of  the  densities  of  gases. 
Thus,  if  two  vessels  of  equal  capacity,  containing 
oxygen  and  hydrogen,  be  separated  by  a  porous 
plug,  diffusion  takes  place  ;  and  after  the  lapse  of 
some  time,  for  every  one  part  of  oxygen  which  has 
passed  into  the  hydrogen,  four  parts  of  hydrogen 
have  passed  into  the  oxygen.  Now  the  density  of 
hydrogen  being  i,  that  of  oxygen  is  16,  hence  the 
force  of  diffusion  is  inversely  as  the  square  roots  of 
these  numbers.  It  is  four  times  as  great  in  the  one 
which  has  j^th  the  density  of  the  other. 

138.    Effusion  and  transpiration   of  grases. — 
Effusion  is  the  term  applied  to  the  phenomenon  of  ^^s-  95- 

the  passage  of  gases  into  vacuum,  through  a  minute  aperture  not  much 

F3 


io6  On  Liquids.  [138- 

more  or  less  than  0-013  millimetre  in  diameter,  in  a  thin  plate  of  metal 
or  of  glass. 

A  gas  can  only  flow  from  one  space  to  another  when  the  pressure  in 
the  one  is  greater  than  in  the  other.  The  term  effusio7i  is  applied  to  the 
phenomenon  of  the  passage  of  gases  through  minute  apertures  not  much 
more  or  less  than  o-oi  3  millimetres  in  diameter.  The  velocity  of  the  efflux  is 
measured  by  the  formula  7/  =  ,^?^/z,in  which  h  represents  the  pressure  under 
M^hich  the  gas  flows,  expressed  in  terms  of  the  height  of  a  column  of  the 
gas,  which  would  exert  the  same  pressure  as  that  of  the  effluent  gas.  Thus 
for  air  under  the  ordinary  pressure  flowing  into  a  vacuum,  the  pressure  is 
equivalent  to  a  column  of  mercury  76  centimetres  high  ;  and  as  mercury 
is  approximately  10,500  times  as  dense  as  air,  the  equivalent  column  of  air 
will  be  76  centimetres  x  10,500  =  7,980  metres.  Hence  the  velocity  of  efflux 
of  air  into  vacuum  is  =  a/2  x  9-8  x  7,980  =  395-5  metres.  This  velocity 
into  vacuum  only  holds,  however,  for  the  first  moment,  for  the  space  con- 
tains a  continually-increasing  quantity  of  air,  so  that  the  velocity  becomes 
continually  smaller,  and  is  null  when  the  pressure  on  each  side  is  the 
same.  If  the  height  of  the  column  of  air  h^,  corresponding  to  the  external 
pressure,  is  known,  the  velocity  may  be  calculated  by  the  formula 
V  =  ,j2g{h-h^. 

For  gases  lighter  than  air  a  greater  height  must  be  inserted  in  the 
formula,  and  for  heavier  gases  a  lower  height ;  and  this  change  must  be 
inversely  as  the  change  of  density.  Hence  the  velocities  of  efflux  of 
various  gases  must  be  inversely  as  the  square  roots  of  their  densities.  A 
simple  inversion  of  this  statement  is  that  the  dejtsities  of  two  gases  are 
inversely  as  the  squares  of  their  velocities  of  effusion.  On  this  Bunsen 
has  based  an  interesting  method  of  determining  the  densities  of  gases 
and  vapours. 

If  gases  issue  through  long,  fine  capillary  tubes  into  a  vacuum,  the 
rate  of  efflux,  or  the  velocity  of  transpiration ^  is  independent  of  the  rate 
of  diffusion. 

i.  For  the  same  gas,  the  rate  of  transpiration  increases^  other  things 
being  equal,  directly  as  the  pressure ;  that  is,  equal  volumes  of  air  of 
different  densities  require  times  inversely  proportional  to  their  densities. 

ii.  With  tubes  of  equal  diameters,  the  volume  transpired  in  equal  times 
is  inversely  as  the  length  of  the  tube. 

iii.  As  the  temperature  rises  the  transpiration  becomes  slower. 

iv.  The  rate  of  transpiration  is  independent  of  the  material  of  the  tube. 

139.  Absorption  and  imbibition. — The  words  absorption  and  imbi- 
bition are  used  almost  promiscuously  in  physics ;  they  indicate  the 
penetration  of  a  liquid  or  gas  into  a  porous  body.  Absorption  is  used 
both  for  liquids  and  gases,  while  imbibition  is  restricted  to  liquids. 

In  physiology  an  important  distinction  is  made  between  the  two  words  ; 
absorption  means  the  penetration  of  a  foreign  substance  into  the  tissues 
of  a  living  body,  while  imbibition  refers  to  penetration  into  bodies  deprived 
of  life,  whether  organic  or  not. 

140.  Absorption  of  grases. — The  surfaces  of  all  solid  bodies  exert  an 
attraction  on  the  molecules  of  gases  with  which  they  are  in  contact,  of 


-140]  Absorption  of  Gases.  107 

such  a  nature,  that  they  become  covered  with  a  more  or  less  thick  layer 
of  co7idensed gas.  When  a  porous  body,  which  consequently  presents  an 
immensely  increased  surface  in  proportion  to  its  size,  is  placed  in  a  gas 
over  mercury,  the  great  diminution  of  volume  which  ensues  indicates  that 
considerable  quantities  of  gas  are  absorbed. 

Now,  although  there  is  no  absorption  such  as  arises  from  chemical 
combinations  between  the  solid  and  gas  (as  with  phosphorus  and  oxy- 
gen), still  the  quantity  of  gas  absorbed  is  not  entirely  dependent  on  the 
physical  conditions  of  the  solid  body ;  it  is  influenced  in  spme  measure 
by  the  chemical  nature  both  of  the  solid  and  the  gas.  Of  all  bodies  box- 
wood charcoal  has  the  greatest  absorptive  power.  One  volume  of  this 
substance  at  the  ordinary  temperature  and  pressure  absorbs  the  following 
quantities  of  gas  : — 


Ammonia 

.     90  vol. 

Carbonic  oxide    •     . 

.     9-4  vol. 

Hydrochloric  acid     . 

.     85    . 

Oxygen   . 

•     9-2    „ 

Sulphurous        ,, 

.     65    „ 

Nitrogen. 

.     7-5    ,. 

Sulphuretted  hydrogen 

.     55    ,, 

Hydrogen 

•     175 » 

Carbonic  acid    . 

•    35    ,, 

The  absorption  of  gases  is  in  general  greatest  in  the  case  of  those  which 
are  most  easily  liquefied. 

The  absorptive  power  of  pine  charcoal  is  half  as  much  as  that  of  box- 
wood. The  charcoal  made  from  corkwood,  which  is  very  porous,  is  not 
absorbent ;  neither  is  graphite.  Platinum,  in  the  finely  divided  form 
known  as  platinum  sponge,  is  said  to  absorb  250  times  its  volume  of 
oxygen  gas.  Many  other  porous  substances,  such  as  meerschaum, 
gypsum,  silk,  etc.,  are  also  highly  absorbent.  Graham  found  that  at  a 
high  temperature  platinum  and  iron  allow  hydrogen  to  traverse  them  even 
more  readily  than  does  caoutchouc  in  the  cold.  Thus  while  a  square 
metre  of  caoutchouc  0-014  millimetres  in  thickness  allowed  129  cubic 
centimetres  of  hydrogen  at  20°  to  traverse  it  in  a  minute,  a  platinum  tube 
n  millimetres  in  thickness  of  the  same  surface  allowed  489  cubic  centi- 
metres to  traverse  it  at  a  bright  red  heat. 

This  is  probably  connected  with  the  property  which  some  metals, 
though  destitute  of  physical  pores,  possess  of  absorbing  gases  either  on 
their  surface  or  in  their  mass  ;  and  to  which  Graham  has  applied  the  term 
occlusion.  It  is  best  observed  by  allowing  the  heated  metal  to  cool  in 
contact  with  the  gas.  The  gas  cannot  then  be  extracted  by  the  air 
pump,  but  is  disengaged  on  heating.  In  this  way  Graham  found  that 
platinum  occluded  four  times  its  volume  of  hydrogen  ;  iron  wire  0-44  times 
its  volume  of  hydrogen,  and  4*15  volumes  of  carbonic  oxide;  silver 
reduced  from  the  oxide,  absorbed  about  seven  volumes  of  oxygen,  and 
nearly  one  volume  of  hydrogen  when  heated  to  dull  redness  in  these  gases. 
This  property  is  most  remarkable  in  palladium,  which  absorbs  hydrogen, 
not  only  in  cooling  after  being  heated,  but  also  in  the  cold.  When,  for 
instance,  a  palladium  electrode  is  used  in  the  decomposition  of  water,  one 
volume  of  the  metal  can  absorb  980  times  its  volume  of  the  gas.  This 
gas  is  again  drawn  out  on  being  heated,  in  which  respect  there  is  a 


io8 


On  Liquids. 


[140- 


resemblance  to  the  solution  of  gases  in  liquids.  By  the  occlusion  of 
hydrogen  the  volume  of  palladium  is  increased  by  0-09827  of  its  original 
amount,  from  which  it  follows  that  the  hydrogen  which  under  ordinary 
circumstances  has  a  density  of  0-000089546  of  water  has  here  a  density 
nearly  9,868  times  as  great,  or  about  0-88  that  of  water.  Hence  the 
hydrogen  must  be  in  the  liquid  or  even  solid  state  ;  it  probably  forms  thus 
an  alloy  with  palladium,  like  a  true  metal,  a  view  of  this  gas,  which  is 
strongly  supported  by  independent  chemical  considerations.  The  physical 
properties,  in  so  far  as  they  have  been  examined,  support  this  view  of  its 
being  an  alloy. 


-141]  Properties  of  Gases.  109 


BOOK   IV. 

ON   GASES. 


CHAPTER  I. 
PROPERTIES  OF  GASES.      ATMOSPHERE.      BAROMETERS. 

141.  Pbysical  properties  of  g-ases. — Gases  are  bodies  whose  mole- 
cules are  in  a  constant  state  of  repulsion,  in  virtue  of  which  they  possess 
the  most  perfect  mobility,  and  are  continually  tending  to  occupy  a  greater 
space.  This  property  of  gases  is  known  by  the  names  expansibility^ 
tension^  or  elastic  force,  from  which  they  are  often  called  elastic  fluids. 

Gases  and  liquids  have  several  properties  in  common,  and  some  in 
which  they  seem  to  differ  are  in  reality  only  different  degrees  of  the  same 
property.  Thus,  in  both,  the  particles  are  capable  of  moving  :  in  gases 
quite  freely  ;  in  liquids  not  quite  freely,  owing  to  a  certain  degree  of  vis- 
cosity. Both  are  compressible,  though  in  very  different  degrees  ;  if  a 
liquid  and  a  gas  both  exist  under  the  pressure  of  one  atmosphere,  and  then 
the  pressure  be  doubled,  the  water  is  compressed  by  about  the  200*000^^ 
part,  while  the  gas  is  compressed  by  one-half.  In  density  there  is  a  great 
difference  ;  water,  which  is  the  type  of  liquids,  is  770  times  as  heavy  as 
air,  the  type  of  gaseous  bodies,  while  under  a  pressure  of  one  atmosphere. 
The  property  by  which  gases  are  distinguished  from  liquids  is  their  ten- 
dency to  indefinite  expansion. 

Matter  assumes  the  solid,  liquid,  or  gaseous  form  according  to  the 
relative  strength  of  the  cohesive  and  repulsive  forces  exerted  between 
their  particles.  In  liquids  these  forces  balance  ;  in  gases  repulsion  pre- 
ponderates. 

By  the  aid  of  pressure  and  of  very  low  temperatures,  the  force  of  co- 
hesion may  be  so  far  increased  in  many  gases  that  they  are  converted 
into  liquids,  and  there  is  every  reason  for  believing  that  with  sufficient 
pressure  and  cold  they  might  all  be  liquefied.  On  the  other  hand,  heat, 
which  increases  the  force  of  repulsion,  converts  liquids,  such  as  water, 
alcohol,  and  ether,  into  the  aeriform  state  in  which  they  obey  all  the  laws 
of  gases.  This  aeriform  state  of  liquids  is  known  by  the  name  of  vapour^ 
while  gases  are  bodies  which,  under  ordinary  temperature  and  pressure, 
remain  in  the  aeriform  state. 

In  describing  the  properties  of  gases  we  shall,  for  obvious  reasons, 
have  exclusive  reference  to  atmospheric  air  as  their  type. 


On  Gases. 


[142- 


142.  Expansibility  of  gases.— This  property  of  gases,  their  tendency 
to  assume  continually  a  greater  volume,  is  exhibited  by  means  of  the 
following  experiment.  A  bladder  closed  by  a  stopcock  and  about  half 
full  of  air  is  placed  under  the  receiver  of  the  air  pump  (fig.  96),  and  a 

vacuum  is  produced,  on  which  the  bladder 
immediately  distends.  This  arises  from, 
the  fact  that  the  molecules  of  air  repel 
each  other  and  press  against  the  sides  of 
the  bladder.  Under  ordinary  conditions 
this  internal  pressure  is  counterbalanced 
by  the  air  in  the  receiver,  which  exerts  an 
equal  and  contrary  pressure.  But  when 
this  pressure  is  removed  by  exhausting 
the  receiver,  the  internal  pressure  becomes 
evident.  When  air  is  admitted  into  the 
receiver,  the  bladder  resumes  its  original 
form. 

143.  Compressibility  of  grases. — The 
compressibility  of  gases  is  readily  shown 
by  the  pneimiatic  syringe  (fig.  97).  This 
consists  of  a  stout  glass  tube  closed  at 
one  end,  and  provided  with  a  tight-fitting 
solid  piston.  ^i^hen  the  rod  of  the 
down   in   the  tube,  and  the  air  becomes 


Fie.  96. 

piston   is   pressed,   it   moves 


compressed  into  a  smaller  volume  ;  but  as  soon  as  the  force  is  removed 


Fig.  97. 


the  air  regains  its  original  volume,  and  the  piston  rises  to  its  former 
position. 

144.  VTeigrlit  of  g-ases. — From  their  extreme  fluidity  and  expansibility 
gases  seem  to  be  uninfluenced  by  the  force  of  gravity  ;  they  nevertheless 
possess  weight,  like  solids  and  liquids.  To  show  this,  a  glass  globe  of 
3  or  4  quarts  capacity  is  taken  (fig.  98),  the  neck  of  which  is  provided 
with  a  stopcock,  which  hermetically  closes  it,  and  by  which  it  can  be 
screwed  to  the  plate  of  the  air  pump.  The  globe  is  then  exhausted,  and 
its  weight  determined  by  means  of  a  delicate  balance.  Air  is  now  allowed 
to  enter,  and  the  globe  again  weighed.  The  weight  in  the  second  case 
will  be  found  to  be  greater  than  before,  and  if  the  capacity  of  the  vessel 
is  known,  the  increase  will  obviously  be  the  weight  of  that  volume 
of  air. 


145] 


Pressure  Exerted  by  Gases. 


II 


Fig.  98. 


By  a  modification  of  this  method,  and  with  the  adoption  of  certain  pre- 
cautions, the  weight  of  air  and  of  other  gases  has  been  de- 
termined. Perhaps  the  most  accurate  are  those  of  Reg- 
nault,  who  found  that  a  htre  of  dry  air  at  0°  C,  and  under 
a  pressure  of  760  milhmetres  weighs  1-293187  grammes. 
Since  a  Htre  (or  1000  cubic  centimetres)  at  0°  weighs 
0*999877  grammes,  the  density  of  air  is  0-00129334  that  of 
water  under  the  same  circumstances  ;  that  is,  water  is  773 
times  as  heavy  as  air.  Expressed  in  Enghsh  measures,  100 
cubic  inches  of  dry  air  under  the  ordinary  atmospheric  pres- 
sure of  30  in.  and  at  the  temperature  of  16°  C,  weigh  31 
grains  ;  the  same  volume  of  carbonic  acid  gas  under  the 
same  circumstances  weighs  47*25  grains  ;  100  cubic  inches 
of  hydrogen  the  Hghtest  of  all  gases,  weigh  2*14  grains  : 
and  100  cubic  inches  of  hydriodic  acid  gas  weigh  146 
grains. 

145.  Pressure  exerted  by  grases  — Gases  exert  on  their 
own  molecules  and  on  the  sides  of  vessels  which  contain 
them,  pressures  which  may  be  regarded  from  two  points 
of  view  :  First,  we  may  neglect  the  weight  of  the  gas  ; 
secondly,  we  may  take  account  of  its  weight.  If  we  neglect  the  weight  of 
any  gaseous  mass  at  rest,  and  only  consider  its  expansive  force,  it  will  be 
seen  that  the  pressures  due  to  this  force  act  with  the  same  intensity  on 
all  points,  both  of  the  mass  itself  and  of  the  vessel  in  which  it  is  con- 
tained. For  it  is  a  necessary  consequence  of  the  elasticity  and  fluidity  of 
gases,  that  the  repulsive  force  between  the  molecules  is  the  same  at  all 
points,  and  acts  equally  in  all  directions.  '  This  principle  of  the  equality 
of  the  pressure  of  gases  in  all  directions  may  be  shown  experimentally  by 
means  of  an  apparatus  resembling  that  by  which  the  same  principle  is 
demonstrated  for  Hquids  (fig.  51). 

If  we  consider  the  weight  of  any  gas  we  shall  see  that  it  gives  rise  to 
pressures  which  obey  the  same  laws  as  those  produced  by  the  weight  of 
liquids.  Let  us  imagine  a  cylinder,  with  its  axis  vertical,  several  miles 
high,  closed  at  both  ends  and  full  of  air.  Let  us  consider  any  small 
portion  of  the  air  enclosed  between  two  horizontal  planes.  This  portion 
must  sustain  the  weight  of  all  the  air  above  it,  and  transmit  that  weight 
to  the  air  beneath  it,  and  likewise  to  the  curved  surface  of  the  cylinder 
which  contains  it  ;  and  at  each  point  in  a  direction  at  right  angles  to  the 
surface.  Thus  the  pressure  increases  from  the  top  of  the  column  to  the 
base  ;  at  any  given  layer,  it  acts  equally  on  equal  surfaces,  and  at  right 
angles  to  them,  whether  they  are  horizontal,  vertical,  or  inclined.  The 
pressure  acts  on  the  sides  of  the  vessel,  and  on  any  small  surface  it  is 
equal  to  the  weight  of  a  column  of  gas,  whose  base  is  this  surface,  and 
whose  height  its  distance  from  the  summit  of  the  column.  The  pressure 
is  also  independent  of  the  shape  and  dimensions  of  the  supposed  cylinder, 
provided  the  height  remains  the  same. 

For  a  small  quantity  of  gas  the  pressures  due  to  its  weight  are  quite 
insignificant,  and  may  be  neglected;  but  for  large  quantities,  like  the 
atmosphere,  the  pressures  are  considerable,  and  must  he  allowed  for. 


112  On  Gases,  [146- 

146.  Tlte  atmospbere.  Its  composition. — The  atmosphere  is  the 
layer  of  air  which  surrounds  our  globe  in  every  part.  It  partakes  of  the 
rotatory  motion  of  the  globe,  and  would  remain  fixed  relatively  to  terrestrial 
objects,  but  for  local  circumstances,  which  produce  winds,  and  are  con- 
stantly disturbing  its  equihbrium. 

Air  was  regarded  by  the  ancients  as  one  of  the  four  elements.  Modern 
chemistry,  however,  has  shown  that  it  is  a  mixture  of  oxygen  and  nitro- 
gen gases  in  the  proportion  of  20-8  volumes  of  the  former  to  79*2  volumes 
of  the  latter.  By  weight  it  consists  of  23  parts  of  oxygen  to  JJ  parts  of 
nitrogen. 

The  atmosphere  also  contains  a  quantity  of  aqueous  vapour,  which 
varies  with  the  temperature,  the  season,  the  locality,  and  the  direction  of 
the  winds.  It  further  contains  a  minute  quantity  of  ammoniacal  gas,  and 
from  3  to  6  parts  in  10,000  of  its  volume  of  carbonic  acid. 

The  carbonic  acid  arises  from  the  respiration  of  animals,  from  the 
processes  of  combustion,  and  from  the  decomposition  of  organic  substances. 
M.  Boussingault  has  estimated  that  in  Paris,  the  following  quantities  of 
carbonic  acid  are  produced  every  24  hours  : — 

By  the  population  and  by  animals    .         .     11,895,000  cubic  feet 
By  processes  of  combustion      .        .         .     92,101,000         „ 

103,996,000 

Notwithstanding  this  enormous  continual  production  of  carbonic  acid 
on  the  surface  of  the  globe,  the  composition  of  the  atmosphere  does  not 
vary ;  for  plants  in  the  process  of  vegetation  decompose  the  carbonic 
acid,  assimilating  the  carbon,  and  restoring  to  the  atmosphere  the  oxygen 
which  is  being  continually  consumed  in  the  processes  of  respiration  and 
combustion. 

147.  Atmospberic  pressure. — If  we  neglect  the  perturbations  to 
which  the  atmosphere  is  subject,  as  being  inconsiderable,  we  may  con- 
sider it  as  a  fluid  sea  of  a  certain  depth,  surrounding  the  earth  on  all 
sides,  and  exercising  the  same  pressure  as  if  it  were  a  liquid  of  very  small 
density.  Consequently,  the  pressure  on  the  unit  of  area  is  constant  at  a 
given  level,  being  equal  to  the  weight  of  the  column  of  atmosphere  above 
that  level  whose  horizontal  section  is  the  unit  of  area.  It  will  act  at  right 
angles  to  the  surface,  whatever  be  its  position.  It  will  diminish  as  we 
ascend,  and  increase  as  we  descend  from  that  level.  Consequently,  at 
the  same  height,  the  atmospheric  pressures  on  unequal  plane  surfaces  will 
be  proportional  to  the  areas  of  those  surfaces,  provided  they  be  small  in 
proportion  to  the  height  of  the  atmosphere. 

In  virtue  of  the  expansive  force  of  the  air,  it  might  be  supposed  that 
the  molecules  would  expand  indefinitely  into  the  planetary  spaces.  But, 
in  proportion  as  the  air  expands,  its  expansive  force  decreases,  and  is 
further  weakened  by  the  low  temperature  of  the  upper  regions  of  the 
atmosphere,  so  that,  at  a  certain  height,  an  equilibrium  is  established 
between  the  expansive  force  which  separates  the  molecules,  and  the  action 
of  gravity  which  draws  them  towards  the  centre  of  the  earth.  It  is  there- 
fore concluded  that  the  atmosphere  is  limited. 

From  the  weight  of  the  atmosphere,  and  its  decrease  in  density,  and 


-148] 


Crushing  Force  of  the  A  tmosphere. 


113 


from  the  observation  of  certain  phenomena  of  twilight,  its  height  has  been 
estimated  at  from  30  to  40  miles.  Above  that  height  the  air  is  extremely 
rarefied,  and  at  a  height  of  60  miles  it  is  assumed  that  there  is  a  perfect 
__^___  vacuum.     On  the  other  hand  meteorites  have  - 

been  seen  at  a  height  of  200  miles,  and  as 
their  luminosity  is  due  to  the  action  of  air, 
there  must  be  air  at  such  a  height.  Again, 
from  certain  observations  made  in  the  tropi- 
cal zone,  and  particularly  at  Rio  Janeiro,  on 
the  twilight  arc,  M.  Liais  estimates  the  height 
of  the  atmosphere  at  between  198  and  212 
miles,  considerable  higher,  therefore,  than 
what  has  hitherto  been  believed. 

As  it  has  been  previously  stated  that  100 
cubic  inches  of  air  weigh  31  grains,  it  will 
readily  be  conceived  that  the  whole  atmo- 
sphere exercises  a  considerable  pressure  on 
the  surface  of  the  earth.  The  existence  of 
this  pressure  is  shown  by  the  following  ex- 
periments. 

148.  Crushing:  force  of  tbe  atmospbere. 
-On  one  end  of  a  stout  glass  cylinder,  about  5  inches  high,  and  open  at 


Fig.  100.  Fig.  loi. 

both  ends,  a  piece  of  bladder  is  tied  quite  air-tight.  The  other  end,  the 
edge  of  which  its  ground  and  well-greased,  is  pressed  on  the  plate  of  the 
air  pump  (fig.  99).  As  soon  as  a  vacuum  is  produced  in  the  vessel,  by 
working  the  air  pump,  the  bladder  is  depressed  by  the  weight  of  the  atmo- 
sphere above  it,  and  finally  bursts  with  a  loud  report  caused  by  the  sudden 
entrance  of  the  air. 


114 


On  Gases. 


[149- 


149.  nxagrdeburgr  hemispheres. — The  preceding  experiment  only 
serves  to  illustnate  the  downward  pressure  of  the  atmosphere.  By  means 
of  the  Magdeburg  heinispheres  (figs.  100  and  loi),  the  invention  of  which  is 
due  to  Otto  von  Guericke,  burgomaster  of  Magdeburg,  it  can  be  shown 
that  the  pressure  acts  in  all  directions.  This  apparatus  consists  of  two 
hollow  brass  hemispheres  of  4  to  4^  inches  diameter,  the  edges  of  which 
are  made  to  fit  tightly,  and  are  well  greased.  One  of  the  hemispheres  is 
provided  with  a  stopcock,  by  which  it  can  be  screwed  on  the  air  pump, 
and  on  the  other  there  is  a  handle.  As  long  as  the  hemispheres  contain 
air  they  can  be  separated  without  any  difficulty,  for  the  external  pressure 
of  the  atmosphere  is  counterbalanced  by  the  elastic  force  of  the  air  in 
the  interior.  But  when  the  air  in  the  interior  is  pumped  out  by  means 
of  the  air  pump,  the  hemispheres  cannot  be  separated  without  a  power- 
ful effort ;  and  as  this  is  the  case  in  whatever  position  they  are  held,  it 
follows  that  the  atmospheric  pressure  is  transmitted  in  all  directions. 


DETERMINATION   OF  THE  ATMOSPHERIC   PRESSURE.      BAROMETERS. 

150.  Torricelli's  experiment. — The  above  experiments  demonstrate 
the  existence  of  the  atmospheric  pressure,  but  they  give  no  precise  indica- 
tions as  to  its  amount.  The  following 
experiment,  which  was  first  made,  in 
1643,  by  Torricelli,  a  pupil  of  Galileo, 
gives  an  exact  measure  of  the  weight 
of  the  atmosphere. 

A  glass  tube  is  taken,  about  a  yard 
long  and  a  quarter  of  an  inch  mternal 
diameter  (fig.  102).  It  is  sealed  at  one 
end,  and  is  quite  filled  with  mercury. 
The  aperture  C  being  closed  by  the 
thumb,  the  tube  is  inverted,  the  open 
end  placed  in  a  small  mercury  trough, 
and  the  thumb  removed.  The  tube 
being  in  a  vertical  position,  the  column 
of  mercury  sinks,  and,  after  oscillating 
some  time,  it  finally  comes  to  rest  at  a 
height  A,  which  at  the  level  of  the 
sea  is  about  30  inches  above  the  mer- 
cury in  the  trough.  The  mercury  is 
raised  in  the  tube  by  the  pressure  cf 
the  atmosphere  on  the  mercury  in 
the  trough.  There  is  no  contrary 
pressure  on  the  mercury  in  the  tube, 
because  it  is  closed.  But  if  the  end 
of  the  tube  be  opened,  the  atmosphere 
will  press  equally  inside  and  outside 
the  tube,  and  the  mercury  will  sink  to 
the  level  of  that  in  the  trough.  It 
has  been  shown  in  hydrostatics  (104)  that  the  heights  of  two  columns  of 


-152]  A  mount  of  the  A  tmospheric  Pr^iire.  1 1 5 

liquid  in  communication  with  each  other  are  inversely  as  their  densities, 
and  hence  it  follows,  that  the  pressure  of  the  atmosphere  is  equal  to  that 
of  a  column  of  mercury,  the  height  of  which  is  30  inches.  If,  however, 
the  weight  of  the  atmosphere  diminishes,  the  height  of  the  column  which 
it  can  sustain  must  also  diminish. 

151.  Pascal's  experiments. — Pascal,  who  wished  to  prove  that  the 
force  which  sustained  the  mercury  in  the  tube  was  really  the  pressure 
of  the  atmosphere,  made  the  following  experiments,  i.  If  it  were  the 
case,  the  column  of  mercury  ought  to  descend  in  proportion  as  we  ascend 
in  the  atmosphere.  He  accordingly  requested  one  of  his  relations  to 
repeat  Torricelli's  experiment  on  the  summit  of  the  Puy  de  Dome  in 
Auvergne.  This  was  done,  and  it  was  found  that  the  mercurial  column 
was  about  3  inches  lower,  thus  proving  that  it  is  really  the  weight  of 
the  atmosphere  which  supports  the  mercury,  since,  when  this  weight 
diminishes,  the  height  of  the  column  also  diminishes,  ii.  Pascal  re- 
peated Torricelli's  experiment  at  Rouen,  in  1646,  with  other  liquids.  He 
took  a  tube  closed  at  one  end,  nearly  50  feet  long,  and  having  filled  it 
with  water,  placed  it  vertically  in  a  vessel  of  water,  and  found  that  the 
water  stood  in  the  tube  at  a  height  of  34  feet;  that  is,  13-6  times  as 
high  as  mercury.  But  since  mercury  is  13-6  times  as  heavy  as  water, 
the  weight  of  the  column  of  water  was  exactly  equal  to  that  of  the 
column  of  mercury  in  Torricelli's  experiment,  and  it  was  consequently 
the  same  force,  the  pressure  of  the  atmosphere,  which  successively  sup- 
ported the  two  liquids.  Pascal's  other  experiments  with  oil  and  with 
wine  gave  similar  results. 

152.  Amount  of  the  atmospheric  pressure. — Let  us  assume  that  the 
tube  in  the  above  experiment  is  a  cylinder,  the  section  of  which  is  equal 
to  a  square  inch,  then  since  the  height  of  the  mercurial  column  in  round 
numbers  is  30  inches,  the  column  will  contain  30  cubic  inches,  and  as  a 
cubic  inch  of  mercury  weighs  3433*5  grains  =  0-49  of  a  pound,  the  pressure 
of  such  a  column  on  a  square  inch  of  surface  is  equal  to  147  pounds.  In 
round  numbers  the  pressure  of  the  atmosphere  is  taken  at  1 5  pounds  on 
the  square  inch.  A  surface  of  a  foot  square  contains  144  square  inches, 
and  therefore  the  pressure  upon  it  is  equal  to  2,160  pounds,  or  nearly 
a  ton.  Expressed  in  the  metrical  system,  the  standard  atmospheric 
pressure  at  0°  and  the  sea  level  is  760  millimetres,  which  is  equal  to  29-9217 
inches ;  and  a  similar  calculation  to  the  above  shows  that  the  pressure  on 
a  square  centimetre  is  =  i  -03296  kilogrammes. 

A  gas  or  Hquid  which  acts  in  such  a  manner  that  a  square  inch  of 
surface  is  exposed  to  a  pressure  of  15  pounds,  is  called  a  pressure  of  one 
atmosphe^-e.  If,  for  instance,  the  elastic  force  of  the  steam  of  a  boiler 
is  so  great  that  each  square  inch  of  the  internal  surface  is  exposed  to  a 
pressure  of  90  pounds  (  =  6x  15),  we  say  it  is  under  a  pressure  of  six 
atmospheres. 

The  surface  of  the  body  of  a  man  of  middle  size  is  about  16  square 
feet ;  the  pressure,  therefore,  which  a  man  supports  on  the  surface  of  his 
body  is  35,560  pounds,  or  nearly  16  tons.  Such  an  enormous  pressure 
might  seem  impossible  to  be  borne  ;  but  it  must  be  remembered  that  in 


Ii6  jj^  On  Gases.  [152 

all  directions  there  are  equal  and  contrary  pressures  which  counter- 
balance one  another.  It  might  also  be  supposed  that  the  effect  of  this 
force,  acting  in  all  directions,  would  be  to  press  the  body  together  and 
crush  it.  But  the  solid  parts  of  the  skeleton  could  resist  a  far  greater 
pressure  ;  and  as  to  the  air  and  liquids  contained  in  the  organs  and 
vessels,  the  air  has  the  same  density  as  the  external  air,  and  cannot  be 
further  compressed  by  the  atmospheric  pressure  ;  and  from  what  has 
been  said  about  liquids  (94)  it  is  clear  that  they  are  virtually  incom- 
pressible. When  the  external  pressure  is  removed  from  any  part  of  the 
body,  either  by  means  of  a  cupping  vessel  or  by  the  air  pump,  the  pres- 
sure from  within  is  seen  by  the  distension  of  the  surface. 

153.  Different  kinds  of  barometers. — The  instruments  used  for 
measuring  the  atmospheric  pressure  are  called  baj-ometers.  In  ordinary 
barometers,  the  pressure   is   measured  by  the  height  of  a   column  of 

"mercury,  as  in  Torricelli's  experiment :  the  barometers  which  we  are 
about  to  describe  are  of  this  kind.  But  there  are  barometers  without 
any  liquid,  one  of  which,  the  aneroid  (173),  is  remarkable  for  its  simplicity 
and  portability. 

1 54.  Cistern  barometer. — The  cistern  barometer  consists  of  a  straight 
glass  tube  closed  at  one  end,  about  33  inches  long,  filled  with  mercury, 
and  dipping  into  a  cistern  containing  the  same  metal.  In  order  to  render 
the  barometer  more  portable,  and  the  variations  of  the  level  in  the  cistern 
less  perceptible  when  the  mercury  rises  or  falls  in  the  tube,  several  dif- 
ferent forms  have  been  constructed.  Fig.  103  represents  one  form  of  the 
cistern  barometer.  The  apparatus  is  fixed  to  a  mahogany  stand,  on  the 
upper  part  of  which  there  is  a  scale  graduated  in  millimetres  or  inches 
from  the  level  of  the  mercury  in  the  cistern  ;  a  moveable  index,  i,  shows 
on  the  scale  the  level  of  the  mercury.  A  thermometer  on  one  side  of  the 
tube  indicates  the  temperature. 

There  is  one  fault  to  which  this  barometer  is  liable,  in  common  with 
all  others  of  the  same  kind.  The  zero  of  the  scale  does  not  always  cor- 
respond to  the  level  of  the  mercury  in  the  cistern.  For  as  the  atmo- 
spheric pressure  is  not  always  the  same,  the  height  of  the  mercurial 
column  varies  :  sometimes  mercury  is  forced  from  the  cistern  into  the 
tube,  and  sometimes  from  the  tube  into  the  cistern,  so  that,  in  the 
majority  of  cases,  the  graduation  of  the  barometer  does  not  indicate  the 
true  height.  If  the  diameter  of  the  cistern  is  large,  relatively  to  that  of  the 
tube,  the  error  from  this  source  is  lessened.  The  height  of  the  barometer 
is  the  distance  between  the  levels  of  the  mercury  in  the  tube  and  in  the 
cistern.  Hence  the  barometer  should  always  be  perfectly  vertical ;  for, 
if  not,  the  tube  being  inclined,  the  column  of  mercury  is  elongated 
(fig.  104),  and  the  number  read  off  on  the  scale  is  too  great.  As  the 
pressure  which  the  mercury  exerts  by  its  weight  at  the  base  of  the  tube 
is  independent  of  the  form  of  the  tube  and  of  its  diameter  (104),  provided 
it  is  not  capillary,  the  height  of  the  barometer  is  independent  of  the 
diameter  of  the  tube  and  of  its  shape,  but  is  inversely  as  the  density  of 
the  liquid.  With  mercury  the  mean  height  at  the  level  of  the  sea  is 
29*92,  or  in  round  numbers  30,  inches  ;  in  a  water  barometer  it  would  be 
about  34  feet,  or  10-33  metres. 


-155] 


Barometers. 


117 


155.  Fortin's  barometer. — Fortiii^s  barometer  differs  from  that  just 
described,  in  the  shape  of  the  cistern.  The  base  of  the  cistern  is  made  of 
leather,  and  can  be  raised  or  lowered  by  means  of  a  screw ;  this  has  the 
advantage,  that  a  constant  level  can  be  obtained,  and  also  that  the  in- 
strument is  made  more  portable.  For,  in  travelling,  it  is  only  necessary 
to  raise  the  leather  until  the  mercury,  which  rises  with  it,  quite  fills  the 
cistern;  the  barometer  may  then  he  inclined,  and  even  inverted  without. 
aii,y  fear  that  a  bubble  of  air  may  enter,  or  that  the  shock  of  the  mercury 
may  crack  the  tube. 


'^M^o.>^-'^^ 


^ 


A.' 

IB 


Fig.  103. 


Fig.  104. 


Fig.  105. 


Fio-.  105  represents  the  arrangement  of  the  barometer,  the  tube  of  which 
is  placed  in  a  brass  case.  At  the  top  of  this  case,  there  are  two  longitudi- 
nal apertures,  on  opposite  sides,  so  that  the  level  of  the  mercury,  B,  is 
seen.  The  scale  on  the  case  is  graduated  in  millimetres.  An  index  A, 
moved  by  the  hand,  gives,  by  means  of  a  vernier,  the  height  of  the  mer- 


ii8 


On  Gases. 


[155 


cury  to  j'^th  of  a  millimetre.     At  the  bottom  of  the  case  there  is  a  cistern 
by  containing  mercury,  O. 

Fig.  io6  shows  the  details  of  the  cistern  on  a  larger  scale.  It  consists 
of  a  glass  cylinder  b,  through  which  the  mercury  can  be  seen ;  this  is 
closed  at  the  top  by  a  box-wood  disc  fitted  on  the  under-surface  of  the 
brass  cover  M.  Through  this  passes  the  barometer  tube  E,  which  is 
^drawn  out  at  the  end,  and  dips  in  the  mercury;  the  cistern  and  the  tube 
are  connected  by  a  piece  of  buckskin  ce,  which  is  firmly  tied  at  ^  to  a 
contraction  in  the  tube,  and  at  <?  to  a  brass  tubulure  in  the  cover  of  the  cis- 
tern.    This  mode  of  closing  prevents  the  mercury  from  escaping  when 


Fig.  io6. 


Fig.  107. 


the  barometer  is  inverted,  while  the  pores  of  the  leather  transmit  the  at- 
mospheric pressure.  The  bottom  of  the  cylinder  b  is  cemented  on  a  box- 
wood cylinder ^s-^",  on  a  contraction  in  which,  ii^  is  firmly  tied  the  buckskin 
in7i,  which  forms  the  base  of  the  cistern.  On  this  skin  is  fastened  a 
wooden  button  x,  which  rests  against  the  end  of  a  screw  C.  According  as 
this  is  turned  in  one  direction  or  the  other,  the  skin  m7i  is  raised  or  low- 
ered ;  and  with  it  the  mercury.    In  using  this  barometer  the  mercury  is  first 


156] 


Barometers. 


119 


made  exactly  level  with  the  point  a,  which  is  effected  by  turning  the 
screw  C  either  in  one  direction  or  the  other.  The  graduation  of  the  scale 
is  counted  from  this  point  a,  and  thus  the  distance  of  the  top  B  of  the 
column  of  mercury  from  a  gives  the  height  of  the  barometer.  The  bottom 
of  the  cistern  is  surrounded  by  a  brass  case,  which  is  fastened  to  the  cover 
M  by  screws,  k,  k,  k.  We  have  already  seen  (154)  the  importance  of 
having  the  barometer  quite  vertical,  which  is  effected  by  the  following 
means,  known  as  Cardan^s  suspension. 

The  metal  case  containing  the  barometer  is  fixed  in  a  copper  sheath  X 
by  two  screws  a  and  b  (fig.  107).  This  is  provided  with  two  axles  (only 
one  of  which,  0,  is  seen  in  the  figure),  which  turn  freely  in  two  holes  in  a 
ring  Y.     In  a  direction  at  right  angles  to  that  of  the  axles,  00,  ^^ 

the  ring  has  also  two  similar  axles,  w  and  n,  resting  on  a  sup- 
port Z.  By  means  of  this  double  suspension,  the  barometer 
can  oscillate  freely  about  the  axes,  7nn  and  00,  in  two  directions 
at  right  angles  to  each  other.  But  as  care  is  taken  that  the 
point  at  which  these  axes  cross  corresponds  to  the  tube  itself, 
the  centre  of  gravity  of  the  system,  which  must  always  be 
lower  than  the  axis  of  suspension,  is  below  the  point  of  inter- 
section, and  the  barometer  is  then  perfectly  vertical. 

156.  Gay-Iiussac's  syphon  barometer. — The  syphon 
barometer  is  a  bent  glass  tube,  one  of  the  branches  of  which 
is  much  longer  than  the  other.  The  longer  branch,  which 
is  closed  at  the  top,  is  filled  with  mercury  as  in  the  cistern 
barometer,  while  the  shorter  branch,  which  is  open,  serves 
as  a  cistern.  The  difference  between  the  two  levels  is  the 
height  of  the  barometer. 

Fig.  108  represents  the  syphon  barometer  as  modified  by 
Gay-Lussac.     In  order  to  render  it  more  available  for  tra- 
velling by  preventing  the  entrance  of  air,  he  joined  the  two 
branches  by  a  capillary  tube ;   when  the  instrument  is  in- 
verted, the  tube  always  remains  full  in  virtue  of  its  capil- 
larity, and  air  cannot  penetrate  into  the  longer 
branch.       A    sudden    shock,    however,    might 
separate    the    mercury  and    admit    some    air. 
To  avoid  this,  M.  Bunten  has   introduced   an 
ingenious     modification     into     the     apparatus. 
The  longer  branch  is  drawn  out  to  a  fine  point, 
and  is  joined  to  a  tube  K,  of  the  form  repre- 
sented  in  fig.    109.      By   this    arrangement,   if 
air  passes  through  the  capillary  tube  it  cannot 
penetrate  the  drawn  out  extremity  of  the  longer 
branch,  but  lodges  in  the  upper  part  of  the  en- 
largement  K.      In   this  position    it    does    not 
affect   the   observations,   since   the  vacuum    is 
always   at  the  upper   part   of  the   tube;    it   is 
moreover  easily  removed. 

In  Gay-Lussac's  barometer  the  shorter  branch  is  closed,  but  there  is 


£20  On  Gases.  [156- 

a  lateral  capillary  aperture  «,  through  which  the  atmospheric  pressure  is 
transmitted. 

The  barometric  height  is  determined  by  means  of  two  scales,  which 
have  a  common  zero  at  O,  towards  the  middle  of  the  longer  branch,  and 
are  graduated  in  contrary  directions,  the  one  from  O  to  E,  and  the  other 
from  O  to  B,  either  on  the  tube  itself,  or  on  brass  rules  fixed  parallel  to 
the  tube.  Two  sliding  verniers,  m  and  «,  indicate  /^th  of  a  millimetre. 
The  total  height  of  the  barometer,  AB,  is  the  sum  of  the  distances  from 
O  to  A  and  from  O  to  B. 

157.  Precautions  in  reference  to  barometers. — In  constructing 
barometers,  mercury  is  chosen  in  preference  to  any  other  liquid.  For 
being  the  densest  of  all  liquids,  it  stands  at  the  least  height.  When  the 
mercurial  barometer  stands  at  30  inches,  the  water  barometer  would  stand 
at  about  34  feet.  It  also  deserves  preference  because  it  does  not  moisten 
the  glass.  It  is  necessary  that  the  mercury  be  pure  and  free  from  oxide ; 
otherwise  it  adheres  to  the  glass  and  tarnishes  it.  Moreover,  if  it  is  im- 
pure its  density  is  changed,  and  the  height  of  the  barometer  is  too  great 
or  too  small.  Mercury  is  purified,  before  being  used  for  barometers,  by 
treatment  with  dilute  nitric  acid,  and  by  distillation. 

The  space  at  the  top  of  the  tube  (figs.  102  and  103),  which  is  called 
the  Torricellian  vacuum^  must  be  quite  free  from  air  and  from  aqueous 
vapour,  for  otherwise  either  would  depress  the  mercurial  column  by  its 
elastic  force.  To  obtain  this  result,  a  small  quantity  of  pure  mercury  is 
placed  in  the  tube  and  boiled  for  some  time.  It  is  then  allowed  to 
cool,  and  a  further  quantity,  previously  warmed,  added,  which  is  boiled, 
and  so  on,  until  the  tube  is  quite  full ;  in  this  manner  the  moisture  and 
the  air  which  adhere  to  the  sides  of  the  tube  pass  off  with  the  mercurial 
vapour. 

A  barometer  is  free  from  air  and  moisture  if,  when  it  is  inclined,  the 
mercury  strikes  with  a  sharp  metallic  sound  against  the  top  of  the  tube. 
If  there  is  air  or  moisture  in  it,  the  sound  is  deadened. 

158.  Correction  for  capillarity. — In  cistern  barometers  there  is  always 
a  certain  depression  of  the  mercurial  column  due  to  capillarity,  unless  the 
internal  diameter  of  the  tube  exceeds  o-8  inch.  To  make  the  correc- 
tion due  to  this  depression,  it  is  not  enough  to  know  the 
diameter  of  the  tube,  we  must  also  know  the  height  of 
the  meniscus  od  (fig.  1 10),  which  varies  according  as  the 
meniscus  has  been  formed  during  an  ascending  or  de- 
scending motion  of  the  mercury  in  the  tube.  Conse- 
quently, the  height  of  the  meniscus  must  be  determined 
by  bringing  the  pointer  to  the  level  ab^  and  then  to  the 
level  d,  when  the  difference  of  the  readings  will  give  the 
height  od  required.  These  two  terms,  namely,  the  in-  "  Fig.  no. 
ternal  diameter  of  the  tube  and  the  height  of  the  menis- 
cus, being  known,  the  resulting  correction  can  be  taken  out  of  the  follow- 
ing table,  which  follows  the  arrangement  usually  adopted  for  a  multipli- 
cation table  : — 


-160] 


Barometers. 


121 


Internal 

Height  of  Sagitta  of  Meniscus  in  inches 

Diameter 

HJi:  inches 

O'OIO 

o"oi5 

0'020 

0'025 

0*030 

0-035 

0*040 

0-I57 

0-0293 

.0-0431 

0-0555 

0-0677 

0-0780 

0-0870 

0-0948 

0-236 

O-OII9 

0-0176 

0-0231 

0-0294 

0-0342 

0-0398 

0-0432 

0-315 

o-oo6o 

0-0088 

O-OII8 

0-0144 

0-0175 

0-0196 

0-022I 

0-394 

0-0039 

0-0048 

0-0063 

0-0078 

0-0095 

o-oiio 

0-0125 

0-472 

0-0020 

0-0029 

0-0036 

0-0045 

0-0053 

0-0063 

0-0073 

0-550 

0-00 10 

0-0017 

0-0024 

0-0029 

0-0034 

0-0039 

0-0044 

In  Gay-Lussac's  barometer  the  two  tubes  are  made  of  the  same  dia- 
meter, so  that  the  error  caused  by  the  depression  in  the  one  tube  very 
nearly  corrects  that  caused  by  the  depression  in  the  other.  As,  however, 
the  meniscus  in  the  one  tube  is  formed  by  a  column  of  mercury  with  an 
ascending  motion,  while  that  in  the  other  by  a  column  with  a  descending 
motion,  their  heights  will  not  be  the  same,  and  the  reciprocal  correction 
will  not  be  quite  exact. 

159.  Correction  for  temperature. — In  all  observations  with  baro- 
meters, whatever  be  their  construction,  a  correction  must  be  made  for 
temperature.  Mercury  contracts  and  expands  with  different  temperatures; 
hence  its  density  changes,  and  consequently  the  barometric  height,  for 
this  height  is  in  the  inverse  ratio  of  the  density  of  the  mercury  ;  so  that 
for  different  atmospheric  pressures  the  mercurial  column  might  have  the 
same  height.  Accordingly,  in  each  observation,  the  height  observed 
must  be  reduced  to  a  determinate  temperature  ;  the  choice  of  this  is  quite 
arbitrary,  but  that  of  melting  ice  is  always  adopted.  It  will  be  seen,  in 
the  Book  on  Heat,  how  this  correction  is  made. 

By  the  aid  of  tables  which  have  been  prepared  for  this  purpose,  the 
height  of  the  barometer  is  readily  reduced  to  zero  Centigrade. 

160.  Variations  in  the  belgrht  of  tfcie  barometer. — When  the  baro- 
meter is  observed  for  several  days,  its  height  is  found  to  vary  in  the  same 
place,  not  only  from  one  day  to  another,  but  also  during  the  same  day. 

The  extent  of  these  variations,  that  is,  the  difference  between  the 
greatest  and  the  least  height,  is  different  in  different  places.  It  increases 
from  the  equator  towards  the  poles.  Except  under  extraordinary  circum- 
stances, the  greatest  variations  do  not  exceed  six  millimetres  under  the 
equator,  30  under  the  tropic  of  Cancer,  40  in  France,  and  60  at  25  degrees 
from  the  pole.     The  greatest  variations  are  observed  in  winter. 

The  mean  daily  height  is  the  height  obtained  by  dividing  the  sum  of 
24  successive  hourly  observations  by  24.  In  our  latitudes  the  barometric 
height  at  noon  corresponds  to  the  mean  daily  height. 

The  meari  monthly  height  is  obtained  by  adding  together  the  mean 
daily  heights  for  a  month,  and  dividing  by  30. 

The  mea7i  yearly  height  is  similarly  obtained. 

Under  the  equator,  the  mean  annual  height  at  the  level  of  the  sea  is 

G 


/^%*a4 '****'»*»^ '5r»^T^^^    7  '^  '* 

♦»   //i2i  4^ -»--*n^-— *-^    ..        Cm  Gases. 


o'"758,  or  29*84  inched     It  increases  from  the  equator,  and  between  the 
latitudes  30°  and  40°  it  attains  a  maximum  of  o'"763,  or  30*04  inches.    In 
lower  latitudes  it  decreases,  and  in  Paris  it  does  not  exceed  o"'*7568. 
The  general  mean  at  the  level  of  the  sea  is  o'"*76i,  or  29*96  inches. 
The  mean  monthly  height  is  greater  in  winter  than  in  summer,  in  con- 
sequence of  the  cooler  atmosphere. 

Two  kinds  of  variations  are  observed  in  the  barometer: — ist,  the  acci- 
dcjital  variations^  which  present  no  regularity  ;  they  depend  on  the 
seasons,  the  direction  of  the  winds,  and  the  geographical  position,  and 
are  common  in  our  climates  ;  2nd,  the  daily  variations,  which  are  pro- 
duced periodically  at  certain  hours  of  the  day. 

At  the  equator,  and  between  the  tropics,  no  accidental  variations  are 
observed  ;  but  the  daily  variations  take  place  with  such  regularity  that  a 
barometer  may  serve  to  a  certain  extent  as  a  clock.  The  barometer  sinks 
from  midday  till  towards  four  o'clock  ;  it  then  rises,  and  reaches  its 
maximum  at  about  ten  o'clock  in  the  evening.  It  then  again  sinks,  and 
reaches  a  second  minimum  towards  four  o'clock  in  the  morning,  and  a 
second  maximum  at  ten  o'clock. 

In  the  temperate  zones  there  are  also  daily  variations,  but  they  are 
detected  with  difficulty,  since  they  occur  in  conjunction  with  accidental 
variations. 

^  The  hours  of  the  maxima  and  minima  appear  to  be  the  same  in  all 
climates,  whatever  be  the  latitude  ;  they  merely  vary  a  little  with  the 
seasons. 

161.  Causes  of  barometric  variations. — It  is  observed  that  the 
course  of  the  barometer  is  generally  in  the  opposite  direction  to  that  of 
the  thermometer;  that  is,  that  when  the  temperature  rises  the  barometer 
falls,  and  vice  versa  ;  which  indicates  that  the  barometric  variations  at 
any  given  place  are  produced  by  the  expansion  or  contraction  of  the  air, 
and  therefore  by  its  change  in  density.  If  the  temperature  were  the  same 
throughout  the  whole  extent  of  the  atmosphere,  no  currents  would  be 
produced,  and,  at  the  same  height,  the  atmospheric  pressure  would  be 
everywhere  the  same.  But  when  any  portion  of  the  atmosphere  becomes 
warmer  than  the  neighbouring  parts,  its  specific  gravity  is  diminished, 
and  it  rises  and  passes  away  through  the  upper  regions  of  the  atmosphere, 
whence  it  follows  that  the  pressure  is  diminished,  and  the  barometer  falls. 
If  any  portion  o.f  the  atmosphere  retains  its  temperature,  while  the 
neighbouring  parts  become  cooler,  the  same  effect  is  produced ;  for  in 
this  case,  too,  the  density  of  the  first-mentioned  portion  is  less  than  that 
of  the  others.  Hence,  also,  it  usually  happens  that  an  extraordinary  fall 
of  the  barometer  at  one  place  is  counterbalanced  by  an  extraordinary  rise 
at  another  place.  The  daily  variations  appear  to  result  from  the  expan- 
sions and  contractions  which  are  periodically  produced  in  the  atmosphere 
by  the  heat  of  the  sun  during  the  rotation  of  the  earth, 

162.  Relation  of  barometric  variations  to  tbe  state  of  tbe  weather. 
— It  has  been  observed  that,  in  our  climate,  the  barometer  in  fine  weather 
is  generally  above  30  inches,  and  is  below  this  point  when  there  is  rain, 
snow,  wind,  or  storm,  and  also,  that  for  any  given  number  of  days  at 


163] 


Barometer's. 


l'2l 


which  the  barometer  stands  at  30  inches,  there  are  as  many  fine  as 
rainy  days.  From  this  coincidence  between  the  height  of  the  barometer 
and  the  state  of  the  weather,  the  following  indications  have  been 
maiked  on  the  barometer,  counting  by  thirds  of  an  inch  above  and  below 
30  inches  : 

Height  State  of  the  weather 

31   inches  .  .  ,  .  .     Very  dry. 

3o§      „     .  .  .  .  .     Settled  weather. 

30^      „     .  .  .  .  ,     Fine  weather. 

30        „     .  ,  .  .  .     Variable. 

29I      „     .  .  .  .  .     Rain  or  wind. 

29^      „     .  .  .  .  .     Much  rain. 

29       „     .  .  .  .  .     Tempest. 

In  using  the  barometer  as  an  indicator  of  the  state  of  the  weather,  we 
must  not  forget  that  it  really  only  serves  to  measure  the  weight  of  the 
atmosphere,  and  that  it  only  rises  or  falls 
as  the  weight  increases  or  diminishes  ; 
and  although  a  change  of  weather  fre- 
quently coincides  with  a  change  in  the 
pressure,  they  are  not  necessarily  con- 
nected. This  coincidence  arises  from 
meteorological  conditions  peculiar  to  our 
climate,  and  does  not  always  occur.  That 
a  fall  in  the  barometer  usually  precedes 
rain  in  our  latitudes,  is  caused  by  the 
position  of  Europe.  The  south-west  winds, 
which  are  hot  and  consequently  light, 
make  the  barometer  sink  ;  but  at  the 
same  time,  as  they  become  charged  with 
aqueous  vapour  in  crossing  the  ocean, 
they  bring  us  rain.  The  winds  of  the 
north  and  north-east,  on  the  contrary, 
being  colder  and  denser,  make  the  baro- 
meter rise  ;  and  as  they  only  reach  us 
after  having  passed  over  vast  continents, 
they  are  generally  dry. 

When  the  barometer  rises  or  sinks 
slowly,  that  is,  for  two  or  three  days, 
towards  fine  weather  or  towards  rain,  it 
has  been  found  from  a  great  number  of 
observations  that  the  indications  are  then 
extremely  probable.  Sudden  variations 
in  either  direction  indicate  bad  weather 
or  wind. 

163.    IXTbeel  barometer. — The  wheel  '^"  "^"  '^'  "^' 

barometer,  which  was  invented  by  Hooke,  is  a  syphon  barometer,  and  is 
especially  intended  to  indicate  good  and  bad  weather  (fig.  in).     In  the 

G  2 


124 


On  Gases. 


[163- 


shorter  leg  of  the  syphon  there  is  a  float,  which  rises  and  falls  with  the 
mercury  (fig.  112).  A  string  attached  to  this  float  passes  round  a  pulley, 
O,  and  at  the  other  end  there  is  a  weight,  P,  somewhat  lighter  than  the 
float.  A  needle  fixed  to  the  pulley  moves  round  a  graduated  circle,  on 
which  is  marked,  variable,  rain,  fine  iveather,  etc.  When  the  pressure 
varies  the  float  sinks  or  rises,  and  moves  the  needle  round  to  the  corre- 
sponding points  on  the  scale. 

The  barometers  ordinarily  met  with  in  houses,  and  which  are  called 
weather  glasses,  are  of  this  kind.  They  are,  however,  of  little  use,  for  two 
reasons.  The  first  is,  that  they  are  neither  very  delicate  nor  precise  in 
their  indications.  The  second,  which  applies  equally  to  all  barometers, 
is  that  those  commonly  in  use  in  this  country  are  made  in  London,  and 
the  indications,  if  they  are  of  any  value,  are  only 
so  for  a  place  of  the  same  level  and  of  the  same 
climatic  conditions  as  London.  Thus  a  barometer 
standing  at  a  certain  height  in  London  would  in- 
dicate a  certain  state  of  weather,  but  if  removed  to 
^hooter's  Hill  it  would  stand  half  an  inch  lower, 
and  would  indicate  a  different  state  of  weather. 
As  the  pressure  differs  with  the  level  and  with 
geographical  conditions,  it  is  necessary  to  take  these 
into  account  if  exact  data  are  wanted. 

164.  Fixed  barometer. — For  accurate  observa- 
tions Regnault  uses  a  barometer  the  height  ot 
which  he  measures  by  means  of  a  cathetometer  (85). 
The  cistern  (fig,  113)  is  of  cast  iron  ;  against  the 
frame  on  which  it  is  supported  a  screw  is  fitted, 
which  is  pointed  at  both  ends,  and  the  length  of 
which  has  been  determined,  once  for  all,  by  the 
cathetometer.  To  measure  the  barometric  height 
the  screw  is  turned  until  its  point  grazes  the  surface 
of  the  mercury  in  the  bath,  which  is  the  case  when 
the  point  and  its  image  are  in  contact.  The 
distance  then  from  the  top  of  the  point  to  the  level 
of  the  mercury  in  the  tube  b  is  measured  by  the 
cathetometer,  and  this,  together  with  the  length  of 
the  screw,  gives  the  barometric  height  with  great 
accuracy.  This  barometer  has  moreover  the  ad- 
vantage that,  as  a  tube  an  inch  in  diameter  may 
be  used,  the  influence  of  capillarity  becomes  inap- 
preciable. Its  construction  moreover  is  very  simple, 
and  the  position  of  the  scale  leads  to  no  kind  of 
error  since  this  is  transferred  to  the  cathetometer. 
Unfortunately  the  latter  instrument  requires  great 
accuracy  in  its  construction,  and  is  very  expensive. 
165.  Betermination  of  bei^lits  by  the  barometer. — Since  the  atmo- 
spheric pressure  decreases  as  we  ascend,  it  is  obvious  that  the  barometer 
will  keep  on  falling  as  it  is  taken  to  a  greater  and  greater  height — a  fact 


,^^ 


p 


-165]        Determination  of  Heights  by  the  Barometer.  125 

which  suggests  a  very  useful  method  of  determining  the  difference 
between  the  elevations  of  two  stations,  such  as  the  base  and  summit  of  a 
mountain.     The  method  may  be  explained  as  follows. 

It  will  be  seen  in  the  next  chapter  that  if  the  temperature  of  an  enclosed 
portion  of  air  continues  constant,  its  volume  will  vary  inversely  as  the 
pressure.  That  is  to  say,  if  we  double  the  pressure  we  shall  halve  the 
volume.  This  is  usually  known  as  Boyle's  law  (166).  But  if  we  _ 
halve  the  volume  we  manifestly  double  the  quantity  of  air  in  each 
cubic  inch,  that  is  to  say,  we  double  the  density  of  the  air;  and  so  on 
in  any  proportion.  Consequently,  the  law  is  equivalent  to  this  : — 
That  for  a  constant  temperature  the  density  of  air  is  proportional 
to  the  pressure  which  it  sustains. 

Now  suppose  A  and  B  (fig.  114)  to  represent  two  stations,  and  "^ 
that  it  is  required  to  determine  the  vertical  height  of  B  above  A  ; 
it  being  borne  in  mind  that  A  and  B  are  not  necessarily  in  the 
same  vertical  line.  Take  P  any  point  in  AB,  and  Q  a  point  at  a 
small  distance  above  P.  Suppose  the  pressure  on  a  square  inch  of 
the  atmosphere  at  P  to  be  denoted  by  p^  and  at  O  let  it  be 
diminished  by  a  quantity  denoted  by  dp.  It  is  plain  that  this 
diminution  equals  the  weight  of  the  column  of  aii  between  P  and  -L4 
Q,  whose  section  is  one  square  inch.  But;  since  the  density  of  the  p-jg 
air  is  directly  proportional  to  p^  the  weight  of  a  cubic  inch  of  air 
will  equal  kgp..  where  k  denotes  a  certain  quantity  to  be  determined  here- 
after, and  g  the  accelerating  force  of  gravity  (76).  Hence,  if  we  denote 
PQ  in  inches  by  dx,  the  pressure  will  be  diminished  by  kpg.dx,  and  we 
may  represent  this  fact  algebraically  by  the  equation 

kpg.dx  =  dp. 

By  a  well-known  algebraical  process  this  leads  to  the  conclusion  that 

^^X  =  logP 

where  X  denotes  the  height  of  AB,  and  P  and  P^  the  atmospheric 
pressures  at  A  and  B  respectively,  the  logarithms  being  what  are 
called  '  Napierian  logarithms.'  Now,  if  H  and  Hj  are  the  heights  of 
the  barometer  at  A  and  B  respectively,  the  temperature  of  the  mercury 
being  the  same  at  both  stations,  their  ratio  equals  that  of  P  to  Pj,  and 
therefore 

It  remains  to  determine  >^  and  ^. 

(i)  Since  the  force  of  gravity  is  different  for  places  in  different  lati- 
tudes, ^  will  depend  upon  the  latitude  (79).  It  is  found  that  if  ^  is  the 
accelerating  force  of  gravity  in  latitude  (p,  and  /  that  force  in  latitude  45°.- 
then 

^~  I  +0-00256  cos  29;' 
where  /  has  a  definite  numerical  value. 

(2)  From  what  has  been  stated  above  it  will  be  seen,  that  if  p  is  the 


126  On  Gases.  [165- 

density  of  air  at  a  temperature  of  t°  C,  under  Q  the  pressure  exerted  by 
29-92  inches  of  mercury,  we  shall  have 

But  it  will  be  afterwards  shown  that  if  p^  is  the  density  of  air  under  the 
same  pressure  O  at  0°  C,  we  shall  have 

where  a  has  a  definite  numerical  value.     Therefore 

-^     I  +^/ 

Now  if  <r  is  the  density  of  mercury,  and  if  the  latitude  is  45°,  we  shall 
have 

0  =  29-92.  r/j 
and  therefore 


29-92  (i  +at) 

Now  pQ-^(y  is  the  ratio  which  the  density  of  dry  air  at  a  temperature  0°  C, 
in  latitude  45°,  under  a  pressure  of  29-92  inches  of  mercury,  bears  to  the 
density  of  mercury  at  0°  C,  and  therefore  Pq-t-it  is  a  determinate  number. 
Substituting,  we  have 

X  =  29-92  in.   -  ~  (i  +  0-00256  cos  2  ).  (i  +  at)  log  u  • 
/'o  -"i 

The  value  of  a  is  0-003665,  which  is  nearly  equal  to  y^^^^.  If  we  substitute 
the  proper  values  for  CH-p^,  and  change  the  logarithms  into  common  log- 
arithms, and  instead  of  /  use  the  mean  of  T  and  T^,  the  temperatures  at 
the  upper  and  lower  stations,  it  will  be  found  that 

/         2(T  +  T,>\         H 
X  (in  feet)  -  60346  (i  +  0-00256  cos  2  4.)    (^1  +   —^^~')  log  ^  ' 

which  is  La  Place's  barometric  formula.  In  using  it,  it  must  be  remem- 
bered that  T  and  Tj  ar>e  temperatures  on  the  Centigrade  thermometer, 
and  that  H  and  H,  are  the  heights  of  the  barometer  reduced  to  0°  C. 
Thus  if  //  is  the  measured  height  of  the  barometer  at  the  lower  station 
we  have 


\         6=;oo/ 


6500. 

If  the  height  to  be  measured  is  not  great,  one  observer  is  enough.  For 
greater  heights  the  ascent  takes  some  time,  and  in  the  interval  the  pres- 
sure may  vary.  Consequently  in  this  case  there  must  be  two  observers, 
one  at  each  station,  who  make  simultaneous  observations. 

Let  us  take  the  following  example  of  the  above  formula:— Suppose 
that  in  latitude  65°  N.  at  the  lower  of  the  two  stations  the  height  of  the 
barometer  were  30-025  inches,  and  the  temperature  of  air  and  mercury 
17^-32  C,  while  at  the  upper  the  height  of  the  barometer  was  28-230 
inches,  and  the  temperature  of  air  and  mercury  was  io°-55  C.  Determine 
the  height  of  the  upper  station  above  the  lower. 


-166]  \^oyles  Law/)  127 

(i)  P'ind  H  and  H^•.  viz. 

H  =30-025(1-^^)  =  20-945; 

hence  log  —  =  i  -4763243  -  i  -4500026  =  0-02632 1 7. 

(2)  Find  I  +  ^- lo^Q--  VIZ.  1-05574. 

(3)  Find  1+0-002560052^. 

Since  0-00256   cos    130"^= -0*00256  cos  50^ 

=  —0-001645, 
therefore  i  +  0-00256  cos  2p=  -0-998355  ; 

hence  the  required  height  in  feet  equals 

60346x0-998355  X  1-05574  X  0-263217  =  1674. 
It  may  be  easily  proved  that  if  H  and  H^  do  not  greatly  differ,  the 

TT  TT   TJl 

Napierian  logarithm  of  —7-  equals  2  -^ —    ^     if  for  instance  H  equals  30 

inches,  and  Hj  equals  29  inches,  the  resulting  error  would  not  exceed  the 
5,j^^^y  part  of  the  whole.  Accordingly  for  heights  not  exceeding  2000  ft. 
we  may  without  much  error  use  the  formula, 

X  (m  feet)  =  52500  (i  -f  -^^^^)  x  -^-^^• 


CHAPTER  11. 

MEASUREMENT  OF  THE   ELASTIC   FORCE   OF  GASES. 

166.  Boyle's  law. — The  law  of  the  compressibihty  of  gases  was  dis- 
covered by  Boyle  and  Mariotte  independently.  In  consequence  it  is  in 
England  commonly  called  '  Boyle's  law,'  and,  on  the  Continent,  'Mariotte's 
law.'     It  is  as  follows  : 

The  temperature  remaining  the  sa?ne,  the  volume  of  a  given  qiiajitity 
of  gas  is  inversely  as  the  pressure  which  it  bears  ? 

This  law  maybe  verified  by  means  of  an  apparatus  called  Ma?-iotte's  tube 
(fig.  115).  It  consists  of  a  long  glass  tube  fixed  to  a  vertical  support  ;  it 
is  open  at  the  upper  part,  and  the  other  end,  which  is  bent  into  a  short 
vertical  leg,  is  closed.  On  the  shorter  leg  there  is  a  scale,  which  indi- 
cates equal  capacities  ;  the  scale  against  the  long  leg  gives  the  heights. 
The  zero  of  both  scales  is  in  the  same  horizontal  line. 


128 


On  Gases. 


[166 


A  small  quantity  of  mercury  is  poured  into  the  tube,  so  that  its  level  in 
both  branches  is  at  zero,  which  is  effected  without  much  difficulty  after  a 
few  trials  (fig.  115).  The  air  in  the  short  leg  is  thus  under  the  ordinary 
atmospheric  pressure  which  is  exerted  through  the  open  tube.  Mercury 
is  then  poured  into  the  longer  tube  until  the  volume  of  the  air  in  the 
smaller  tube  is  reduced  to  one-half ;  that  is,  until  it  is  reduced  from  10  to 
5,  as  shown  in  fig.  116.  If  the  height  of  the  riiercurial  column,  CA,  be 
measured,  it  will  be  found  exactly  equal  to  the  height  of  the  barometer  at 


g 

A 

^80' 

. 

r^o 

-!    1 

-1 

~—i<i, 

S 

;-lO 

ilijLi 

W\ 

Fig.  115.  Fig.  116.  Fig.  117.     Fig.  118. 

the  time  of  the  experiment.  The  pressure  of  the  column  CA  is  therefore 
equal  to  an  atmosphere  which,  with  the  atmospheric  pressure  acting  on 
the, surface  of  the  column  at  C,  makes  two  atmospheres.  Accordingly, 
by  doubling  the  pressure,  the  volume  of  the  gas  has  been  diminished  to 
one-half 

If  mercury  be  poured  into  the  longer  branch  until  the  volume  of  the 
air  is  reduced  to  one-third  its  original  volume,  it  will  be  found  that  the 
distance  between  the  level  of  the  two  tubes  is  equal  to  two  barometric 
columns.     The  pressure  is  now  three  atmospheres,  while  the  volume  is 


-167]  Boyle  s  Lazv.  129 

reduced  to  one-third.  Dulong  and  Petit  have  verified  the  law  for  air  up 
to  27  atmospheres,  by  means  of  an  apparatus  analogous'  to  that  which 
has  been  described. 

The  law  also  holds  good  in  the  case  of  pressures  of  less  than  one  at- 
mosphere.  To  establish  this,  mercury  is  poured  into  a  graduated  tube 
until  it  is  about  two-thirds  full,  the  rest  being  air.  It  is  then  inverted  in 
a  deep  trough  containing  mercury  (fig.  117),  and  lowered  until  the  levels 
of  the  mercury  inside  and  outside  the  tube  are  the  same,  and  the  volume 
noted.  .  The  tube  is  then  raised,  as  represented  in  the  figure,  until  the 
volume  of  air  AC  is  double  that  of  AB  (fig.  118).  The  height  of  the 
mercury  in  the  tube,  above  the  mercury  in  the  trough  CD,  is  then  found 
to  be  exactly  half  the  height  of  the  barometric  column.  The  air,  whose 
volume  is  now  doubled,  is  now  only  under  the  pressure  of  half  an  atmo- 
sphere ;  for  it  is  the  elastic  force  of  this  air  which,  added  to  the  weight  of 
the  column  CD,  is  equivalent  to  the  atmospheric  pressure.  Hence  the 
volume  is  inversely  as  the  pressure. 

In  the  experiment  with  Mariotte's  tube,  as  the  quantity  of  air  remains 
the  same,  its  density  must  obviously  increase  as  its  volume  diminishes, 
and  vice  versd.  The  law  may  thus  be  enunciated  :  ^  For  the  same  tem- 
perature the  density  of  a  gas  is  proportional  to  its  pressure^  Hence  as 
water  is  773  times  as  heavy  as  air,  under  a  pressure  of  773  atmospheres, 
air  would  be  as  dense  as  water. 

Boyle's  law  must  not  be  understood  to  mean  that  gases  of  equal  density 
have  equal  elastic  force  ;  different  gases  of  various  densities  have  the 
same  tension  when  they  are  under  the  same  pressure.  A  given  volume 
of  hydrogen  under  the  ordinary  atmospheric  pressure  has  the  same  elastic 
force  as  the  same  volume  of  air,  although  the  latter  is  14  times  as  heavy 
as  the  former.  Since,  for  the  same  volume,  there  are  the  same  number  of 
atoms  in  all  gases,  the  lighter  atoms  must  possess  a  greater  velocity  in 
order  to  exert  the  same  pressure  as  the  same  number  of  atoms  of  greater 
\  »(ass. 
yC  167.  Boyle's  law  is  only  approximately  true. — Until  within  the  last 
■^  few  years  Boyle's  law  was  supposed  to  be  absolutely  true  for  all  gases  at 
all  pressures,  but  Despretz,  who  examined  the  compressibility  of  gases, 
obtained  results  incompatible  with  the  law.  He  took  two  graduated  glass 
tubes  of  the  same  length,  and  filled  one  with  air  and  the  other  with  the 
gas  to  be  examined.  These  tubes  were  placed  in  the  same  mercury 
trough,  and  the  whole  apparatus  immersed  in  a  strong  glass  cylinder  filled 
with  water.  By  means  of  a  piston  moved  by  a  screw  which  worked  in 
a  cap  at  the  top  of  a  cylinder,  the  liquid  could  be  subjected  to  an  in- 
creasing pressure,  and  it  could  be  seen  whether  the  compression  of  the 
two  gases  was  the  same  or  not.  The  apparatus  resembled  that  used  for 
examining  the  compressibility  of  liquids  (fig.  49).  In  this  manner 
Despretz  found  that  carbonic  acid,  sulphuretted  hydrogen,  ammonia, 
and  cyanogen,  are  more  compressible  than  air  :  hydrogen,  which  has  the 
same  compressibility  as  air  up  to  15  atmospheres,  is  then  less  compres- 
sible. From  these  experiments  it  was  concluded  that  the  law  of  Boyle  was 
not  general. 


130 


On  Gases. 


[167- 


In  some  experiments  on  the  elastic  force  of  vapours,  Dulong  and 
Arago  had  occasion  to  test  the  accuracy  of  Boyle's  law.  The  method 
adopted  was  exactly  that  of  Mariotte,  but  the  apparatus  had  gigantic 
dimensions. 

The  gas  to  be  compressed  was  contained  in  a  strong  glass  tube,  GF 
(fig.  1 19),  about  six  feet  long  and  closed  at  the  top,  G.  The  pressure  was 
produced  by  a  column  of  mercury,  which  could  be  increased  to  a  height 


'  .  !■  ig.  119. 

of  65  feet,  contained  in  a  long  vertical  tube,  KL,  fomied  of  a  number  of 
tubes  firmly  joined  by  good  screws,  so  as  be  perfectly  tight. 

The  tubes  KL  and  GF  were  hermetically  fixed  in  a  horizontal  iron 
pipe,  DE,  which  formed  part  of  a  mercurial  reservoir,  A.  On  the  top  of 
this  reservoir  there  was  a  force  pump,  BC,  by  which  mercury  could  be 
forced  into  the  apparatus. 

At  the  commencement  of  the  experiment,  the  volume  of  the  air  in  the 


-167]  Boyle  s  Laiv.  131 

manometer  (171)  was  observed,  and  the  initial  pressure  determined,  by 
adding  to  the  pressure  of  the  atmosphere  the  height  of  the  mercury  in  K 
above  its  level  in  H.  If  the  level  of  the  mercury  in  the  manometer  had 
been  above  the  level  in  KL,  it  would  have  been  necessary  to  subtract  the 
difference. 

By  means  of  the  pump,  water  was  injected  into  A.  The  mercury 
being  then  pressed  by  the  water,  rose  in  the  tube  GF,  where  it  compressed 
the  air,  and  in  the  tube  KL,  where  it  rose  freely.  It  was  only  then 
necessary  to  measure  the  volume  of  the  air  in  GF  ;  the  height  of  the 
mercury  in  KL  above  the  level  in  GF,  together  with  the  pressure  of  the 
atmosphere,  was  the  total  pressure  to  which  the  gas  was  exposed.  These 
were  all  the  elements  necessary  for  comparing  different  volumes  and  the 
corresponding  temperatures.  The  tube  GF  was  kept  cold  during  the 
experiment  by  a  stream  of  cold  water. 

The  long  tube  was  attached  to  a  long  mast  by  means  of  staples.  The 
individual  tubes  w^ere  supported  at  the  junction  by  cords,  which  passed 
round  pulleys  R  and  R',  and  were  kept  stretched  by  small  buckets,  P, 
containing  shot.  In  this  manner,  each  of  the  thirteen  tubes  having  been 
separately  counterpoised,  the  whole  column  was  perfectly  free  notwith- 
standing its  weight. 

Dulong  and  Arago  investigated  the  pressure  up  to  27  atmospheres,  and 
observed  that  the  volume  of  air  always  diminished  a  little  more  than  is 
required  by  Boyle's  law.  But  as  these  differences  were  very  small,  they 
attributed  them  to  errors  of  observation,  and  concluded  that  the  law  was 
perfectly  exact,  at  any  rate  up  to  27  atmospheres. 

M.  Regnault  investigated  the  same  subject  with  an  apparatus  resem- 
bling that  of  Dulong  and  Arago,  but  in  which  all  the  sources  of  error 
were  taken  into  account,  and  the  observations  made  with  remarkable  pre- 
cision. He  experimented  with  air,  nitrogen,  carbonic  acid,  and  hydrogen. 
He  found  that  air  does  not  exactly  follow  Boyle's  law,  but  experiences  a 
greater  compressibility,  which  increases  with  the  pressure;  so  that  the 
difference  between  the  calculated  and  the  observed  diminution  of  volume 
is  greater  in  proportion  as  the  pressure  increases. 

M.  Regnault  found  that  nitrogen  was  like  air,  but  is  less  compressible. 
Carbonic  acid  exhibits  considerable  deviation  from  Boyle's  law  even  under 
small  pressures.  Hydrogen  also  deviates  from  the  law,  bu-t  its  compressi- 
bility diminishes  with  increased  pressure. 

Recently  M.  Cailletet  has  examined  the  compressibility  of  gases  by  a 
special  method  in  which  the  pressure  could  be  carried  as  high  as  6ao 
atmospheres.  His  results  confirm  those  of  M.  Regnault  as  regards 
hydrogen  ;  air  was  found  to  present  the  curious  feature  that  towards  80 
atmospheres  it  has  a  maximum  relative  compressibility ;  beyond  this  point 
it  gradually  becomes  less  compressible  ;  its  compressibility  diminishing 
more  rapidly  than  that  of  hydrogen. 

Carbonic  acid  deviates  less  from  the  law  in  proportion  as  the  tempera- 
ture is  higher.  This  is  also  the  case  with  other  gases.  And  experiment 
shows  that  the  deviation  from  the  law  is  greater  in  proportion  as  the  gas 
is  nearer  its  liquefying  point ;   and,  on  the  contrary,  the  farther  a  gas  is 


132  'On  Gases.  [167- 

from  this  point,  the  more  closely  does  it  follow  the  law.  For  gases  which 
have  not  been  liquefied,  the  deviations  from  the  law  are  inconsiderable, 
and  may  be  quite  neglected  in  ordinary  physical  and  chemical  experi- 
ments, where  the  pressures  are  not  great. 

1 68.  Applications  of  Boyle's  law. — Observations  on  the  volumes  ot 
gases  are  only  comparable  when  made  at  the  same  pressure.  Usually, 
therefore,  in  gas  analyses,  all  measurements  are  reduced  to  the  standard 
pressure  of  760  millimetres,  or  29"92  inches.  This  is  easily  done  by 
Boyle's  law,  for,  since  the  volumes  are  inversely  as  the  pressures 
V  :  V  =  P' :  P.  Knowing  the  volume  V  at  the  pressure  P  we  can  easily 
calculate  its  volume  V  at  the  given  pressure  P',  for 

VT'  =  VP, 

that  is,  W^^, 

Suppose  a  volume  of  gas  to  measure  340  cubic  inches  under  a  pressure 
of  535  mm.,  what  will  be  its  volume  at  the  standard  pressure,  760  mm..^ 

We  have  v_34ox  535  ^-2%^  cubic  inches. 

760 

In  like  manner  let  it  be  asked,  if  D'  is  the  density  of  a  gas  when  the 
barometer  stands  at  H'  mm.,  what  will  be  its  density  D  at  the  same  tem- 
perature when  the  barometer  stands  at  H  mm..^  Let  M  be  the  mass  of 
the  gas,  V  its  volume  in  the  first  case,  V  its  volume  in  the  second. 
Therefore, 

^^'  D'    V      P'     H'* 

Thus,  if  H'  denote  760  mm.,  we  have 

TT 

Density  at  H  =  (Density  at  standard  pressure)    - — 

760 

169.  nxanoxneters. — Manometers  are  instruments  for  measuring  the 
tension  of  gases  or  vapours.  In  all  manometers  the  unit  chosen  is  the 
pressure  of  one  atmosphere  or  30  inches  of  mercury  at  the  standard  tem- 
perature, which,  as  we  have  seen,  is  nearly  I5lbs.  to  the  square  inch. 

170.  Open-air  manometer. — The  open-air  manometer  consists  of  a 
bent  glass  tube  BD  (fig.  120),  fastened  to  the  bottom  of  a  reservoir  AC, 
of  the  same  material,  containing  mercury,  which  is  connected  with  the 
closed  recipient  containing  the  gas  or  vapour  the  pressure  of  which  is  to 
be  measured.  The  whole  is  fixed  on  a  long  plank  kept  in  a  vertical 
position. 

In  graduating  this  manometer  C  is  left  open,  and  the  number  i  marked 
at  the  level  of  the  mercury,  for  this  represents  one  atmosphere.  From 
this  point  the  numbers  2,  3,  4,  5,  6  are  marked  at  each  30  inches,  indi- 
cating so  many  atmospheres,  since  a  column  of  mercury  30  inches  repre- 
sents a  pressure  of  one  atmosphere.  The  intervals  from  i  to  2,  and  from 
2  to  3,  &c.,  are  divided  into  tenths.  C  being  then  placed  in  connection 
with  a  boiler,  for  example,  the  mercury  rises  in  the  tube  BD  to  a  height 
w^hich  measures  the  tension  of  the  vapour.     In  the  figure  the  manometer 


-171] 


Manometers. 


133 


marks  2  atmospheres,  which  represents  a  height  of  30  inches,  plus  the 
atmospheric  pressure  exerted  at  the  top  of  the  column  through  the  aper- 
ture D. 

This  manometer  is  only  used  when  the  pressures  do  not  exceed  5  to  6 
atmospheres.  Beyond  this,  the  length  of  tube  necessary  makes  it  very 
inconvenient,  and  the  following  apparatus  is  commonly  used. 

171.  2MEanoiueter  witb  compressed  air. — The  mmwineter  with  co??i- 


2t 


Fig.  121. 


Fig.  122. 


pressed  air  is  founded  on  Boyle's  law  :  it  consists  of  a  glass  tube  closed 
at  the  top,  and  filled  with  dry  air.  It  is  firmly  cemented  in  a  small  iron 
box  containing  mercury.  By  a  tubulure,  A,  in  the  side  (fig.  121),  this 
box  is  connected  with  the  closed  vessel  containing  the  gas  or  vapour 
whose  tension  is  to  be  measured. 


134 


On  Gases. 


[171- 


In  the  graduation  of  this  manometer,  the  quantity  of  air  contained  in 
the  tube  is  such,  that  when  the  aperture  A  communicates  freely  with  the 
atmosphere,  the  level  of  the  mercury  is  the  same  in  the  tube  and  in  the 
tubulure.  Consequently,  at  this  level,  the  number  i  is  marked  on  the 
scale  to  which  the  tube  is  affixed.  As  the  pressure  acting  through  the 
tubulure  A  increases,  the  mercury  rises  in  the  tube,  until  its  weight,  added 
to  the  tension  of  the  compressed  air,  is  equal  to  the  external  pressure. 
It  would  consequently  be  incorrect  to  mark  two  atmospheres  in  the 
middle  of  the  tube  ;  for  since  the  volume  of  the  air  is  reduced  to  one-half, 
its  tension  is  equal  to  two  atmospheres,  and,  together,  with  the  weight  of 
the  mercury  raised  in  the  tube,  is  therefore  more  than  two  atmospheres. 
The  position  of  the  number  is  a  little  below  the  middle,  at  such  a  height 
that  the  elastic  force  of  the  compressed  air,  together  with  the  weight  of  the 
mercury  in  the  tube,  is  equal  to  two  atmospheres.  The  exact  position  of 
the  numbers,  2,  3,  4,  &c.  on  the  manometer  scale  can  only  be  deterhiined 
by  calculation.  Sometimes  this  manometer  is  made  of  one  glass  tube, 
as  represented  in  fig.  122.     The  principle  is  obviously  the  same. 

172.  Xtegrnault's  barometric  manometer. — For  measuring  pressures 
of  less  than  one  atmosphere,  M.  Regnault  has  the  following  arrangement, 
which  is  a  modification  of  his  fixed  barometer  (fig.  113).  In  the  same 
cistern  dips  a  second  tube  a,  of  the  same  diameter,  open  at  both  ends,  and 
provided  at  the  top  with  a  three-way  cock,  one  of  which  is  connected  with 
an  air  pump  and  the  other  with  the  space  to  be  exhausted.  The  farther 
the  exhaustion  is  carried  the  higher  the  mercury  rises  in  the  tube  a.  The 
difference  of  level  in  the  tubes  b  and  a  gives  the  pressures.  Hence,  by 
measuring  the  height  ab,  by  means  of  the  cathetometer,  the  pressure  in 

the  space  that  is  being  ex- 
hausted is  accurately  given. 
This  apparatus  is  also  called 
the  differential  baronieter. 

173.  Aneroid  barome- 
ter.— This  instrument  de- 
rives its  name  from  the  cir- 
cumstance that  no  liquid  is 
used  in  its  construction  (a, 
without,  v7/p6t-,  moist).  Fig. 
123  represents  one  of  the 
forms  of  these  instruments, 
constructed  by  Mr.  Casella  : 
it  consists  of  a  cylindrical 
metal  box,  exhausted  of  air, 
the  top  of  which  Is  made 
of  thin  corrugated  metal,  so 
elastic  that  it  readily  yields 
to  alterations  in  the  pressure 
of  the  atmosphere. 
When  the  pressure  increases,  the  top  is  pressed  inwards  ;  when  on 
the  contrary  it  decreases,  the  elasticity  of  the  lid,  aided  by  a  spring. 


Fig.  123. 


-174]  Laws  of  the  Mixture  of  Gases.  135 

tends  to  move  it  in  the  opposite  direction.  These  motions  are  transmitted 
by  delicate  multiplying  levers  to  an  index  which  moves  on  a  scale.  The 
instrument  is  graduated  empirically  by  comparing  its  indications  under 
different  pressures  with  those  of  an  ordinary  mercurial  barometer. 

The  aneroid  has  the  advantage  of  being  portable,  and  can  be  constructed 
of  such  delicacy  as  to  indicate  the  difference  in  pressure  between  the 
height  of  an  ordinary  table  and  the  ground.  It  is  hence  much  used  in 
determining  heights  in  mountain  ascents.  But  it  is  liable  somewhat  to 
get  out  of  order,  especially  when  it  has  been  subjected  to  great  variations 
of  pressure  ;  and  its  indications  must  from  time  to  time  be  compared  by 
means  of  a  standard  barometer. 

174.  ]Laws  of  tbe  mixture  of  grases. — If  a  communication  is  opened 
between  two  closed  vessels  containing  gases,  they  at  once  begin  to  mix, 
whatever  be  their  density,  and  in  a  longer  or  shorter  time  the  mixture  is 
complete,  and  will  continue  so,  unless  chemical  action  or  some  other  ex- 
traneous cause  intervene.  The  laws  which  govern  the  mixture  of  gases 
may  be  thus  stated  : 

I.  The  mixture  takes  place  rapidly  and  is  homogetteous,  that  is,  each 
Portion  of  the  mixture  contains  the  two  gases  in  the  same  proportioii. 

II.  If  the  gases  severally  and  the  7nixture  have  the  same  temperature, 
and  if  the  gases  severally  and  the  mixture  occupy  the  same  volume, then'^he 
p7-essure  on  the  imit  of  area  exerted  by  the  mixture  will  equal  the  sum  of 
pressures  o?i  the  unit  of  a7'ea  exerted  by  the  gases  severally. 

From  the  second  law  a  very  convenient  formula  can  be  easily  deduced. 
Let  v^,  v^,v^....  be  the  volumes  of  several  gases  under  pressure  of 
Px,po,pc^  ....  respectively.  Suppose  these  gases  when  mixed  to  have 
a  volume  V,  under  a  pressure  P,  the  temperatures  being  the  same.  By 
Boyle's  law  we  know  that  v^  will  occupy  a  volume  V  under  a  pressure// 
provided  that 

Similarly  V/./  =  v.p.^ 

and  so  on.     But  we  learn  from  the  above  law  that 

therefore  V?  =  v^p^  +  vj>^  +  v^^+   . 

It  obviously  follows  that  if  the  pressures  are  all  the  same,  the  volume  of 
the  mixture  equals  the  sum  of  the  separate  volumes. 

The  first  law  was  shown  experimentally  by  Berthollet,  by  means  of  an 
apparatus  represented  in  fig.  124.  It  consists  of  two  glass  globes  pro- 
vided with  stopcocks,  which  can  be  screwed  one  on  the  other.  The 
upper  globe  was  filled  with  hydrogen,  and  the  lower  one  with  carbonic 
acid,  which  has  22  times  the  density  of  hydrogen.  The  globes  having 
been  fixed  together  were  placed  in  the  cellars  of  the  Paris  Observatory 
and  the  stopcocks  then  opened,  the  globe  containing  hydrogen  being 
uppermost.  Berthollet  found  after  some  time  that  the  pressure  had  not 
changed,  and  that,  in  spite  of  the  difference  in  density,  the  two  gases 
had  become  uniformly  mixed  in  the  two  globes.     Experiments  made  in 


136 


On  Gases. 


[174- 


the  same  manner  with  other  gases  gave  the  same  results,  and  it  was 

found  that  the  diffusion  was  more  rapid  in  proportion  as  the  difference 

between  the  densities  was  greater. 

The  second  law  may  be  demonstrated  by  passing  into  a  graduated 

tube,  over  mercury,  known  volumes  of  gas  at  known  pressures.     The 

pressure  and  volume  of  the  whole  mixture 
are  then  measured,  and  found  to  be  in  ac- 
cordance with  the  law. 

Gaseous  mixtures  follow  Boyle's  law,  like 
simple  gases,  as  has  been  proved  for  air 
(i66),  which  is  a  mixture  of  nitrogen  and 
oxygen. 

175.  Mixture  of  g^ases  and  liquids. 
Absorption.  —  Water  and  many  liquids 
possess  the  property  of  absorbing  gases. 
Under  the  same  conditions  of  pressure  and 
temperature  a  liquid  does  not  absorb  equal 
quantities  of  different  gases.  At  the  ordi- 
nary temperature  and  pressure  water  dis- 
solves jflo  its  volume  of  nitrogen,  ^^f-  its 
volume  of  oxygen,  its  own  volume  of  carbonic 
acid,  and  430  times  its  volume  of  ammo- 
niacal  gas. 

The  whole  subject  of  gas  absorption  has 
^^'  ^^'^'  been  investigated  by  Bunsen,  to  whose  work* 

the  student  is  referred  for  further  information.     The  general  laws  of  gas 

absorption  are  the  following  : — 

I.  I^or  the  same  gas,  the  same  liquid,  and  the  same  temperature,  the 
weight  of  gas  absorbed  is  propoi'tional  to  the  pressure.  This  may  also  be 
expressed  by  saying  that  at  all  pressures  the  volume  dissolved  is  the  same  ; 
or  that  the  density  of  the  gas  absorbed  is  in  a  constant  relation  with  that 
of  the  external  gas  which  is  not  absorbed. 

Accordingly,  when  the  pressure  diminishes,  the  quantity  of  dissolved 
gas  decreases.  If  a  solution  of  gas  be  placed  under  the  air-pump  and  a 
vacuum  created,  the  gas  obeys  its  expansive  force  and  escapes  with  effer- 
vescence. 

II.  The  quantity  of  gas  absorbed  is  greater  when  the  temperature  is 
lower-,  that  is  to  say,  when  the  elastic  force  of  the  gas  is  less. 

III.  The  quantity  of  gas  which  a  liquid  can  dissolve  is  independent  of 
the  nature  and  of  the  quantity  of  other  gases  which  it  may  already  hold  in 
solution. 

In  every  gaseous  mixture  each  gas  exercises  the  same  pressure  as  it 
would  if  its  volume  occupied  the  whole  space ;  and  the  total  pressure  is 
equal  to  the  sum  of  the  individual  pressures.  When  a  liquid  is  in  contact 
with  a  gaseous  mixture,  it  absorbs  a  certain  part  of  each  gas,  but  less  than 
it  would  if  the  whole  space  were  occupied  by  each  gas.  The  quantity  of 
each  gas  dissolved  is  proportional  to  the  pressure  which  the  unabsorbed 
*  Gasometric  Methods,  by  R.  Bunsen,  translated  by  Prof.  Roscoe. 


176] 


A  rchimedes'  Principle  applied  to  Gases. 


m 


gas  exercises  alone.  For  instance,  oxygen  forms  only  about  I  the  quantity 
of  air  ;  and  water,  under  ordinary  conditions,  absorbs  exactly  the  same 
quantity  of  oxygen  as  it  would  if  the  atmosphere  were  entirely  formed  of 
this  gas  under  a  pressure  equal  to  \  that  of  the  atmosphere. 


t 


CHAPTER   III. 

PRESSURE  ON  BODIES  IN  AIR.   BALLOONS. 

176.  Archimedes'  principle  applied  to  g:ases. — The  pressure  exerted 
by  gases  on  bodies  immersed  in  them  is  transmitted  equally  in  all  direc- 
tions, as  has  been  shown  by  the  experiment  with  the  Magdeburg  hemi- 
spheres. It  therefore  follows  that  all  which  has  been  said  about  the 
equilibrium  of  bodies  in  hquids  applies  to  bodies  in  air ;  they  lose  a  part 
of  their  weight  equal  to  that  of  the  air 
which  they  displace. 

The  loss  of  weight  in  air  is  demon- 
strated by  means  of  the  baroscope, 
which  consists  of  a  scalebeam,  at  one 
of  whose  extremities  a  small  leaden 
weight  is  supported,  and  at  the  other 
there  is  a  hollow  copper  sphere 
(fig.  125).  In  the  air  they  exactly 
balance  one  another;  but  when  they 
are  placed  under  the  receiver  of  the 
air  pump  and  a  vacuum  is  produced, 
the  sphere  sinks;  thereby  showing 
that  in  reality  it  is  heavier  than  the 
small  leaden  weight.  Before  the  air 
is  exhausted  each  body  is  buoyed'  up 
by  the  weight  of  the  air  which  it  dis- 
places. But  as  the  sphere  is  much  the 
larger  of  the  two,  its  weight  undergoes 
most  apparent  diminution,  and  thus, 
though  in  reality  the  heavier  body,  it  is  balanced  by  the  small  leaden 
weight.  It  may  be  proved  by  means  of  the  same  apparatus  that  this  loss 
is  equal  to  the  weight  of  the  displaced  air.  Suppose  the  volume  of  the 
sphere  is  10  cubic  inches.  The  weight  of  this  volume  of  air  is  3-1  grains. 
If  now  this  weight  be  added  to  the  leaden  weight,  it  will  overbalance  the 
sphere  in  air,  but  will  exactly  balance  it  in  vacuo. 

The  principle  of  Archimedes  is  true  for  bodies  in  air  ;  all  that  has  been 
said  about  bodies  immersed  in  liquids  applies  to  them,  that  is,  that  when 
a  body  is  heavier  than  air,  it  will  sink,  owing  to  the  excess  of  its  weight 
over  the  buoyancy.  If  it  is  as  heavy  as  air,  its  weight  will  exactly  counter- 
balance the  buoyancy,  and  the  body  will  float  in  the  atmosphere.  If  the 
body  is  lighter  than  air,  the  buoyancy  of  the  air  will  prevail,  and  the  body 


Fig. 


138  On  Gases.  [176- 

will  rise  in  the  atmosphere  until  it  reaches  a  layer  of  the  same  density  as 
its  own.  The  force  of  the  ascent  is  equal  to  the  excess  of  the  buoyancy 
over  the  weight  of  the  body.  This  is  the  reason  why  smoke,  vapours, 
clouds,  and  air  balloons  rise  in  the  air. 


*  ,  AIR   BALLOONS. 

177.  Air  balloons. — Air  balloons  are  hollow  spheres  made  of  some  light 
impermeable  material,  which,  when  filled  with  heated  air,  with  hydrogen 
gas,  or  with  coal  gas,  rise  in  the  air  in  virtue  of  their  relative  lightness. 

They  were  invented  by  the  brothers  Mongolfier,  of  Annonay,  and  the 
first  experiment  was  made  at  that  place  in  June  1783.  Their  balloon  was 
a  sphere  of  40  yards  in  circumference,  and  weighed  500  pounds.  At  the 
lower  part  there  was  an  aperture,  and  a  sort  of  boat  was  suspended,  in 
which  fire  was  lighted  to  heat  the  internal  air.  The  balloon  rose  to  a  height 
of  2,200  yards,  and  then  descended  without  any  accident. 

Charles,  a  professor  of  physics  in  Paris,  substituted  hydrogen  for  hot  air. 
He  himself  ascended  in  a  balloon  of  this  kind  in  December  1783.  The  use 
of  hot  air  balloons  was  entirely  given  up  in  consequence  of  the  serious 
accidents  to  which  they  were  liable. 

Since  then,  the  art  of  ballooning  has  been  greatly  extended,  and  many 
ascents  have  been  made.  That  which  Gay-Lussac  made  in  1804  was  the 
most  remarkable  for  the  facts  with  which  it  has  enriched  science,  and  for 
the  height  which  he  attained — 23,000  feet  above  the  sea  level.  At  this 
height  the  barometer  descended  to  I2"6  inches,  and  the  thermometer 
which  was  31°  C.  on  the  ground,  was  9  degrees  below  zero. 

In  these  high  regions,  the  dryness  was  such  on  the  day  of  Gay-Lussac's 
ascent,  that  hygrometric  substances,  such  as  paper,  parchment,  etc.,  became 
dried  and  crumpled  as  if  they  had  been  placed  near  the  fire.  The  respi- 
ration and  circulation  of  the  blood  were  accelerated  in  consequence  of  the 
great  rarefaction  of  the  air.  Gay-Lussac's  pulse  made  120  pulsations  in  a 
minute,  instead  of  66,  the  normal  number.  At  this  great  height  the  sky 
had  a  very  dark  blue  tint,  and  an  absolute  silence  prevailed. 

One  of  the  most  remarkable  of  recent  ascents  was  made  by  Mr. 
Glaisher  and  Mr.  Coxwell,  in  a  large  balloon  belonging  to  the  latter. 
This  was  filled  with  90,000  cubic  feet  of  coal  gas  (sp.  gr.  0-37  to  o'33)  ; 
the  weight  of  the  load  was  600  pounds.  The  ascent  took  place  at  i  p.m. 
on  September  5,  1861  ;  at  i°  28'  they  had  reached  a  height  of  15,750 
feet,  and  in  eleven  minu^s  after  a  height  of  21,000  feet,  the  temperature 
being-  10*4;  at  1°  50'  they  were  at  26,200  feet,  with  the  thermometer  at 

-  1 5*2°    At  1°  52'  the  height  attained  was  29,000  feet,  and  the  temperature 

—  i6'0  C.  At  this  height  the  rarefaction  of  the  air  was  so  great,  and  the 
cold  so  intense,  that  Mr.  Glashier  fainted,  and  could  no  longer  observe. 
According  to  an  approximate  estimation  the  lowest  barometric  height  they 
attained  was  7  inches,  which  would  correspond  to  an  elevation  of  36,000 
to  37,000  feet. 

1 78.  Construction  and  managrement  of  balloons. — A  balloon  is  made 
of  long  bands  of  silk  sewn  together  and  covered  with  caoutchouc  varnish, 


-178] 


A  ir  Balloons. 


139 


which  renders  it  air-tight.  At  the  top  there  is  a  safety  valve  closed  by  a 
spring  which  the  aeronaut  can  open  at  pleasure  by  means  of  a  cord.  A 
light  wicker-work  boat  is  suspended  by  means  of  cords  to  a  net-work, 
which  entirely  covers  the  balloon. 

A  balloon  of  the  ordinary  dimensions,  which  can  carry  three  persons, 
is  about  16  yards  high,  12  yards  in  diameter,  and  its  volume  when  it  is 
quite  full  is  about  680  cubic  yards.  The  balloon  itself  weighs  200  pounds  ; 
the  accessories,  such  as  the  rope  and  boat,  100  pounds. 

The  balloon  is  filled  either  with  hydrogen  or  with  coal  gas.  Although 
the  latter  is  heavier  than  the  former,  it  is  generally  preferred,  because  it 
is  cheaper  and  more  easily  obtained. 
It  is  passed  into  the  balloon  from 
the  gas  reservoir  by  means  of  a 
flexible  pipe.  It  is  important  not  to  fill 
the  balloon  quite  full,  for  the  atmos- 
pheric pressure  diminishes  as  it  rises 
(fig.  126),  and  the  gas  inside  expand- 
ing in  consequence  of  its  elastic  force, 
tends  to  burst  it.  It  is  sufficient  for 
the  ascent  if  the  weight  of  the  dis- 
placed air  exceeds  that  of  the  balloon 
by  8  or  10  pounds.  And  this  force 
remains  constant  so  long  as  the  balloon 
is  not  quite  distended  by  the  dilata- 
tion of  the  air  in  the  interior.  If  the 
atmospheric  pressure,  for  example 
has  diminished  to  one  half,  the  gas 
in    the  balloon  according    to  Boyle's 


volume  of  the  air  displaced  is  therefore 
twice  as  great ;  but  since  its  density  has 
become  only  one-half,  the  weight,  and 
consequently  the  upward  buoyancy,  are 
the  same.  When  once  the  balloon  is 
completely  dilated,  if  it  continue  to 
rise  the  force  of  the  ascent  decreases, 
for  the  volume  of  the  displaced  air 
remains  the  same,  but  its  density  di- 
minishes, and  a  time  arrives  at  which 
the  buoyancy  is  equal  to  the  weight  of 
tlie  balloon.  The  balloon  can  now 
only  take  a  horizontal  direction,  carried 
by  the  currents  of  air  which  prevail  in 
the  atmosphere.  The  aeronaut  knows 
by  the  barometer  whether  he  is  ascend- 
ing or  descending  ;  and  by  the  same 
means  he  determines  the  height  which  he  has  reached.  A  long  flag  fixed  to 
the  boat  would  indicate,  by  the  position  it  takes  either  above  or  below, 
whether  the  balloon  is  descending  or  ascendino-. 


Fig.  126. 


40 


On  Gases 


[178- 


At     the 
in    1794, 


battle     of 
a    captive 


When  the  aeronaut  wishes  to  descend,  he  opens  the  valve  at  the  top  of 
the  balloon  by  means  of  the  cord,  which  allows  gas  to  escape,  and  the 
balloon  sinks.  If  he  wants  to  descend  more  slowly,  or  to  rise  ao-ain  he 
empties  out  bags  of  sand,  of  which  there  is  an  ample  supply  inihe  car. 
The  descent  is  facilitated  by  means  of  a  grappling  iron  fixed  to  the  boat. 
When  once  this  is  fixed  to  any  obstacle,  the  balloon  is  lowered  by  pulling 
the  cord. 

The  only  practical  applications  which  air  balloons  have  hitherto  had 
_______  have   been    in    military    recon- 

noitring. 
Fleurus, 

balloon,  that  is,  one  held  by  a 
cord,  was  used,  in  which  there 
was  an  observer  who  reported 
the  movements  of  the  enemy 
by  means  of  signals.  At  the 
battle  of  Solferino  the  move- 
ments and  dispositions  of  the 
Austrian  troops  were  watched 
by  a  captive  balloon  ;  and  in 
the  war  in  America  balloons 
were  frequently  used,  while 
their  importance  during  the 
siege  of  Paris  is  fresh  in  all 
memories.  The  whole  subject 
of  military  ballooning  has  been 
treated  in  two  papers  by  Cap- 
tain Grover  and  by  Captain 
Beaumont,  in  a  recent  volume 
of  the  Professional  Papers  of  the 
Royal  Engineers.  Many  as- 
cents have  recently  been  made 
by  Mr.  Glaisher  for  the  purpose 
of  making  meteorological  ob- 
servations in  the  higher  regions  of  the  atmosphere.  Air  balloons  can  only 
be  truly  useful  when  they  can  be  guided,  and  as  yet  all  attempts  made 
with  this  view  have  coriapletely  failed.  There  is  no  other  course  at  pre- 
sent than  tsiWsfe'^lritb^^  until  there  is  a  current  which  has  more  or  less 
the  desired  direction.  '^ 

179.  Parachute. — The  object  of  the  parachute  is  to  allow  the  aeronaut 
to  leave  the  balloon,  by  giving  him  the  means  of  lessening  the  rapidity 
of  his  descent.  It  consists  of  a  large  circular  piece  of  cloth  ffig.  127^ 
about  16  feet  in  diameter,  and  which  by  the  resistance  of  the  air  spreads 
out  like  a  gigantic  umbrella.  In  the  centre  there  is  an  aperture,  through 
which  the  air  compressed  by  the  rapidity  of  the  descent  makes  its 
escape  ;  for  otherwise  oscillations  might  be  produced,  which,  when  com- 
municated to  the  boat,  would  be  dangerous. 

In  '^g.  126  there  is  a  parachute  attached  to  the  net-work  of  the  balloon 


Fig.  127. 


-181]  Air  Pump.  141 

by  means  of  a  cord  which  passes  round  a  pulley,  and  is  fixed  at  the  other 
end  to  the  boat.  When  the  cord  is  cut  the  parachute  sinks,  at  first 
very  rapidly,  but  more  slowly  as  it  becomes  distended,  as  represented 
in  the  figure. 

1 80.  Calculation  of  the  weight  which  a  balloon  can  raise. — To 
calculate  the  weight  which  can  be  raised  by  a  balloon  of  given  dimensions, 
let  us  suppose  it  perfectly  spherical,  and  premise  that  the  formulae  which 
express   the   volume   and    the   superficies   in  terms   of  the   radius   are 

V  =  ~ —  and  S  =  \-k^  ;  tt  being  the  ratio  of  the  circumference  to  the 

diameter,  and  equal  to  3-1416.  The  radius  R  being  measured  in  feet,  let 
p  be,  in  pounds,  the  weight  of  a  square  foot  of  the  material  of  which  the 
balloon  is  constructed  ;  let  P  be  the  weight  of  the  car  and  the  accessories 
a  the  weight  in  pounds  of  a  cubic  foot  of  air  at  zero,  and  under  the 
pressure  076,  and  a'  the  weight  of  the  same  volume  under  the  same  con- 
dition of  the  gas  with  which  the  balloon  is  inflated  (144).  Then  the 
total  weight  of  the  envelope  in  pounds  will  be  "4irR2/  ;  that  of  the  gas 

will  be  ^^^"^'j  and  that  of  the  displaced  air  4!:5!^.  If  X  be  the  weight 
which  the  balloon  can  support,  we  have  , 

x  =  4iR!_^-4':^'-4.R!/^-p. 

3  3 

Whence 

But,  as  we  have  before  seen  (178),  in  order  that  the  balloon  may  rise,  the 
weights  must  be  less  by  8  or  10  pounds  than  that  given  by  this  equation. 


CHAPTER   IV. 

APPARATUS   FOUNDED   ON   THE  PROPERTIES   OF  AlR. 

181.  Air  pump. — The  air  pump  is  an  instrument  by  which  a  vacuum 
can  be  produced  in  a  given  space,  or  rather  by  which  air  can  be  greatly 
rarefied,  for  an  absolute  vacuum  cannot  be  produced  by  its  means.  It 
was  invented  by  Otto  von  Guericke  in  1650,  a  few  years  after  the  inven- 
tion of  the  barometer. 

The  air  pump,  as  now  usually  constructed,  may  be  described  as  follows  : 
In  fig.  128,  which  shows  the  general  arrangement,  E  is  the  receive7%\r\. 
which  the  vacuum  is  to  be  produced.  It  is  a  bell  glass,  resting  on  a  plate 
D,  of  thick  glass  ground  perfectly  smooth.  In  the  centre  of  D,  at  C,  there 
is  an  opening  by  which  a  communication  is  made  between  the  interior  of 
the  receiver  and  of  the  cyHnders  P,  P.  This  communication  is  effected 
by  a  tube  or  pipe  passing  through  the  body  of  the  plate  A,  and  then 
branching  off  at  right  angles,  as  shown  by  Kco  Kcs,  in  fig  129,  which 


142 


On  Gases. 


[181- 


represents  a  horizontal  section  of  the  machine.  In  the  cyHnders — which 
are  commonly  of  glass,  and  which  are  firmly  cemented  to  the  plate  A  — 
are  two  pistons,  P  and  Q,  fitting  air-tight.  Each  piston  is  moved  by  a 
rack,  working  with  a  pinion,  H,  turned  by  a  handle,  M.  This  is  shown 
more  plainly  in  fig.  1 30,  which  represents  a  vertical  section  of  the  machine 
through  the  cylinders  :  here  H  is  the  pinion,  and  MN  the  handle.  When 
M  is  forced  down  one  piston  is  raised,  and  the  other  depressed.  When 
M's  action  is  reversed,  the  former  piston  is  depressed,  and  the  latter 
raised.  ♦ 

The  action  of  the  machine  is  this  :  Each  cylinder  is  fitted  with  a  valve 
so  contrived  that  when  its  piston  is  raised,  communication  is  opened 
between  the  cyhnder  and  the  receiver  :  when  it  is  depressed  the  corn- 


Fig.  128. 

munication  is  closed.  Now  if  P  were  simply  raised,  a  vacuum  would  be 
formed  below  P  ;  but  as  a  communication  is  opened  with  the  receiver  E, 
the  air  in  E  expands  so  as  to  fill  both  the  receiver  and  the  cylinder.  As 
soon  as  the  piston  begins  to  descend,  the  communication  is  closed,  and 
none  of  the  air  in  the  cylinder  returns  to  the  receiver,  but,  by  means  of 
properly  constructed  valves,  escapes  into  the  atmosphere.  Consequently 
the  rarefaction  which  the  air  in  the  receiver  has  undergone  is  permanent. 
By  the  next  stroke  a  further  rarefaction  is  produced  :  and  so  on,  at  each 
succeeding  stroke. 

It  is  plain  that  when  the  rarefaction  has  proceeded  to  a  considerable 
extent  the  atmospheric  pressure  on  the  top  of  P  will  be  very  great,  but  it 


-181] 


Air  Pump. 


143 


will  be  very  nearly  balanced  by  the  atmospheric  pressure  on  the  top  ot 
the  other  piston.     Consequently  the  experimenter  will  have  to  overcome 


Fig.  132. 


Fig.  129. 


Fig.  130.  Fig.  131 


This  is  the  reason  why  two 


The 
130. 


only  the  difference  of  the  two  pressures, 
cylinders  are  employed. 

To  explain  the  action  of  the  valves  we  must  go  into  particulars, 
general  arrangement  of  the  interior  of  the  cylinders  is  shown  in  fig. 
Fig.  133  shows  the  section  of  the  piston  in 
detail.  The  piston  is  formed  of  two  brass 
discs  (X  and  V),  screwed  to  one  another,  and 
compressing  between  them  a  series  of  leathern 
discs  Z,  whose  diameters  are  slightly  greater 
than  those  of  the  brass  discs.  The  leather  is 
thoroughly  saturated  with  oil,  so  as  to  slide  air- 
tight, though  with  but  little  friction,  within  the 
cylinder.  To  the  centre  of  the  upper  disc  is 
screwed  a  piece,  B,  to  which  the  rack  H  is 
riveted.  The  piece  B  is  pierced  so  as  to  put 
the  interior  of  the  cylinder  into  communication 
with  the  external  air.  This  communication  is 
closed  by  a  valve  /,  held  down  by  a  delicate 
spring,  r.  When  the  piston  is  moved  downward 
the  air  below  the  piston  is  compressed  until  it 
forces  up  /  and  escapes.  The  instant  the  action 
is  reversed,  the  valve  /  falls,  and  is  held  down 
by  the  spring,  and  the  pressure  of  the  external 
air,  which  is  thereby  kept  from  coming  in. 
The  communication  between  the  cylinder  below  Fig.  133. 

the  piston  and  the  receiver  is  opened  and  closed 
by  the  valve  marked  o  in   fig.   130,  and  sg  in    fig.   133.     The   rod  sg 


144  On  Gases.  [181- 

passing  through  the  piston  is  held  by  friction,  and  is  raised  with  it  ; 
but  is  kept  from  being  Hfted  through  more  than  a  very  small  distance  by 
the  top  of  the  cylinder,  while  the  piston,  in  continuing  its  upward  motion, 
slides  over  sg.  When  the  piston  descends  it  brings  the  valve  with  it, 
which  at  once  cuts  off  the  communication  between  the  cylinder  and  the 
receiver. 

182.  Air  pump  g:augre. — When  the  pump  has  been  worked  sometime, 
the  pressure  in  the  receiver  is  indicated  by  the  difference  of  level  of  the 
mercury  in  the  two  legs  of  a  glass  tube  bent  like  a  syphon,  one  of  which 
is  opened,  and  the  other  closed  like  the  barometer.  This  little  apparatus, 
which  is  called  \};\&  gauge, '\s  fixed  to  an  upright  scale,  and  placed  under 
a  small  bell  jar,  which  communicates  with  the  receiver  E  by  a  stop- 
cock, A,  inserted  in  the  tube  leading  from  the  orifice  C  to  the  cylinders, 
fig.  128. 

Before  commencing  to  exhaust  the  air  in  the  receiver,  its  elastic  force 
exceeds  the  weight  of  the  column  of  mercury,  which  is  in  the  closed 
branch  and  which  consequently  remains  full.  But  as  the  pump  is 
worked,  the  elastic  force  soon  diminishes,  and  is  unable  to  support  the 
weight  of  the  mercury,  which  sinks  and  tends  to  stand  at  the  same  level 
in  both  legs.  If  an  absolute  vacuum  could  be  produced,  they  would  be 
exactly  on  the  same  level,  for  there  would  be  no  pressure  either  on  the 
one  side  or  the  other.  But  with  the  very  best  machines  the  level  is 
always  about  a  thirtieth  of  an  inch  higher  in  the  closed  branch,  which 
indicates  that  the  vacuum  is  not  absolute,  for  the  elastic  force  of  the 
residue  is  equal  to  the  pressure  of  a  column  of  mercury  of  that  height. 

Practically  the  machine  can  never  give  an  absolute  vacuum,  for,  as  we 
have  seen,  the  air  becomes  ultimately  so  rarefied  that,  when  the  pistons 
are  at  the  bottom  of  the  cylinder,  its  elastic  force  cannot  overcome  the 
pressure  on  the  valves  in  the  inside  of  the  piston,  which,  therefore,  do  not 
open. 

Theoretically  an  absolute  vacuum  is  also  impossible ;  for,  since  the 
volume  of  each  cylinder  is,  say,  ^^  that  of  the  receiver,  only  ^j  of  the  air 
in  the  receiver  is  extracted  at  each  stroke  of  the  piston,  and  consequently 
it  is  impossible  to  exhaust  all  the  air  which  it  contains.  The  theoretical 
degree  of  exhaustion  after  a  given  number  of  strokes  is  easily  calculated 
as  follows  : — Let  A  denote  the  volume  of  the  receiver,  including  in  that 
term  the  pipe ;  B  the  volume  of  the  cylinder  between  the  highest  and 
lowest  positions  of  the  piston  ;  and  assume  for  the  sake  of  distinctness 
that  there  is  only  one  cyhnder ;  then  the  air  which  occupied  A  before 
the  piston  is  lifted  occupies  A  +  B  after  it  is  lifted,  and  consequently  if 
D ,  is  the  density  at  the  end  of  the  first  stroke  and  D  the  original  density, 
we  must  have 

'        A  +  B 
If  Dg  is  the  density  at  the  end  of  the  second  stroke,  we  have  for  just  the 
same  reason 

'        'A+B         Va+B/ 


-183]  Air  Pump.  145 

Now  this  reasoning  will  apply  to  71  strokes  ; 
consequently  D„  =  D  (    — : — )  . 

If  there  are  two  equal  cylinders,  the  same  formula  holds,  but  in  this 
case,  in  counting  71,  upstrokes  and  downstrokes  equally  reckon  as  one. 

It  is  obvious  that  the  exhaustion  is  never  complete,  since  D„  can  be 
zero  only  when  71  is  infinite.  However,  no  very  great  number  of  strokes 
is  required  to  render  the  exhaustion  virtually  complete  even  if  A  is  several 
times  greater  than  B.  Thus  if  A  =  10  B,  a  hundred  strokes  will  reduce  the 
density  from  D  to  0-0004  D  ;  that  is,  if  the  initial  pressure  is  30  in.,  the 
pressure  at  the  end  of  100  strokes  is  0*012  of  an  inch.  . 

Practically,  however,  a  limit  is  placed  on  the  rarefaction  that  can  be 
produced  by  any  given  air  pump  ;  for,  as  we  have  seen,  the  air  becomes 
ultimately  so  rarefied  that,  when  the  pistons  are  at  the  bottom  of  the 
cylinder,  its  elastic  force  cannot  overcome  the  pressure  on  the  valves  in 
the  inside  of  the  piston ;  they  therefore  do  not  open,  and  there  is  no 
further  action  of  the  pump. 

183.  Boubly-exhaustingr  stopcock. — M.  Babinet  has  invented  an  im- 
proved stopcock,  by  which  the  exhaustion  of  the  air  can  be  carried  to 
a  very  high  degree.  This  stopcock  is  placed  in  the  fork  of  the  pipe 
leading  from  the  receiver  to  the  two  cylinders  ;  it  is  perforated  by 
several  channels,  which  are  successively  used  by  turning  it  into  two 
different  positions.  Fig.  129  represents  a  horizontal  section  of  the  stop- 
cock R,  in  such  a  position  that,  by  its  central  opening  and  two  lateral 
openings,  it  forms  a  communication  between  the  orifice  K  of  the  plate, 
and  the  two  valves  o  and  s.  The  machine  then  works  as  has  been 
described.  In  fig.  132  the  stopcock  has  been  turned  a  quarter,  and 
the  transversal  channel  db,  which  was  horizontal  in  fig.  129,  is  now 
vertical,  and  its  extremities  are  closed  by  the  side  of  the  hole  in  which 
the  stopcock  works.  But  a  second  channel,  which  was  closed  before, 
and  which  has  taken  the  place  of  the  first,  now  places  the  right  cylinder 
alo7ie  in  communication  with  the  receiver  by  the  channel  cbs  (fig.  132), 
and  it  further  connects  the  right  with  the  left  cylinder  by  a  channel  aeo 
(fig.  132),  or  aico  (fig.  131).  This  channel  passes  from  a  central  opening 
a,  placed  at  the  base  of  the  right  cylinder,  across  the  stopcock  to  the 
valve  ^,  of  the  other  cylinder,  as  represented  in  figs.  131  and  132  :  but 
this  channel  is  closed  by  the  stopcock  when  it  is  in  its  first  position,  as  is 
seen  in  figs.  129  and  130. 

The  right  piston  in  rising  exhausts  the  air  of  the  receiver,  but  when  it 
descends  the  exhausted  air  is  driven  into  the  left  cylinder  through  the 
orifice  a,  the  channel  io^  and  the  valve  o  (fig.  131),  which  is  open.  When 
the  same  piston  rises,  that  of  the  left  sinks  ;  but  the  air  which  is  above 
it  does  not  return  into  the  right  cylinder,  because  the  valve  o  is  now 
closed.  As  the  right  cylinder  continues  to  exhaust  the  air  in  the  re- 
ceiver, and  to  force  it  into  the  left  cylinder,  the  air  accumulates  here,  and 
ultimately  acquires  sufficient  tension  to  raise  the  valve  of  the  piston  Q, 
which  was  impossible  before  the  stopcock  was  turned,  for  it  is  only  when 
the  valves  in  the  piston  no  longer  open,  that  a  quarter  of  a  turn  is  given 
to  the  stopcock. 


146 


On  Gases. 


[184- 


184.  Siancbi's  air  pump. — M.  Bianchi  has  invented  an  air  pump 
which  has  several  advantages.  It  is  made  entirely  of  iron,  and  it  has 
only  one  cylinder,  which  oscillates  on  a  horizontal  axis  fixed  at  its  base, 
as  seen  in  fig.  1 34.  A  horizontal  shaft,  with  heavy  fly-wheel,  V,  works  in 
a  frame,  and  is  turned  by  a  handle,  M.  A  crank,  m,  which  is  joined  to 
the  top  of  the  piston-rod,  is  fixed  to  the  same  shaft,  and  consequently  at 
every  revolution  of  the  wheel  the  cyHnder  makes  two  oscillations. 


Fig-  134- 

In  some  cases,  as  in  that  shown  in  the  figure,  the  crank  and  the  fly- 
wheel are  on  parallel  axes  connected  by  a  pair  of  cog-wheels.  The  modi- 
fication in  the  action  produced  by  this  arrangement  is  as  follows  : — If  the 
cog-wheel  on  the  former  axis  has  twice  as  many  teeth  as  that  on  the  latter 
axis,  the  pressure  which  raises  the  piston  is  doubled  ;  an  advantage  which 
is  counterbalanced  by  the  inconvenience  that  now  the  piston  will  make 
one  oscillation  for  one  revolution  of  the  fly-wheel. 


-185] 


Air  Pump. 


U7 


The  machine  is  double  acting  ;  that  is  the  piston  PP  (fig.  135)  pro- 
duces a  vacuum  both  in  ascending  and  descending.  This  is  effected  by 
the  following  arrangements  : — In  the  piston  there  is  a  valve,  b,  opening 
upwards  as  in  the  ordinary  machine.  The  piston  rod  AA  is  hollow,  and 
in  the  inside  there  is  a  copper  tube,  X,  by  which  the  air  makes  its  escape 
through  the  valve  b.  At  the  top  of  the  cylinder  there  is  a  second  valve 
a,  opening  upwards.  An  iron  rod,  D,  works  with  gentle  friction  in  the 
piston,  and  terminates  at  its  ends  in  two  conical  valves,  s  and  s\  which 
fit  into  the  openings  of  the  tube  BC  leading  to  the  receiver. 

Let  us  suppose  the  piston  descends.  The  valve  s'  is  then  closed,  and 
the  valve  s  being  open,  the  air  of  the  receiver  passes  in  the  space  above 
the  piston,  while  the  air  in  the  space  below  the  piston  undergoes  com- 
pression, and  raising  the  valve,  escapes  by  the  tube  X,  which  commu- 
nicates with  the  atmosphere.  When  the  piston  ascends,  the  exhaustion 
takes  place  through  s',  and  the 
valve  s  being  closed,  the  com- 
pressed air  escapes  by  the  valves. 

The  machine  has  a  stopcock 
for  double  exhaustion,  similar  to 
that  already  described  (183).  It 
is  also  oiled  in  an  ingenious 
manner.  A  cup,  E,  round  the 
rod  is  filled  with  oil,  which 
passes  into  the  annular  space 
between  the  rod  AA  and  the 
tube  X  ;  it  passes  then  into  a 
tube  00,  in  the  piston,  and  forced 
by  the  atmospheric  pressure,  is 
uniformly  distributed  en  the  sur- 
face of  the  piston. 

The  apparatus  is  of  iron,  and 
can  consequently  be  made  of 
much  greater  dimensions  than 
the  ordinary  machine.  A  va- 
cuum can  also  be  produced  with 
it  in  far  less  time  and  in  appa- 
ratus of  greater  size  than  usual. 

185.  Sprengrel's  air  pump. — 
Sprengel  has  devised  a  form  of 
air  pump  which  depends  on  the 
principle  of  converting  the  space 
to  be  exhausted  into  a  Torri- 
cellian vacuum.  The  idea  and 
construction  of  the  apparatus  are 
thus  described  by  the  inventor. 

If  an  aperture  be  made  in  the 
top  of  a  barometer  tube,  the  mercury  sinks  and  draws  in  air  ;  if  the 
experiment  be  so  arranged  as  to  allow  air  to  enter  along  with  mercury 


148 


On  Gases. 


[185- 


and  if  the  supply  of  air  be  limited  while  that  of  mercury  is  unlimited,  the 
air  will  be  carried  away,  and  a  vacuum  produced.  The  following  is  the 
simplest  form  of  the  apparatus  in  which  this  action  is  realised.  In  fig. 
136  cd\s  a  glass  tube  longer  .than  a  barometer,  open  at  both  ends,  and 
connected  by  means  of  india-rubber  tubing  with  a  funnel,  A,  filled  with 
mercury  and  supported  by  a  stand.  Mercury  is  allowed  to  fall  in  this 
tube  at  a  rate  regulated  by  a  clamp  at  c ;  the  lower  end  of  the  tube  cd 
fits  in  the  flask  B,  which  has  a  spout  at  the  side  a  little  higher  than  the 
lower  end  of  cd ;  the  upper  part  has  a  branch  at  x  to  which  a  receiver 
R  can  be  tightly  fixed.  When  the  clamp  at  c  is  opened,  the  first  portion 
of  mercury  which  runs  out  closes  the  tube  and  prevents  air  from  en- 
tering below.  As  the  mercury  is  allowed  to  run  down,  the  exhaus- 
tion begins,  and  the  whole  length 
of  the  tube  from  x  to  d  \s  filled 
with  cylinders  of  air  and  mercury 
having  a  downward  motion.  Air 
and  mercury  escape  through  the 
spout  of  the  bulb  B  which  is  above 
the  basin  A,  where  the  mercury  is 
collected.  It  is  poured  back  from 
time  to  time  into  the  funnel  A,  to 
be  repassed  through  the  tube  until 
the  exhaustion  is  complete.  As 
this  point  is  approached,  the  en- 
closed air  between  the  mercury 
cylinders  is  seen  to  diminish,  until 
the  lower  part  of  cd  forms  a  con- 
tinuous column  of  mercury  about 
30  inches  high.  Towards  this  stage 
of  the  process  a  noise  is  heard 
like  that  of  a  water  hammer  when 
shaken ;  the  operation  is  com- 
pleted when  the  column  of  mercury 
encloses  no  air,  and  a  drop  of  mer- 
cury falls  on  the  top  of  the  column 
without  enclosing  the  slightest  air 
bubble.  The  height  of  the  column 
then  represents  the  height  of  the 
column  of  mercury  in  the  baro- 
meter ;  in  other  words  it  is  a  baro- 
meter whose  Torricellian  vacuum 
is  the  receiver  R.  This  apparatus 
has  been  used  with  great  success 
in  experiments  in  which  a  very 
complete  exhaustion  is  required, 
as  in  the  preparation  of  Geissler's 
It  may  be  advantageously  combined 


Fig.  136 


tubes.     (See  Book  X.  Chapter  VI.) 

with  an  exhausting  syringe  which  first  removes  the  greater  part  of  the  air, 

the  exhaustion  being  then  completed  as  above. 


-187]  M or r en's  Mercury  Pump.  149 

186.  Aspirating-  actions  of  currents  of  air. — When  a  jet  of  liquid 
or  of  a  gas  passes  through  air  it  carries  the  surrounding  air  along  with  it ; 
fresh  air  rushes  in  to  supply  its  place,  comes  also  in  contact  with  the  jet, 
and  is  in  like  manner  carried  away.  Thus  then  there  is  a  continual  rarefac- 
tion of  the  air  around  the  jet,  in  consequence  of  which  it  exerts  an 
aspiratory  action. 

This  phenomenon  may  be  well  illustrated  by  means  of  an  apparatus 
represented  in  fig.  137,  the  analogy  of  which  to  the  experiment  described 
(203)  will  be  at  once  evident.     It  consists 

of  a  wide  glass  tube  in  the  two  ends  of  |^-^-^^^^_^^ 

which  are  fitted  two  small  tubes  ab  and  c  !g;^£^g^^l^  -b_ 
cd\  in  the  bottom  is  a  manometer  tube  '^  ^^U^^^^^briH^^M 
containing  a  coloured  liquid.    On  blowing  ^ 

through  the  narrow  tube  the  liquid  at  A  ^^hw^^^^ 

is  seen  to  rise.     If  on  the  contrary  the  1 

wide  tube  be  blown  into,  a  depression  is  ^  i^^p 

To  this   class  of  phenomena  belongs  ^^ 

the  following  experiment,  which  is  a  simple  Pig  j-^^ 

modification  by  Faraday  of  one  originally 

described  by  Clement  and  Desormes.  Holding  one  hand  horizontal,  the 
palm  downwards  and  the  fingers  closed  you  blow  through  the  space  be- 
tween the  index  and  middle  finger.  If  a  piece  of  light  paper  of  2  or  3 
square  inches,  is  held  against  the  aperture  it  does  not  fall  as  long  as  the 
blowing  continues. 

The  old  water  bellows  still  used  in  mountainous  places  where  there  is 
a  continuous  fall,  is  a  further  application  of  the  principle.  Water  falling 
from  a  reservoir  down  a  narrow  tube  divides  and  carries  air  along  with  it ; 
and  if  there  are  apertures  in  the  side  through  which  air  can  enter,  this 
also  is  carried  along,  and  becomes  accumulated  in  a  reservoir  placed  below 
from  which  by  means  of  a  lateral  tube  it  can  be  directed  into  the  hearth 
of  a  forge. 

By  the  locomotive  stea7npip3  a  jet  of  steam  entering  the  chimney  of 
the  locomotive  carries  the  air  away,  so  that  fresh  air  must  arrive  through 
the  fire  and  thus  the  draught  be  kept  up.  In  Giffard's  injector  water  is 
pumped  by  means  of  a  jet  of  steam  into  the  boiler  of  a  steam  engine. 

187.  Morren's  mercury  pump. — Figs.  138  and  139  represent  a  mercu- 
rial air  pump,  which  is  an  improvement  by  Alvergniat,  of  a  form  devised 
by  Morren. 

It  consists  of  two  reservoirs,  A  and  B,  figs.  138  and  1 39,  connected  by  a 
barometer  tube  T,  and  a  long  caoutchouc  tube  C.  The  reservoir  B  and 
the  tube  T  are  fixed  to  a  vertical  support  A,  which  is  movable  and  open, 
and  can  be  alternately  raised  and  lowered  through  a  distance  of  nearly 
four  feet.  This  is  effected  by  means  of  a  long  wire  rope,  which  is  fixed  at 
one  end  to  the  reservoir  A,  and  passes  over  two  pulleys,  a  and  b,  the  latter 
of  which  is  turned  by  a  handle.  Above  the  reservoir  B  is  a  three-way 
cock  ;/ ;  to  this  is  attached  a  tube  </,  for  exhaustion,  and  on  the  left  is  an 
ordinary  stopcock  ;;/,  which  communicates  with  a  reservoir  of  mercury  7/, 


ISO 


On  Gases. 


[187- 


and  with  the  air.  The  exhausting  tube  d  is  not  in  direct  communication 
with  the  receiver  to  be  exhausted  :  it  is  first  connected  with  a  reservoir  o^ 
partially  filled  with  sulphuric  acid,  and  designed  to  dry  the  gases  which 
enter  the  apparatus.  A  caoutchouc  tube,  c,  makes  communication  with 
the  receiver  which  is  to  be  exhausted.  On  the  reservoir  6*  is  a  small  mer- 
cury manometer  p. 

These  details  being  understood,  suppose  the  reservoir  A  at  the  top  of 


Fig.  138. 


Fig.  139. 


its  course  (fig  138),  the  stopcock  m  open,  and  the  stopcock  n  turned  as 
seen  in  Z  ;  the  caoutchouc  tube»C,  the  tube  T,  the  reservoir  B,  and  the 
tube  above,  are  filled  with  mercury  as  far  as  v  ;  closing  then  the  stopcock 
m^  and  lowering  the  reservoir  A  (fig.  139),  the  mercury  sinks  in  the 
reservoir  B,  and  in  the  tube  T,  until  the  difference  of  levels  in  the  two 
tubes  is  equal  to  the  barometric  height,  and  there  is  a  vacuum  in  the 


189] 


Condensing  Pinnp. 


151 


reservoir  B.  Turning  now  the  stopcock  n,  as  shown  in  figure  X,  the 
gas  from  the  space  to  be  exhausted  passes  into  the  barometric  chamber 
B,  by  the  tubes  c  and  d,  and  the  level  again  'sinks  in  the  tube  T. 
The  stopcocks  are  now  replaced  in  the  first  position  (fig.  Z),  and  the 
reservoir  A  is  again  lifted,  the  excess  of  pressure  of  mercury  in  the 
caoutchouc  tube  expels  through  the  stopcock,  71  and  w,  the  gas  which 
had  passed  into  the  chamber  B,  and  if  a  few  droplets  of  mercury  are 
carried  along  with  them  they  are  collected  in  the  vessel  v.  The  pro- 
cess is  repeated  until  the  mercury  is  virtually  at  the  same  level  in  both 

legs. 

Like  Sprengel's  pump  this  is  very  slow  in  its  working,  and  like  it  is 
best  employed  in  completing  the  exhaustion  of  a  space  which  has  already 
been  partially  rarefied ;  for  a  vacuum 
of  j^^th  of  a  millimetre  may  be  obtained 
by  its  means. 

i88„  Condensingr  pump. — The  con- 
densing pump  is  an  apparatus  for 
compressing  air,  or  any  other  gas. 
The  form  usually  adopted  is  the  fol- 
lowing:  In  a  cylinder.  A,  of  small 
diameter  (fig.  141  j,  there  is  a  solid 
piston,  the  rod  of  which  is  moved  by 
the  hand.  The  cyhnder  is  provided 
with  a  screw  which  fits  into  the  re- 
ceiver K.  Fig.  140  shows  the  arrange- 
ment of  the  valves,  which  are  so  con- 
structed that  the  lateral  valve  0  opens 
from  the  outside,  and  the  lower  valve 
s  from  the  inside. 

When  the  piston  descends,  the 
valve  0  closes,  and  the  elastic  force 
of  the  compressed  air  opens  the  valve 
J,  which  thus  allows  the  compressed 
air  to  pass  into  the  receiver.  When 
the  piston  ascends,  s  closes  and  o 
opens,  and  permits  the  entrance  of 
fresh  air,  which  in  turn  becomes  com- 
pressed by  the  descent  of  the  piston, 
and  so  on. 

This  apparatus  is  chiefly  used  for  charging  liquids  with  gases.  For 
this  purpose  the  stopcock  B  is  connected  with  a  reservoir  of  the  gas,  by 
means  of  the  tube  D.  The  pump  exhausts  this  gas,  and  forces  it  into 
the  vessel  K,  in  which  the  liquid  is  contained.  The  artificial  gaseous 
waters  are  made  by  means  of  analogous  apparatus. 

1 89.  iTses  of  the  air  pump. — A  great  many  experiments  with  the  air 
pump  have  been  already  described.  Such  are  the  mercurial  rain  (13),  the 
fall  of  bodies  in  vacuo  (73),  the  bladder  (142),  the  bursting  of  a  bladder 
(148 j,  the  Magdeburg  hemispheres  (149},  and  the  baroscope  (176). 


152 


On  Gases. 


[189- 


Ihtjountain  in  vacuo  (fig.  142)  is  an  experiment  made  with  the  air 
pump,  and  shows  the  elastic  force  of  the  air.  It  consists  of  a  glass 
globe,  A,  provided  at  the  bottom  with  a  stopcock,  and  a  tubulure  which 
projects  into  the  interior.  Having  screwed  this  apparatus  to  the  air 
pump  it  is  exhausted,  and,  the  stopcock  being  closed,  it  is  placed  in  a 
vessel  of  water,  R.  Opening  then  the  stopcock,  the  atmospheric  pressure 
upon  the  water  in  the  vessel  makes  it  jet  through  the  tubulure  into  the 
interior  of  the  vessel  as  shown  in  the  drawing. 

Fig.  143  represents  an  experiment  illustrating  the  effect  of  atmospheric 
pressure  on  the  human  body.     A  glass  vessel,  open  at  both  ends,  being 


Fig.  142. 


Fig.  143. 


placed  on  the  plate  of  the  machine,  the  upper  end  of  the  cylinder  is  closed 
by  the  hands,  and  a  vacuum  is  made.  The  hand  then  becomes  pressed 
by  the  weight  of  the  atmosphere,  and  can  only  be  taken  away  by  a  great 
effort.  And  as  the  elasticity  of  the  fluids  contained  in  the  organs  is  not 
counterbalanced  by  the  weight  of  the  atmosphere,  the  palm  of  the  hand 
swells,  and  blood  tends  to  escape  from  the  pores. 

By  means  of  the  air  pump  it  may  be  shown  that  air,  by  reason  of  the 
oxygen  it  contains,  is  necessary  for  the  support  of  combustion  and  of  life. 
For  if  we  place  a  lighted  taper  under  the  receiver,  and  begin  to  exhaust 
the  air,  the  flame  becomes  weaker  as  rarefaction  proceeds,  and  is  finally 
extinguished.  Similarly  an  animal  faints  and  dies,  if  a  vacuum  is  formed 
in  a  receiver  under  which  it  is  placed.     Mammalia  and  birds  soon  die  in 


-190]       Apparatus  founded  on  the  Properties  of  A  ir.  1 5  3 

vacuo.     Fish  and  reptiles  support  the  loss  of  air  for  a  much  longer  time. 
Insects  can  live  several  days  in  vacuo. 

Substances  liable  to  ferment  may  be  kept  in  vacuo  for  a  long  time^ 
without  alteration,  as  they  are   not    in    contact   with   oxygen,  which    is 
necessary  for  fermentation.      Food   kept   in   hermetically-closed   cases, 
from  which  the  air  had  been  expelled,  has  been  found  as  fresh  after 
several  years  as  on  the  first  day. 

190.  Hero's  fountain. — Hero's  fountain,  which  derives  its  name  from 
its  inventor.  Hero,  who  lived  at  Alexandria,  120  B.C.,  depends  on  the 
elasticity  of  the  air.     It  consists  of  a  brass  dish,  D  (fig.  144),  and  of  two 


Fig.  144.  Fig.  145. 

glass  globes,  M  and  N .  The  dish  communicates  with  the  lower  part  ot 
the  globe  N  by  a  long  tube,  B ;  and  another  tube.  A,  connects  the 
two  globes.  A  third  tube  passes  through  the  dish  to  the  lower  part  of 
globe  M.  This  tube  having  been  taken  out,  the  globe  M  is  partially 
filled  with  water,  the  tube  is  then  replaced,  and  water  is  poured  into  the 
dish.  The  water  flows  through  the  tube  B  into  the  lower  globe,  and 
expels  the  air,  which  is  forced  into  the  upper  globe  ;  the  air,  thus  com- 
pressed, acts  upon  the  water,  and  makes  it  jet  out  as  represented  in  the 
figure.     If  it  were  not  for  the  resistance  of  the  atmosphere  and  friction, 

H  3 


154 


On  Gases. 


[190- 


the  liquid  would  rise  to  a  height  above  the  water  in  the  dish  equal  to 
the  difference  of  the  level  in  the  two  globes. 

191.  Znterznlttent  fountain. — The  mtennittent  fountain  depends 
partly  on  the  elastic  force  of  the  air  and  partly  on  the  atmospheric  pre- 
sure.  It  consists  of  a  stoppered  glass  globe  (C,  fig.  145),  provided  with 
two  or  three  capillary  tubulures,  D.  A  glass  tube  open  at  both  ends 
reaches  at  one  end  to  the  upper  part  of  the  globe  C  ;  the  other  end  ter- 
minates just  above  a  little  aperture  in  the  dish  B,  which  supports  the 
whole  apparatus. 

The  water  with  which  the  globe  C  is  nearly  two-thirds  filled,  runs 
out  by  the  tubes  D,  as  shown  in  the  figure;  the  internal  pressure  at  D 
being  equal  to  the  atmospheric  pressure,  together  with  the  weight  of  the 
column  of  water  CD,  while  the  external  pressure  at  that  point  is  only 
that  of  the  atmosphere.  These  conditions  prevail  so  long  as  the  lower 
end  of  the  glass  tube  is  open,  that  is,  so  long  as  air  can  enter  C  and  keep 
the  air  in  C  at  the  same  density  as  the  external  air  ;  but  the  apparatus  is 
arranged  so  that  the  orifice  in  the  dish  B  does  not  allow  so  much  water 
to  flow  out  as  it  receives  from  the  tube  D,  in  consequence  of  which 
the  level  gradually  rises  in  the  dish,  and  closes  the  lower  end  of  the 
glass  tube.  As  the  external  air  cannot  now  enter  the  globe  C,  the  air 
becomes  rarefied  in  proportion  as  the  flow  continues,  until  the  pressure 
of  the  column  of  water  CD,  together  with  the  tension  of  the  air  contained 
in  the  globe,  is  equal  to  this  external  pressure  at  D  :  the  flow  consequently 
stops.  But  as  water  continues  to  flow  out  of  the  dish,  the  tube  D  be- 
comes open  again,  air  enters,  and  the  flow  recommences,  and  so  on,  as 
long  as  there  is  water  in  the  globe  C. 

192.  The  sypbon. — The  syphon  is  a  bent  tube  open  at  both  ends, 
and  with  unequal  legs  (fig.  146).     It  is  used  in  transferring  liquids  in  the 


(r\ 


Fig.  146.  Fig,  147. 

following  manner  :  The  syphon  is  filled  with  some  liquid,  and  the  two 
ends  being  closed,  the  shorter  leg  is  dipped  in  the  liquid,  as  represented 
in  fig.  146  ;  or  the  shorter  leg  having  been  dipped  in  the  liquid,  the  air 
is  exhausted  by  applying  the  mouth  at  B.     A  vacuum  is  thus  produced, 


-193]  The  Syphon,  155 

the  liquid  in  C  rises  and  fills  the  tube  in  consequence  of  the  atmospheric 
pressure.  It  will  then  run  out  through  the  syphon  as  long  as  the  shorter 
end  dips  in  the  liquid. 

A  syphon  ot  the  form  represented  in  fig.  147  is  used  where  the  presence 
of  the  liquid  in  the  mouth  would  be  objectionable.  A  tube,  M,  is  attached 
to  the  longer  branch,  and  it  is  filled  by  closing  the  end  P,  and  sucking  at 
O.  An  enlargement,  M,  renders  the  passage  of  any  liquid  into  the  mouth 
more  difficult. 

To  explain  this  flow  of  water  from  the  syphon,  let  us  suppose  it  filled 
and  the  short  leg  immersed  in  the  liquid.  The  pressure  then  acting  on 
C,  and  tending  to  raise  the  liquid  in  the  tube,  is  the  atmospheric  pressure 
minus  the  height  of  the  column  of  Hquid  DC.  In  like  manner,  the  pres- 
sure on  the  end  of  the  tube,  B,  is  the  Weight  of  the  atmosphere  less  the 
pressure  of  the  column  of  liquid  AB.  But  as  this  latter  column  is  longer 
than  CD,  the  force  acting  at  B  is  less  than  the  force  acting  at  C,  and 
consequently  a  flow  takes  place  proportional  to  the  difference  between 
these  two  forces.  The  flow  will  therefore  be  more  rapid  in  proportion  as 
the  difference  of  level  between  the  aperture  B  and  the  surface  of  the  liquid 
in  C  is  greater. 

It  follows  from  the  theory  of  the  syphon  that  it  would  not  work  in 
vacuo,  nor  if  the  height  CD  were  greater  than  that  of  a  column  of  liquid 
which  counterbalances  the  atmospheric  pressure. 

193.  Tlie  intermittent  sypbon. — In  the  intermittent  syphon  the  flow 
is  not  continuous.     It  is  arranged  in  a  vessel,  so  that  the  shorter  leg  is 
near  the  bottom  of  the  vessel,  while  the  longer  leg  passes  through  it 
(fig.  148).     Being  fed  by  a  constant  supply  of 
water,    the  level  gradually  rises   both   in   the 
vessel  and  in  the  tube  to  the  top  of  the  syphon, 
which   it  fills,   and  water  begins  to    flow  out. 
But  the  apparatus  is  arranged  so  that  the  flow 
of  the  syphon  is  more  rapid  than  that  of  the 
tube  which    supplies    the    vessel,   and   conse- 
quently the  level  sinks  in  the  vessel  until  the 
shorter  branch  no  longer  dips  in  the  hquid ;  the 
syphon  is  then  empty,  and  the  flow  ceases.    But 
as  the  vessel  is  continually  fed  from  the  same 
source,   the  level   again   rises,    and    the   same  pjo-.  148. 

series  of  phenomena  is  reproduced. 

The  theory  of  the  intermittent  syphon  explains  the  natural  intermittent 
springs  which  are  found  in  many  countries,  and  of  which  there  is  an  ex- 
cellent example  near  Giggleswick  in  Yorkshire.  Many  of  these  springs 
furnish  water  for  several  days  or  months,  and  then,  after  stopping  for  a 
certain  interval,  again  recommence.  In  others  the  flow  stops  and  re- 
commences several  times  in  an  hour. 

These  phenomena  are  explained  by  assuming  that  there  are  subter- 
ranean fountains,  which  are  more  or  less  slowly  filled  by  springs,  and 
which  are  then  emptied  by  fissures  so  occurring  in  the  ground  as  to  form 
an  intermittent  syphon. 


156 


On  Gases. 


[194- 


194.  Different  kinds  of  pumps. — Pumps  are  machines  which  serve  to 
raise  water  either  by  suction,  by  pressure,  or  by  both  efforts  combined  : 
they  are  consequently  divided  into  suction  07- lijt  pumps,  force  pumps  ^2svdi. 
suction  and  forcing  pu?nps. 

The  various  parts  entering  into  the  construction  of  a  pump  are  the 
barrel,  the  piston,  the  valves,  and  the  pipes.  The  barrel  is  a  cylinder  of 
metal  or  of  wood,  in  which  is  the  pisto7t.  The  latter  is  a  metal  or  wooden 
cylinder  wrapped  with  tow,  and  working  with  gentle  friction  the  whole 
length  of  the  barrel. 


Fig.  149- 


Fig.  150. 


The  valves  are  discs  of  metal  or  leather,  which  alternately  close  the 


apertures  which  connect  the 
valves  are  the  clack  valve  (fig. 


barrel  with  the  pipes.  The  most  usual 
149)  and  the  conical  valve  (fig.  150).  The 
first  is  a  metal  disc  fixed  to  a  hinge 
on  the  edge  of  the  orifice  to  be 
closed.  In  order  more  effectually 
to  close  it,  the  lower  part  of  the 
disc  is  covered  with  thick  leather. 
Sometimes  the  valve  consists 
merely  of  a  leather  disc,  of  larger 
diameter  than  the  orifice,  nailed  on 
the  edge  of  the  orifice.  Its  flexi- 
bility enables  it  to  act  as  a  hinge. 

The  conical  valve  consists  of  a 
metal  cone  fitting  in  an  aperture  of 
the  same  shape.  Below  this  is  an 
iron  loop,  through  which  passes  a 
bolt-head  fixed  to  the  valve.  The 
object  of  this  is  to  limit  the  play 
of  the  valve  when  it  is  raised  by 
the  water,  and  to  prevent  its  re- 
moval. 

195.  Suction  pump. — Fig.  151 
represents  a  model  of  a  suction 
pump  such  as  is  used  in  lectures, 
but  which  has  the  same  arrange- 
ment as  the  pumps  in  common  use. 
It  consists,  I  St,  of  2i  glass  cylinder, 
B,  at  the  bottom  of  which  there  is 
a  valve,  S,  opening  upwards  ;  2nd, 
of  a  suction  tube,  A,  which  dips  into  the  reservoir  from  which  water  is 


-196]  Pumps.  157 

to  be  raised  ;  3rd  of  a  piston^  which  is  moved  up  and  down  by  a  rod 
worked  by  a  handle,  P.  The  piston  is  perforated  by  a  hole  ;  the  upper 
aperture  is  closed  by  a  valve,  O,  opening  upwards. 

When  the  piston  rises  from  the  bottom  of  the  cylinder,  a  vacuum  is 
produced  below,  and  the  valve  O  is  kept  closed  by  the  atmospheric 
pressure,  while  the  air  in  the  pipe  A,  in  consequence  of  its  elasticity, 
raises  the  valve  S,  and  partially  passes  into  the  cylinder.  The  air  being 
thus  rarefied,  water  rises  in  the  pipe  until  the  pressure  of  the  liquid 
column,  together  with  the  tension  of  the  rarefied  air  which  remains  in  the 
tube,  counterbalances  the  pressure  of  the  atmosphere  on  the  water  of  the 
reservoir. 

When  the  piston  descends,  the  valve  S  closes  by  its  own  weight,  and 
prevents  the  return  of  the  air  from  the  cylinder  into  the  tube  A.  The  air 
compressed  by  the  piston  opens  the  valve  O,  and  escapes  into  the  atmo- 
sphere by  the  pipe  C.  With  a  second  stroke  of  the  piston  the  same  series 
of  phenomena  is  produced,  and  after  a  few  strokes  the  water  reaches  the 
cylinder.  The  effect  is  now  somewhat  modified ;  during  the  descent  ot 
the  piston,  the  valve  S  closes,  and  the  water  raises  the  valve  O,  and  passes 
above  the  piston,  by  which  it  is  lifted  into  the  upper  reservoir  D.  There 
is  now  no  more  air  in  the  pump,  and  the  water,  forced  by  the  atmospheric 
pressure,  rises  with  the  piston,  provided  that  when  it  is  at  the  summit  of 
its  course  it  is  not  more  than  34  feet  above  the  level  of  the  water  in  which 
the  tube  A  dips,  for  we  have  seen  (151)  that  a  column  of  water  of  this 
height  is  equal  to  the  pressure  of  the  atmosphere. 

In  practice  the  height  of  the  tube  A  does  not  exceed  26  to  28  feet, 
for,  although  the  atmospheric  pressure  can  support  a  higher  column,  the 
vacuum  produced  in  the  barrel  is  not  perfect,  owing  to  the  fact  that  the 
piston  does  not  fit  exactly  on  the  bottom  of  the  barrel.  But  when  the 
water  has  passed  the  piston,  it  is  the  ascending  force  of  the  latter  which 
raises  it,  and  the  height  to  which  it  can  be  brought  depends  on  the  force 
which  moves  the  piston. 

196.  Suction  and  force  pump. — The  action  of  this  pump,  a  model  of 
which  is  represented  in  fig.  152,  depends  both  on  exhaustion  and  on 
pressure.  At  the  base  of  the  barrel,  where  it  is  connected  with  the  tube 
A,  there  is  a  valve,  S,  which  opens  upwards.  Another  valve,  O,  opening 
in  the  same  direction,  closes  the  aperture  of  a  conduit,  which  passes  from 
a  hole,  <?,  near  the  valve  S  into  a  vessel,  M,  which  is  called  the  air 
chamber.  From  this  chamber  there  is  another  tube,  D,  up  which  the 
water  is  forced. 

At  each  ascent  of  the  piston  B,  which  is  solid,  the  water  rises  through 
the  tube  A  into  the  barrel.  When  the  piston  sinks,  the  valve  S  closes, 
and  the  water  is  forced  through  the  valve  O  into  the  reservoir  M, 
and  from  thence  into  the  tube  D.  The  height  to  which  it  can  be 
raised  in  this  tube  depends  solely  on  the  motive  force  which  works  the 
pump. 

If  the  tube  D  were  a  prolongation  of  the  tube  ]ao^  the  flow  would  be 
intermittent ;  it  would  take  place  when  the  piston  descended,  and  would 
cease  as  soon  as  it  ascended.     But  between  these  tubes  there  is  an  in- 


158 


On  Gases. 


[196 


terval,  which,  by  means  of  the  air  in  the  reservoir  M,  ensures  a  continuous 
flow.  The  water  forced  into  the  reservoir  M  divides  into  two  parts,  one 
of  which,  rising  in  D,  presses  on  the  water  in  the  reservoir  by  its  weight  ; 
while  the  other,  in  virtue  of  this  pressure,  rises  in  the  reservoir  above  the 


Fig.  152. 

lower  orifice  of  the  tube  D,  compressing  the  air  above.  Consequently, 
when  the  piston  ascends,  and  no  longer  forces  the  water  into  M,  the  air 
of  the  reservoir,  by  the  pressure  it  has  received,  reacts  on  the  Uquid,  and 
raises  it  in  the  tube  D,  until  the  piston  again  descends,  so  that  the  jet  is 
continuous. 

J  97.  Iioad  whicb  the  piston  supports. — In  the  suction  pump,  when 
once  the  water  fills  the  pipe  and  the  barrel  as  far  as  the  spout,  the  effort 
necessary  to  raise  the  piston  is  equal  to  the  weight  of  a  column  of  water ^ 
the  base  of  which  is  this  piston^  and  the  height  the  vertical  distance  of 
the  spout  from  the  level  of  the  water  in  the  reservoir,  that  is,  the  height 
to  which  the  water  is  raised.  For  if  H  is  the  atmospheric  pressure,  h  the 
height  of  the  water  above  the  piston,  and  h'  the  height  of  the  column 
which  fills  the  suction  tube  A,  and  the  lower  part  of  the  barrel,  the 
pressure  above  the  piston  is  obviously  H  +  /«,  and  that  below  is  H  — ^', 
since  the  weight  of  the  column  h'  tends  to  counterbalance  the  atmospheric 
pressure.      But  as  the  pressure  \i-h'  tends  to  raise  the  piston,  the  effec- 


^199] 


Pumps.     ' 


159 


tive  resistance  is  equal  to  the  excess  of  H  +  >^  over  H  — /z',  that  is  to  say, 
to  h  +  h'.  _ 

In  the  suction  and  force  pump  it  is  readily  seen  that  the  pressure  which 
the  piston  supports  is  also  equal  to  the  weight  of  a  column  of  water,  the 
base  of  which  is  the  section  of  the  piston,  and  the  height  that  to  which  the 
water  is  raised. 

198,  Fire  engrine. — The  fire  engine  is  a  force  pump  in  which  a  steady 
jet  is  obtained  by  the  aid  of  an  air  chamber,  and  also  by  two  pumps 
working  alternately  (fig.  1 53).  The  two  pumps  in  and  n,  worked  by  the 
same  lever  PO,  are  immersed  in  a  tank,  and  which  is  kept  filled  with 
water  as  long  as  the  pump  works.  From  the  arrangement  of  the  valves  it 
will  be  seen,  that  when  one  pump  n  draws  water  from  the  tank,  the  other 


Fig.  153- 


m  forces  it  into  the  air  chamber  R  ;  whence,  by  an  orifice  Z,  it  passes  into 
the  delivery  tube,  by  which  it  can  be  sent  in  any  direction. 

Without  the  air  chamber  the  jet  would  be  intermittent.  For  as  the 
velocity  of  water  on  entering  the  reservoir  is  less  than  on  emerging,  the 
level  of  the  water  rises  above  the  orifice  Z,  compressing  the  air  which  fills 
the  reservoir.  Hence,  whenever  the  pistons  stop,  the  air  thus  compressed 
reacting  on  the  liquid  forces  it  out  during  its  momentary  stoppage,  and 
thus  keeps  up  a  constant  flow. 

199.  Velocity  of  efflux.  Torricelli's  theorem. — Let  us  imagine  an 
aperture  made  in  the  bottom  of  any  vessel,  and  consider  the  case  of  a 
particle  of  liquid  on  the  surface,  without  reference  to  those  which  are 
beneath.     If  this  particle  fell  freely,  it  would  have  a  velocity  on  reaching 


i6o 


On  Gases. 


[199 


the  orifice  equal  to  that  of  any  other  body  falling  through  the  distance 
between  the  level  of  the  liquid  and  the  orifice.  This,  from  the  laws  of 
falling  bodies,  is  s/2gh,  in  which  g  is  the  accelerating  force  of  gravity,  and 
//  the  height.  If  the  liquid  be  maintained  at  the  same  level,  for  instance, 
by  a  stream  of  water  running  into  the  vessel  sufficient  to  replace  what  has 
escaped,  the  particles  will  follow  one  another  with  the  same  velocity,  and 
will  issue  in  the  form  of  a  stream.  Since  pressure  is  transmitted  equally 
in  all  directions,  a  Hquid  would  issue  from  an  orifice  in  the  side  with  the 
same  velocity  provided  the  depth  were  the  same. 

The  law  of  the  velocity  of  efflux  was  discovered  by  Torricelli.  It  may 
be  enunciated  as  follows  :  The  velocity  of  efflux  is  the  velocity  which  a 
freely  falling  body  would  have  on  reachi?ig  the  orifice  after  having  started 
from  a  state  of  rest  at  the  surface.  It  is  algebraically  expressed  by  the 
formula  v  =  ^/7.gh. 

It  follows  directly  from  this  law,  that  the  velocity  of  efflux  depends  on 
the  depth  of  the  orifice  below  the  surface,  and  not  on  the  nature  of  the 
liquid.  Through  orifices  of  equal  size  and  of  the  same  depth,  water  and 
mercury  would  issue  with  the  same  velocity,  for  although  the  density  of 
the  latter  liquid  is  greater,  the  weight  of  the  column,  and  consequently 
the  pressure,  is  greater  too.  It  follows  further  that  the  velocities  of  efflux 
are  directly  proportional  to  the  square  roots  of  the  depths  of  the  orifices. 
Water  would  issue  from  an  orifice  coo  inches  below  the  surface  with  ten 
times  the  velocity  with  which  it  would  issue  from  one  an  inch  below  the 
surface. 

The  quantities  of  water  which  issue  from  orifices  of  different  areas  are 
very  nearly  proportional  to  the  size  of  the  orifice,  provided  the  level  remains 
constant. 

200.  Direction  of  the  jet  from  lateral  orifices. — From  the  principle 
of  the  equal  transmission  of  pressure,  water  issues  from  an  orifice  in  the 
side  of  a  vessel  with  the  same  velocity  as  from  an  aperture  in  the  bottom 
of  a  vessel  at  the  same  depth.  Each  particle  of  a  jet  issuing  from  the 
side  of  a  vessel  begins  to  move  horizontally  with  the  velocity  above 
mentioned,  but  it  is  at  once  drawn  downward  by  the  force  of  gravity,  in 

the  same  manner  as  a  bullet 
fired  from  a  gun,  with  its  axis 
horizontal.  'It  is  well  known 
that  the  bullet  describes  a  para- 
bola with  a  vertical  axis,  the 
vertex  being  the  muzzle  of  the 
gun.  Now  since  each  particle 
of  the  jet  moves  in  the  same 
curve,  the  jet  itself  takes  the 
parabolic  form,  as  shown  in 
fig.  154. 

Fig.  154.  It  may  be  remarked,  that  in 

every  parabola  there  is  a  certain 

point  called  the  focus,  and  that  the  distance  from  the  vertex  to  the  focus 

fixes   the  magnitude  of  a  parabola  in  much  the  same  manner  as  the 


-203]  Quantity  of  Efflux.  i6i 

distance  from  the  centre  to  the  circumference  fixes  the  magnitude  of  a 
circle.     Now  it  is  easily  capable  of  proof  that  the  focus  is  as  much  below, 
as  the  surface  of  the  water  is  above,  the  orifice.     Accordingly,  the  jets~~^ 
formed  by  water  coming  from   orifices  at   different   depths  below .  the 
surface  take  different  forms,  as  shown  in  fig.  1 54. 

201.  Heigrtit  of  tlie  jet. — If  a  jet  issuing  from  an  orifice  in  a  vertical 
direction  has  the  same  velocity  as  a  body  would  have  which  fell  from  the 
surface  of  the  liquid  to  that  orifice,  the  jet  ought  to  rise  to  the  level  of  the 
liquid.  It  does  not,  however,  reach  this  ;  for  the  particles  which  fall 
hinder  it.  But  by  inclining  the  jet  at  a  small  angle  with  the  vertical,  it 
reaches  about  j^ths  of  the  theoretical  height,  the  difference  being  due  to 
friction  and  to  the  resistance  of  the  air.  By  experiments  of  this  nature 
the  truth  of  Torricelli's  law  has  been  demonstrated. 

202.  Quantity  of  efflux.  Vena  contracta. — If  we  suppose  the  sides 
of  a  vessel  containing  water  to  be  thin,  and  the  orifice  to  be  a  small  circle 
whose  area  is  A,  we  might  think  that  the  quantity  of  water  E  discharged 
in  a  second  would  be  given  by  the  expression  A^2gh,  since  each  particle 
has,  on  the  average,  a  velocity  equal  to  V2ghj  and  particles  issue  from 
each  point  of  the  orifice.  But  this  is  by  no  means  the  case.  This  may 
be  explained  by  reference  to  fig.  155,  in  which  AB  represents  an  orifice 
in  the  bottom  of  a  vessel — what  is  true  in  this  case  being  equally  true  of 
an  orifice  in  the  side  of  the  vessel.  Every  particle  above  AB  endeavours 
to  pass  out  of  the  vessel,  and  in  so  doing  exerts  a  pressure  on  those  near 
it.  Those  that  issue  near  A  and  B  exert  pressures  in  the  directions  MM 
and  NN  ;  those  near  the  centre  of  the  orifice  in  the  direction  RQ,  those 
in  the  intermediate  parts  in  the  directions  PQ,  PQ.  In  consequence,  the 
water  within  the  space  PQP  is  unable  to  escape,  and  that  which  does 
escape,  instead  of  assuming  a  cylindrical  form,  at  first  contracts,  and 
takes  the  form  of  a  truncated  cone.  It  is  found  that  the  escaping  jet  con- 
tinues to  contract,  until  at  a  distance  from  the  orifice  about  equal  to  the 
diameter  of  the  orifice.  This  part  of  the  jet  is  called  the  vena  contracta. 
It  is  found  that  the  area  of  its  smallest  section  is  abotit  |  or  0*62  of  that 
of  the  orifice.     Accordingly,  the  true  value  of  the  efflux 

per  second  is  given  approximately  by  the  formula  ^^  ^  ■?  n 

E  =  o-62AV^,  ==V\j^#== 

or  the  actual  value  of  E  is  about  0"62  of  its  theoretical 
a??io7int. 

203.  Influence  of  tubes  on  the  quantity  of  efflux. —  ^  , 

The  result  given  in  the  last  article  has  reference  to  an  { 

aperture  in  a  thin  wall.     If  a  cylindrical  or  conical  efflux-  | 

tube  or  ajutage  is  fitted  to  the  aperture,  the  amount  of  Y\g.  155. 

the  efflux  is  considerably  increased,  and  in  some  cases 
falls  but  a  little  short  of  its  theoretical  amount. 

A  short  cylindrical  ajutage,  whose  length  is  from  two  to  three  times  its 
diameter,  has  been  found  to  increase  the  efflux  per  second  to  about 
O'ZiKsJ^gh.  In  this  case,  the  water  on  entering  the  ajutage  forms  a  con- 
tracted vein  (fig.  157),  just  as  it  would  do  on  issuing  freely  into  the  air  ; 


62 


On  Gases. 


[203- 


Fig.  156. 


but  afterwards  it  expands,  and,  in  consequence  of  the  adhesion  of  the 
water  to  the  interior  surface  of  the  tube,  has,  on  leaving  the  ajutage,  a 
section  greater  than  that  of  the  contracted  vein.  The  contraction  of  the 
jet  within  the  ajutage  causes  a  partial  vacuum.  If  an  aperture  is  made 
in  the  ajutage,  near  the  point  of  greatest  con- 
traction, and  fitted  with  a  vertical  tube,  the, 
other  end  of  which  dips  into  water  (fig.  156), 
it  is  found  that  water  rises  in  the  vertical  tube, 
thereby  proving  the  formation  of  a  partial 
vacuum. 

If  the  ajutage  has  the  form  of  a  conic  frustrum 
whose  larger  end  is  at  the  aperture,  if  the 
dimensions  are  properly  chosen,  the  efflux  in  a 
second  may  be  raised  to  o-()2 A ^2gh.  If  the 
smaller  end  of  a  frustrum  of  a  cone  of  suitable 
dimensions  be  fitted  to  the  orifice,  the  efflux 
may  be  still  further  increased,  and  fall  very 
little  short  of  the  theoretical  amount. 

When  the  adjutage  has  more  than  a  certain 
length,  a  considerable  diminution  takes  place  in 
the  amount  of  the  efflux  :  for  example,  if  its  length  is  48  times  its 
diameter,  the  efflux  is  reduced  to  0-62, A  ^2gk.  This  arises  from  the  fact, 
that,  when  water  passes  along  cylindrical  tubes,  the  resistance  increases 
with  the  length.  The  resistance  which  gives  rise  to  this  result  is  called 
hydraulic  frictio7i  ;  it  is  independent  of  the  material  of  the  tube,  provided 
it  be  not  roughened  ;  but  depends  in  a  considerable  degree  on  the 
viscosity  of  the  liquid  ;  for  instance,  ice-cold  water  experiences  a  greater 
resistance  than  lukewarm  water. 

The  velocity  of  efflux  through  capillary  ajutages  have  been  found  by 
Poiseuille  to  be  proportioned  to  the  heights  and  not  to  the  square  roots, 
a  striking  exception  from  Torricelli's  theorem. 

204.  Form  of  the  jet. — After  the  contracted  vein,  the  jet  has  the  form 
of  a  solid  rod  for  a  short  distance,  but  then  begins  to  separate  into  drops 
which  present  a  peculiar  appearance.  They  seem  to  form  a  series  of 
ventral  and  nodal  segments  (fig.  157).  The  ventral  segments  consist  of 
drops  extended  in  a  horizontal  direction,  and  the  nodal  segments  in  a 
longitudinal  direction.  And  as  the  ventral  and  nodal  segments  have  re- 
spectively a  fixed  position,  each  drop  must  alternately  become  elongated 
and  flattened  while  it  is  falling  (fig.  158).  Between  any  two  drops  there 
are  smaller  ones,  so  that  the  whole  jet  has  a  tube-like  appearance. 

If  the  aperture  is  not  circular  the  form  of  the  jet  undergoes  curious 
changes. 

205.  Hydraulic  tourniquet. — If  water  be  contained  in  a  vessel,  and  an 
aperture  made  in  one  of  the  sides,  the  pressure  at  this  point  is  removed, 
for  it  is  expended  in  forcing  out  the  water  ;  but  it  remains  on  the  other 
side  ;  and  if  the  vessel  were  moveable  in  a  horizontal  direction,  it  would 
move  in  a  direction  opposite  that  of  the  issuing  jet.  This  is  illustrated  by 
the  apparatus  known  as  the  hydraulic  iourniquetj  or  Barker's  inill{^%.  159). 


206] 


Hydraulic  Tourniquet. 


163 


It  consists  of  a  glass  vessel,  M,  containing  water,  and  capable  of  moving 
about  its  vertical  axis.  At  the  lower  part  there  is  a  tube,  C,  bent  horizon- 
tally in  opposite  directions  at  the  two  ends.  If  the  vessel  were  full  of 
water  and  the  tubes  closed,  the  pressures  on  the  sides  of  C  would  balance 
each  other,  being  equal  and  acting  in  contrary  directions  ;  but,  being  open, 
the  water  runs  out,  the  pressure  is  not  exerted  on  the  open  part,  but  only 
on  the  opposite  side,  as  shown  in  the  figure  A.     And  this  pressure,  not 


'I 

7;^ 


''0: 
I 


Fig-  157- 


Fig.  158. 


being  neutralised  by  an  opposite  pressure,  imparts  a  rotatory  motion  in 
the  direction  of  the  arrow,  the  velocity  of  which  increases  with  the  height 
of  the  liquid  and  the  size  of  the  aperture. 

The  same  principle  may-be  illustrated  by  the  following  experiment.  A 
tall  cylinder  containing  water  and  provided  with  a  lateral  stopcock  near 
the  bottom  is  placed  on  a  light  shallow  dish  on  water,  so  that  it  easily  floats. 
On  opening  the  stopcock  so  as  to  allow  water  to  flow  out,  the  vessel  is 
observed  to  move  in  a  direction  diametrically  opposite  to  that  in  which 
the  water  is  issuing. 

Segner's  water-wheel  and  the  reaction  machine  depend  on  this  prin- 
ciple. Rotating  fireworks  also  act  on  the  same  principle  ;  that  is,  an 
unbalanced  reaction  from  the  heated  gases  which  issue  from  openings  in 
them  gives  them  motion  in  the  opposite  direction. 

206.  IVater-wlieels.  Turbines. — When  water  is  continuously  flowing 
from  a  higher  to  a  lower  level,  it  may  be  used  as  a  motive  power.  This 
is  effected  by  means  of  water-wheels  ;  that  is,  wheels  provided  with 
buckets  or  float-boards  at  the  circumference,  and  on  which  the  water  acts 
either  by  pressure  or  by  impact. 


164 


On  Gases. 


[206- 


Water-wheels  turn  in  a  vertical  plane  round  a  horizontal  axis,  and  are 
of  two  principal  kinds,  7indershot  and  overshot. 

In  undershot  wheels  the  float-boards  are  at  right  angles  to  the  circum- 
ference of  the  wheel.  The  lowest  float-boards  are  immersed  in  the  water, 
which  flows  with  a  velocity  depending  on  the  height  of  the  fall.  Such 
wheels  are  applicable  where  the  quantity  of  water  is  great,  but  the  fall  in- 
considerable. 

Overshot  wheels  are  used  with  a  small  quantity  of  water  which  has  a 
high  fall,  as  with  small  mountain  streams.  On  the  circumference  of  the 
wheel  there  are  buckets  of  a  peculiar  shape.  The  water  falls  into  the 
buckets  on  the  upper  part  of  the  wheel,  which  is  thus  moved  by  the 
weight  of  the  water,  and  as  each  bucket  arrives  at  the  lowest  point  of  re- 
volution it  discharges  all  the  water,  and  ascends  empty. 

The  turbine  is  a  horizontal  water-wheel,  and  is  similar  in  principle  to 
the  hydraulic  tourniquet.  But  instead  of  the  horizontal  tubes  there  is  a 
horizontal  drum,  containing  curved  vertical  walls  ;  the  water,  in  issuing 
from  the  turbine,  pressing  against  these  walls,  exerts  a  reaction,  and  turns 
the  whole  wheel  about  a  vertical  axis. 

Turbines  have  the  advantage  of  being  of  small  bulk  for  their  power, 
and  equally  efficient  for  the  highest  and  the  lowest  falls. 

207.  mxariotte's  bottle,  its  use. — Mariotte's 
bottle  presents  many  curious  effects  of  the 
pressure  of  the  atmosphere,  and  furnishes  a 
means  of  obtaining  a  constant  flow  of  water. 
It  consists  of  a  large  narrow- mouthed  bottle,  in 
the  neck  of  which  there  is  a  tightly-fitting 
cork  (fig.  160).  Through  this  a  tube  passes 
open  at  both  ends.  In  the  sides  of  the  bottle 
there  are  three  tubulures,  each  with  a  narrow 
orifice,  and  which  can  be  closed  at  will. 

The  bottle  and  the  tube  being  quite  filled 
with  water,  let  us  consider  what  will  be  the 
effect  of  opening  successively  one  of  the  tubu- 
lures, a.  b,  and  c,  supposing,  as  represented  in 
the  figure,  that  the  lower  extremity  of  ^  is  be- 
tween the  tubulures  b  and  c. 
i.  If  the  tubulure  b  is  open  the  water  flows  out,  and  the  surface  sinks 
in  the  tube  g  until  it  is  on  the  same  level  as  b,  when  the  flow  stops.  This 
flow  arises  from  the  excess  of  pressure  at  the  point  e  over  that  at  b. 
The  pressure  at  e  is  the  same  as  the  pressure  of  the  atmosphere.  But 
when  once  the  level  is  the  same  at  b  and  at  e,  the  efflux  ceases,  for  the 
atmospheric  pressure  on  all  points  of  the  same  horizontal  layer,  be,  is  the 
same  (95). 

ii.  If  now  the  tubulure  b  is  closed,  and  a  opened,  no  efflux  takes  place  ; 
on  the  contrary,  air  enters  by  the  orifice  a,  and  water  ascends  in  the  tube 
g,  as  high  as  the  layer  ad,  and  then  equilibrium  is  established. 

iii.  If  the  orifices  a  and  b  are  closed,  and  c  opened,  an  efflux  having 
constant  velocity  takes  place,  as  long  as  the  level  of  the  water  is   not 


-207]  Mariotte's  Bottle.  165 

below  the  open  end,  /,  of  the  tube.     Air  enters  bubble  by  bubble  at  /,  and 
takes  the  place  of  the  water  which  has  flowed  out. 

In  order  to  show  that  the  efflux  at  the  orifice  c  is  constant,  it  is  neces^ 
sary  to  demonstrate  that  the  pressure  on  the  horizontal  layer  ch  is  always 
equal  to  that  of  the  atmosphere  in  addition  to  the  pressure  of  the  column 
///.  Now  suppose  that  the  level  of  the  water  has  sunk  to  the  layer  ad 
The  air  which  has  penetrated  into  the  flask  supports  a  pressure  equal  to 
that  of  the  atmosphere  diminished  by  that  of  the  column  of  liquid  /;;,  or 
H  — /«.  In  virtue  of  its  elasticity  this  pressure  is  transmitted  to  the 
layer  ch.  But  this  layer  further  supports  the  weight  of  a  column  of  water, 
/;;/,  so  that  the  pressure  at  rn  is  really /w  +  H  — /«,  or  H  -h  w;/,  that  is  to 
say,  H  +  hi. 

In  the  same  manner  it  may  be  shown  that  this  pressure  is  the  same 
when  the  level  sinks  to  b,  and  so  on  as  long  as  the  level  is  higher  than 
the  aperture  /.  The  pressure  on  the  layer  ch  is  therefore  constant,  and 
consequently  the  velocity  of  the  efflux.  But  when  once  the  level  is  below 
the  point  /,  the  pressure  decreases,  and  with  it  the  velocity. 

To  obtain  a  constant  flow  by  means  of  Mariotte's  bottle,  it  is  filled  with 
water,  and  the  orifice  which  is  below  the  tube  /  is  opened.  The  rapidity 
of  the  flow  is  proportional  to  the  square  root  of  the  height  hi. 


1 66  '  Acoustics,  [208 


4 


BOOK  V. 

ACOUSTICS. 


CHAPTER    I. 

PRODUCTION,   PROPAGATION,  AND   REFLECTION   OF   SOUND. 

2o3.  Object  of  acoustics. — The  study  of  sounds,  and  that  of  the 
vibrations  of  elastic  bodies,  form  the  object  of  acoustics. 

Music  considers  sounds  with  reference  to  the  pleasurable  feelings  they 
are  calculated  to  excite.  Acoustics  is  concerned  with  the  questions  of 
the  production,  transmission,  and  comparison  of  sounds  ;  to  which  may 
be  added,  the  physiological  question  of  the  perception  of  sounds. 

209.  Sound  and  noise. — Sound  is  a  peculiar  sensation  excited  in  the 
organ  of  hearing  by  the  vibratory  motion  of  bodies,  when  this  motion  is 
transmitted  to  the  ear  through  an  elastic  medium. 

All  sounds  are  not  identical ;  they  present  differences  by  which  they 
may  be  distinguished,  compared,  and  their  relations  determined. 

Sounds  are  distinguished  from  noises.  Sound  properly  so  called,  or 
musical  sound,  is  that  which  produces  a  continuous  sensation,  and  the 
musical  value  of  which  can  be  determined  :  while  noise  is  either  a  sound 
of  too  short  a  duration  to  be  determined,  like  the  report  of  a  cannon,  or 
else  it  is  a  confused  mixture  of  many  discordant  sounds,  like  the  rolling 
of  thunder  or  the  noise  of  the  waves.  Nevertheless,  the  difference  be- 
tween sound  and  noise  is  by  no  means  precise  ;  Savart  has  shown  that 
there  are  relations  of  height  in  the  case  of  noise,  as  well  as  in  that  of 
sound  ;  and  there  are  said  to  be  certain  ears  sufficiently  well  organised  to 
determine  the  musical  value  of  the  sound  produced  by  a  carriage  rolling 
on  the  pavement. 

210.  Cause  of  sound. — Sound  is  always  the  result  of  rapid  oscillations 
imparted  to  the  molecules  of  elastic  bodies,  when  the  state  of  equilibrium 
of  these  bodies  has  been  disturbed  either  by  a  shock  or  by  friction.  Such 
bodies  tend  to  regain  their  first  position  of  equilibrium,  but  only  reach  it 
after  performing,  on  each  side  of  that  position,  very  rapid  vibratory  move- 
ments, the  amplitude  of  which  quickly  decreases. 

A  body  which  produces  a  sound  is  called  a  sonorous  body.  As  under- 
stood in  England  and  Germany,  a  vibration  comprises  a  motion  to  and 
fro  ;  in  France,  on  the  contrary,  a  vibration  means  a  movement  to  or  fro. 
The  French  vibrations  are  with  us  semi-vibrations,  an  oscillation  or  vi- 


-213] 


Propagation  of  Sound. 


167 


bration  is  the  movement  of  the  vibrating  molecule  in  only  one  direction  : 
a  double  or  complete  vibration  comprises  the  oscillation  both  backwards 
and  forwards.  Vibrations  are  very  readily  observed.  If  a  light  powder 
is  sprinkled  on  a  body  which  is  in  the  act  of  yielding  a  musical  sound,  a 
bell  jar  held  horizontally  in  the  hand,  for  example,  a  rapid  motion  is 
imparted  to  the  powder  which  renders  visible  the  vibrations  of  the  body  ; 
and  in  the  same  manner,  if  a  stretched  cord  be  smartly  pulled  and  let  go 
its  vibrations  are  apparent  to  the  eye. 

211.  Sounds  not  propagrated  in  vacuo.— The  vibrations  of  elastic 
bodies  can  only  produce  the  sensation  of  sound  in  us  by  the  intervention 
of  a  medium  interposed  between  the  ear  and  the  sonorous  body,  and 
vibrating  with  it.  This  medium  is  usually  the  air,  but  all  gases,  vapours, 
liquids,  and  solids  also  transmit  sounds. 

The  following  experiment  shows  that  the  presence  of  a  ponderable 
medium  is  necessary  for  the  propagation  of  sound.  A  small  metallic  bell, 
which  is  continually  struck  by  a  small 
hammer  by  means  of  clockwork,  or  an 
ordinary  musical  box,  is  placed  under  the 
receiver  of  the  air-pump  (fig.  161).  As 
long  as  the  receiver  is  full  of  air  at  the 
ordinary  pressure,  the  sound  is  trans- 
mitted, but  in  proportion  as  the  air  is 
exhausted  the  sound  becomes  feebler,  and 
is  imperceptible  in  a  vacuum. 

To  ensure  the  success  of  the  experi- 
ment, the  bellwork  or  musical  box  must 
be  placed  on  wadding  ;  for  otherwise  the 
vibrations  would  be  transmitted  to  the 
air  through  the  plate  of  the  machine. 

212.  Sound  is  propagrated  in  all 
elastic  bodies. — If,  in  the  above  experi- 
ment, after  the  vacuum  has  been  made, 
any  vapour  or  gas  be  admitted,  the  sound 
of  the  bell  will  be  heard,  showing  that 
sound  is  propagated  in  this  medium  as  in 
air. 

Sound  is  also  propagated,  in  liquids. 
When  two  bodies  strike  against  each  other  under  water,  the  shock  is 
distinctly  heard.  And  a  diver  at  the  bottom  of  the  water  can  hear  the 
sound  of  voices  on  the  bank. 

The  conductibility  of  solids  is  such,  that  the  faint  scratching  of  a  pen 
at  the  end  of  a  long  piece  of  wood  is  heard  at  the  other  end.  The  earth 
conducts  sound  so  well,  that  at  night,  when  the  ear  is  applied  to  the 
ground,  the  steps  of  horses  or  any  other  noise  at  great  distances  is  heard. 

213.  Propagration  of  sound  in  the  air. — In  order  to  simplify  the 
theory  of  the  propagation  of  sound  in  the  air,  we  shall  first  consider  the 
case  in  which  it  is  propagated  in  a  cylindrical  tube  of  indefinite  length. 
Let  MN,  fig.  162,  be  a  tube  filled  with  air  at  a  constant  pressure  and 
temperature,  and  let  P  be  a  piston  oscillating  rapidly  from  A  to  a.     When 


Fig.  161. 


1 68  Acoustics.  [213- 

the  piston  passes  from  A  to  ^  it  compresses  the  air  in  the  tube.     But  in 
consequence  of  the  great  compressibiHty,  the  condensation  of  the  air  does 


Fig.  162. 

not  take  place  at  once  throughout  the  whole  length  of  the  tube,  but  solely 
within  a  certain  length,  aW,  which  is  called  the  condensed  wave. 

If  the  tube  MN  be  supposed  to  be  divided  into  lengths  equal  to  «H, 
and  each  of  these  lengths  divided  into  layers  parallel  to  the  piston,  it  may 
be  shown  by  calculation,  that  when  the  first  layer  of  the  wave  d\i\.  comes 
to  rest,  the  motion  is  communicated  to  the  first  layer  of  the  second  wave 
HH',  and  so  on  from  layer  to  layer  in  all  parts  of  H'H'^,  WW.  The 
condensed  wave  advances  in  the  tube,  each  of  its  parts  having  successively 
the  same  degree  of  velocity  and  condensation. 

When  the  piston  returns  in  the  direction  ^A,  a  vacuum  is  produced 
behind  it,  which  causes  an  expansion  of  the  air  in  contact  with  its  pos- 
terior face.  The  next  layer  expanding  in  turn  brings  the  first  to  its 
original  state  of  condensation,  and  so  on  from  layer  to  layer.  Thus  when 
the  piston  has  returned  to  A,  an  expatided  wave  is  produced  of  the  same 
length  as  the  condensed  wave,  and  directly  following  it  in  the  tube  where 
they  are  propagated  together,  the  corresponding  layers  of  the  two  waves 
possessing  equal  and  contrary  velocities. 

The  whole  of  a  condensed  and  expanded  wave  forms  an  undulation; 
that  is,  an  undulation  comprehends  that  part  of  the  column  of  air  affected 
during  the  backward  and  forward  motion  of  the  piston.  The  length  of 
an  undulation  is  the  space  which  sound  traverses  during  a  complete  vi- 
bration of  the  body  which  produces  it.  This  length  is  less  in  proportion 
as  the  vibrations  are  more  rapid. 

It  is  important  to  remark  that  if  we  consider  a  single  row  of  particles, 
which  when  at  rest  occupy  a  line  parallel  to  the  axis  of  the  cylinder,  for 
instance,  those  along  AH^'  (fig.  162),  we  shall  find  they  will  have  respec- 
tively at  the  same  instant  all  the  various  velocities  which  the  piston  has 
had  successively  while  oscillating  from  Kio  a  and  back  to  A.  So  that  if 
in  fig.  26  AH'  represents  the  length  of  one  undulation,  the  curved  line 
H'PQA  will  represent  the  various  velocities  which  all  the  points  in  the 
line  AH'  have  simultaneoiisly  :  for  instance,  at  the  instant  the  piston  has 
returned  to  A,  the  particle  at  M  will  be  moving  to  the  right  with  a  velo- 
city represented  by  QM,  the  particle  at  N  will  be  moving  to  the  left  with 
a  velocity  represented  by  PN,  and  so  on  of  the  other  particles. 

When  an  undulatory  motion  is  transmitted  through  a  medium,  the 
motions  of  any  two  particles  are  said  to  be  in  the  same  phase  when  those 
particles  move  with  equal  velocities  in  the  same  direction  ;  the  motions 
are  said  to  be  in  opposite  phases  when  the  particles  move  with  the  same 
velocities  in  opposite  directions.     It  is  plain,  from  an  inspection  of  fig.  26, 


-214]  Intensity  of  Sound.  1 69 

that  when  any  two  particles  are  separated  by  a  distance  equal  to  half  an 
undulation,  their  motions  are  always  in  opposite  phases,  but  if  their  dis- 
tance equals  the  length  of  a  complete  undulation  their  motions  are  in 
the  same  phase. 

A  little  consideration  will  show  that  in  the  conde^ised  wave  the  con- 
densation will  be  greatest  at  the  middle  of  the  wave,  and  likewise  that  the 
expanded  wave  will  be  most  rarefied  at  its  middle. 

It  is  an  easy  transition  from  the  theory  of  the  motion  of  sonorous 
waves  in  a  cylinder  to  that  of  their  motion  in  an  unenclosed  medium. 
It  is  simply  necessary  to  apply,  in  all  directions,  to  each  molecule  of  the 
vibrating  body,  what  has  been  said  about  a  piston  movable  in  a  tube. 
A  series  of  spherical  waves  alternately  condensed  and  rarefied  is  pro- 
duced around  each  centre  of  disturbance.  As  these  waves  are  contained 
within  two  concentrical  spherical  surfaces,  whose  radii  gradually  increase, 
while  the  length  of  the  undulation  remains  the  same,  their  mass  increases 
with  the  distance  from  the  centre  of  disturbance,  so  that  the  amplitude  of 
the  vibration  of  the  molecules  gradually  lessens,  and  the  intensity  of  the 
sound  diminishes. 

It  is  these  spherical  waves,  alternately  condensed  and  expanded,  which 
in  being  propagated  transmit  sound.  If  many  points  are  disturbed  at 
the  same  time,  a  system  of  waves  is  produced  around  each  point.  But 
all  these  waves  are  transmitted  one  through  the  other  without  modifying 
either  their  lengths  or  their  velocities.  Sometimes  condensed  or  expanded 
waves  coincide  with  others  of  the  same  nature  to  produce  an  effect  equal 
to  their  sum  ;  sometimes  they  meet  and  produce  an  effect  equal  to  their 
difference.  If  the-  surface  of  still  water  be  disturbed  at  two  or  more 
points,  the  co;^e^istence  of  waves  becomes  sensible  to  the  eye. 

214.  Catdises  wbicli  influence  the  intensity  of  sound.. — Many  causes 
modify  t^  force  or  the  ititeiisity  of  the  sound.  These  are,  the  distance 
of  the>^norous  body,  the  amplitude  of  the  vibrations,  the  density  of  the 
air  aj/'the  place  where  the  sound  is  produced,  the  direction  of  the  currents 
of  air,  and,  lastly,  the  neighbourhood  of  other  sonorous  bodies. 

i.  The  intensity  of  sound  is  inversely  as.  the  square  of  the  distance  of  the 
sonorotis  body  from  the  ear.  This  law  has  been  deduced  by  calculation, 
bat  it  may  be  also  demonstrated  experimentally.  Let  us  suppose  several 
sounds  of  equal  intensity — for  instance,  bells  of  the  same  kind,  struck 
by  hammers  of  the  same  weight,  falling  from  equal  heights.  If  four  of 
these  bells  are  placed  at  a  distance  of  20  yardls  from  the  ear,  and  one  at 
a  distance  of  10  yards,  it  is  fau,n,d  that  the  single  bell  produces/a  sound  of 
the  same  intensity  as  the  four  bjells  struck  simultaneoiisly.  Coj|lsequently, 
for'.double  the  distance  the-  intengity  of  the  sound  is  only  one /ourth. 

l^he  distance  at  which  sounds  can  be  heard  depends  on  thfeir  intensity. 
The  f-eport  of  a  volcano  at  St.  Vincent  was  heard  at  Demerfira,  300  miles 
off,  an'd  the  firing  at  Waterloo  was  heard  at  Dover. 

ii.  The  ititensity  of  the  sound  increases  with  the  amplitude  of  the  vibra- 
tions of  the  sonorous  body.  The  connection  between  the  intensity  of  the 
sound  and  the  amplitude  of  the  vibrations  is  readily  observed  by  means  of 
vibrating  cords.     For  if  the  cords  are^  somewhat  long,  the  oscillations  are 

I 


170 


Acoustics. 


[214- 


perceptible  to  the  eye,  and  it  is  seen  that  the  sound  is  feebler  in  propor- 
tion as  the  amphtude  of  the  oscillations  decreases. 

iii.  The  intensity  of  soimd  depends  on  tJie  density  of  the  air  in  the  place 
in  which  it  is  prodicced.  As  we  have  already  seen  (202),  when  an  alarum 
moved  by  clockwork  is  placed  under  the  bell-jar  of  the  air  pump,  the 
sound  becomes  weaker  in  proportion  as  the  air  is  rarefied. 

In  hydrogen,  which  is  about  j^th  the  density  of  air,  sounds  are  much 
feebler,  although  the  pressure  is  the  same.  In  carbonic  acid  on  the  con- 
trary, whose  density  is  1*529,  sounds  are  more  intense.  On  high  moun- 
tains, where  the  air  is  much  rarefied,  it  is  necessary  to  speak  with  some 
effort  in  order  to  be  heard,  and  the  discharge  of  a  gun  produces  only  a 
feeble  sound. 

The  ticking  of  a  watch  is  heard  in  water  at  a  distance  of  23  feet,  in  oil 
of  161,  in  alcohol  of  13,  and  in  air  of  only  10  feet. 

iv.  The  ititensity  of  sound  is  modified  by  the  motion  of  the  atmosphere^ 
and  the  direction  of  the  wind.  In  calm  weather  sound  is  always  better 
propagated  than  when  there  is  wind  ;.in  the  latter  case,  for  an  equal  dis- 
tance, sound  is  more  intense  in  the  direction  of  the  wind  than  in  the  con- 
trary direction. 

V.  Lastly,  sound  is  strengthened  by  the  proximity  of  a  sojtorous  body. 
A  string  made  to  vibrate  in  free  air  and  not  near  a  sounding  body  has  but 
a  very  feeble  sound  ;  but  when  it  vibrates  above  a  sounding-box,  as  in 
the  case  of  the  violin,  guitar,  or  violoncello,  its  sound  is  much  more 
intense.  This  arises  from  the  fact  that  the  box  and  the  air  which  it  con- 
tains vibrate  in  unison  with  the  strjxig:. — Hen^g^e  use  of  sounding-boxes 
in  stringed  instruments. 


Fig.  163. 

215.  Apparatd^o  streng-then  sound. — The  apparatus  refffesented  in 
fig.  163  was  used  by  S^art  to  show  the  influence  of  boxesjil^trengthening 
sound.     It  consists  of  aSumnispherical  brass  vesspli<?C  which  is  set  in 


-217]  Velocity  of  Soimd  in  Gases.  1 7 1 

vibration  by  means  of  a  violin  bow.  Near  it  there  is  a  hollow  cardboard 
cylinder,  B,  closed  at  the  further  end.  By  means  of  a  handle  this 
cylinder  can  be  turned  on  its  support,  so  as  to  be  inclined  at  any  given 
degree  towards  the  vessel.  The  cylinder  is  fixed  on  a  slide,  C,  by  which 
means  it  can  be  placed  at  any  distance  from  A.  When  the  vessel  is  made 
to  vibrate,  the  strengthening  of  the  sound  is  very  remarkable.  But  the 
sound  loses  almost  all  its  intensity  if  the  cylinder  is  turned  away,  and  it 
becomes  gradually  weaker  when  the  cylinder  is  removed  to  a  greater  dis- 
tance, showing  that  the  strengthening  is  due  to  the  vibration  of  the  air  in 
the  cylinder. 

The  cylinder  B  is  made  to  vibrate  in  unison  with  the  brass  vessel  by 
adjusting  it  to  a  certain  depth,  which  is  effected  by  making  one  part  slide 
into  the  other. 

Vitruvius  states  that,  in  the  theatres  of  the  ancients,  resonant  brass 
vessels  were  placed  to  strengthen  the  voices  of  the  actors. 

216.  Influence  of  tubes  on  tbe  transmission  of  sound. — The  law 
that  the  intensity  of  sound  decreases  in  inverse  proportion  to  the  square 
of  the  distance  does  not  apply  to  the  case  of  tubes,  especially  if  they  are 
straight  and  cylindrical.  The  sonorous  waves  in  that  case  are  not  propa- 
gated in  the  form  of  increasing  concentrical  spheres,  and  sound  can  be 
transmitted  to  a  great  distance  without  any  perceptible  alteration.  M.  Biot 
found  that  in  one  of  the  Paris  water  pipes,  1040  yards  long,  the  voice  lost 
so  little  of  its  intensity,  that  a  conversation  could  be  kept  up  at  the  ends 
of  the  tube  in  a  very  low  tone.  The  weakening  of  sound  becomes,  how- 
ever, perceptible  in  tubes  of  large  diameter,  or  where  the  sides  are  rough. 
This  property  of  transmitting  sounds  was  first  used  in  England  for 
speaking  tubes.  They  consist  of  caoutchouc  tubes  of  small  diameter 
passing  from  one  room  to  another.  If  a  person  speaks  at  one  end  of  the 
tube,  he  is  distinctly  heard  by  a  person  with  his  ear  at  the  other  end. 

From  M.  Biot's  experiments  it  is  evident  that  a  communication  might 
be  made  between  two  towns  by-means  of  speaking  tubes.  The  velocity 
of  sound  is  1 125  feet  in  a  second  at  i6-6  C,  so  that  a  distance  of  50  miles 
would  be  traversed  m  four  minutes. 

217.  Velocity  of  sound  in  g:ases. — Since  the  propagation  of  sonorous 
waves  is  gradual,  sound  requires  a  certain  time  for  its  transmisson  from 
one  place  to  another,  as  is  seen  in  numerous  phenomena.  For  example, 
the  sound  of  thunder  is  only  heard  some  time  after  the  flash  of  lightning 
has  been  seen,  although  both  the  sound  and  the  light  are  produced  simul- 
taneously ;  and  in  like  manner  we  see  a  mason  in  the  act  of  striking  a 
stone  before  hearing  the  sound. 

The  velocity  of  sound  in  air  has  often  been  the  subject  of  experimental 
determination. 

The  most  accurate  of  the  direct  measurements  was  made  by  Moll 
and  Van  Beck  in  1823.  Two  hills,  near  Amsterdam,  Kooltjesberg  and 
Zevenboomen,  were  chosen  as  stations  ;  their  distance  from  each  oth^ 
determined  trigonometrically  was  57,971  feet,  or  nearly  elevei 
Cannon  were  fired  at  stated  intervals  simultaneously  at  each  str 
the  time  which  elapsed  between  seeing  the  flash  and  hearing  tf  e  sound 

I  2 


172  Acoustics.  [217- 

was  noted  by  chronometers.  This  tune  could  be  taken  as  ihat  which 
the  sound  required  to  travel  between  the  two  stations  :  for  it  will  be  subse- 
quently seen  that  light  takes  an  inappreciable  time  to  traverse  the 
above  distance.  Introducing  corrections  for  the  barometric  pressure, 
temperature  and  hygrometric  state,  and  eliminating  the  influence  of  the 
wind,  Moll  and  Van  Beck's  results  as  recalculated  by  Schroder  van  der 
Kolk  give  109278  feet  as  the  velocity  of  sound  in  one  second  in  dry  air 
at  o^C  and  under  a  pressure  of  760  mm. 

The  velocity  of  sound  at  zero  may  be  taken  at  1093  feet  or  333  metres. 
This  velocity  increases  with  the  increase  of  temperature  ;  it  may  be  calcu- 
lated for  any  temperature  f  from  the  formula, 


( 


v=  1093-v/i  +0-003665/ 
where  1093  is  the  velocity  in  feet  at  0°  C,  and  0-003665  the  coefficient  of 
expansion  for  1°  C.  This  amounts  to  an  increase  of  nearly  two  feet  for 
every  degree  centigrade.  For  the  same  temperature  it  is  independent  of 
the  density  of  the  air,  and  consequently  of  the  pressure.  It  is  the  same 
for  the  same  temperature  with  all  sounds,  whether  they  be  strong  or  weak, 
deep  or  acute.  M.  Biot  found,  in  his  experiments  on  the  conductivity  of 
sound  in  tubes,  that  when  a  well-known  air  was  played  on  a  flute  at  one 
end  of  a  tube  1040  yards  long,  it  was  heard  without  alteration  at  the 
other  end,  from  which  he  concluded  that  the  velocity  of  different  sounds 
is  the  same.  For  the  same  reason  the  tune  played  by  a  band  is  heard 
at  a  great  distance  without  alteration,  except  in  intensity,  which  could 
not  be  the  case  if  some  sounds  travelled  more  rapidly  than  others. 

This  cannot,  however,  be  admitted  as  universally  true.  Earnshaw,  by 
a  profound  mathematical  investigation  of  the  laws  of  the  propagation  of 
sound,  has  found  that  the  velocity  of  a  sound  depends  on  its  strength  ; 
and,  accordingly,  that  a  violent  sound  ought  to  be  propagated  with  greater 
velocity  than  a  gentler  one.  This  conclusion  is  confirmed  by  an  observa- 
tion made  by  Captain  Parry  on  his  Arctic  expedition.  During  artillery 
practice  it  was  found,  by  persons  stationed  at  a  considerable  distance  from 
the  guns,  that  the  report  of  the  cannon  was  heard  before  the  command  of 
fire  given  by  the  officer.  And  more  recently,  Mallet  made  a  series  of 
experiments  on  the  velocity  with  which  sound  is  propagated  in  rocks,  by 
observing  the  times  which  elapsed  before  blastings  made  at  Holyhead  were 
heard  at  a  distance.  He  found  that  the  larger  the  charge  of  gunpowder, 
and  therefore  the  louder  the  report,  the  more  rapid  was  the  transmission. 
With  a  charge  of  2000  pounds  of  gunpowder  the  velocity  was  967  feet  in 
a  second,  while  with  a  charge  of  12,000  it  was  12 10  feet  in  the  same  time. 

MM.  Brav^ais  and  Martins  found^  in  1844,  that  sound  travelled  with  the 
same  velocity  from  the  base,  to  the  summit  of  the  Faulhorn,  as  from  the 
summit  to  the  base. 

Mallet  has  investigated  the  velocity  of  the  transmission  of  sound  in 
various  rocks,  and  finds  that  it  is  as  follows  ; 

v^tsand ,.         .        .       825  ft.  in  a  second. 

Contorted,  stratified  quartz  and  slate  rock       .  1088  „ 

Discontinuous  granite 1306  ,, 

Solid  granite     .        .         .         .  >   ;  .         .         .  1664  „ 


,0^W 


-218]  Velocity  of  Sound  in  Gases.  173 

218.  Formulae  for  calculating-  tlie  velocity-  of  sound  in  grases. — 

For  calculating  the  velocity  of  sound  in  gases  Newton  gave  a  rule  equiva- 
lent to  the  formula 


'-y 


e 


in  which  v  represents  the  velocity  of  the  sound  or  the  distance  it  travels 
in  a  second,  e  the  elasticity  of  the  gas,  and  d  its  density. 

This  formula  expresses  that  the  velocity  of  the  propagation  of  sound 
in  gases  is  directly  as  the  square  root  of  the  elasticity  of  the  gas,  and  in- 
versely as  the  square  root  of  its  density.  It  follows  that  the  velocity  of 
sound  is  the  same  under  any  pressure,  for  although  the  elasticity  increases 
with  greater  pressure,  the  density  increases  in  the  same  ratio.  At  Quito, 
where  the  mean  pressure  is  only  21*8  inches,  the  velocity  is  the  same  as 
at  the  sea  level,  provided  the  temperature  is  the  same. 

If  g  be  the  force  of  gravity,  h  the  barometric  height  reduced  to  the 
temperature  zero,  and  r  the  density  of  mercury,  also  at  zero,  then  for 
a  gas  under  the  atmospheric  pressure,  and  for  zero,  e  =gho  ;  Newton's 
formula  accordingly  becomes 


/  gh^ 


Now  if  we  suppose  the  temperature  of  a  gas  to  increase  from  0°  to  /°, 
its  volume  will  increase  from  unity  at  zero  to  i  ■{■  at  aX  t,  a  being  the 
coefficient  of  expansion  of  the  gas.  But  the  density  varies  inversely  as 
the  volume,  therefore  d  becomes  d-i-{i  +  at).     Hence 


y^:^(.-'). 


The  values  of  v,  obtained  by  this  formula,  are  less  than  the  experimen- 
tal results.  Laplace  assigned  as  a  reason  for  this  discrepancy  the  heat 
produced  by  pressure  in  the  condensed  waves  ;  and,  by  considerations 
based  on  this  idea,  Poisson  and  Biot  have  found  that  Newton's  formula 


ought  to  be  written  "^  =  ^  ^-(i'^^^)-,;  ^  being  the  specific  heat  of  the 

gas  for  a  constant  pressure,  and  d  its  specific  heat  for  a  constant  volume 
(see  Book  VI.).  When  thus  modified  the  results  calculated  by  the  for- 
mula agree  with  the  experimental  results. 

The  physical  reason  for  introducing  the  constant  -^  into  the  equation 

c 

for  the  velocity  of  sound  may  be  understood  from  the  following  con- 
siderations. We  have  already  seen  that  sound  is  propagated  in  air  by  a 
series  of  alternate  condensations  and  rarefactions  of  the  layers.  At  each 
condensation  heat  is  evolved,  and  this  heat  increases  the  elasticity,  and 
thus  the  rapidity,  with  which  each  condensed  layer  acts  on  the  next;  but, 
in  the  rarefaction  of  each  layer,  the  same  amount  of  heat  disappears  as 
was  developed  by  the  condensation,  and  its  elasticity  is  diminished  by  the 
cooling.     The  effect  of  this  diminished  elasticity  of  the  cooled  layer  is 


1/4  Acoustics,  [218- 

the  same  as  if  the  elasticity  of  an  adjacent  wave  had  been  increased,  and 
the  rapidity  with  which  this  latter  would  expand  upon  the  dilated  wave 
would  be  greater.  Thus,  while  the  average  temperature  of  the  air  is 
unaltered,  both  the  heating  which  increases  the  elasticity  and  the  chilling 
which  diminishes  it  concur  in  increasing  velocity. 

Knowing  the  velocity  of  sound,  we  can  calculate  approximately  the 
distance  at  which  it  is  produced.  Light  travels  with  such  velocity  that 
the  flash  or  the  smoke  accompanying  the  report  of  a  gun  may  be  con- 
sidered to  be  seen  simultaneously  with  the  explosion.  Counting  then 
the  number  of  seconds  which  elapse  between  seeing  the  flash  and  hear- 
ing the  sound,  and  multiplying  this  number  by  1125,  we  get  the  distance 
in  feet  at  which  the  gun  is  discharged.  In  the  same  way  the  distance  of 
thunder  may  be  estimated. 

219.  Velocity  of  sound  in  various  grases. — Approximately  the  same 
results  have  been  obtained  for  the  velocity  of  sound  in  air,  by  another 
method  by  which  the  velocity  in  other  gases  could  be  determined.  As 
the  wave  length  ^,  is  the  distance  which  sound  travels  during  the  time  of 
one  oscillation,  that  is  n  of  a  second,  the  velocity  of  sound  or  the  distance 
traversed  in  a  second  is  v  =  n\.  Now  the  length  of  an  open  pipe  is 
half  the  wave  length  of  the  fundamental  note  of  that  pipe ;  and  that  of 
a  closed  pipe  is  a  quarter  of  the  wave  length  (259).  Hence  if  we  know 
the  number  of  vibrations  of  the  note  emitted  by  any  particular  pipe, 
which  can  be  easily  ascertained  by  means  of  the  syren,  and  we  know  the 
length  of  this  pipe,  we  can  calculate  v.  Taking  the  temperature  into 
account,  Wertheim  found  1086  feet  for  the  velocity  of  sound  at  zero. 

Further,  since  indifferent  gases  which  have  the  same  elasticity,  but 
differ  in  density,  the  velocity  of  sound  varies  inversely  as  the  square 
root  of  the  density,  knowing  the  velocity  of  sound  in  air,  we  may  calculate 
it  for  other  gases ;  thus,  in  hydrogen  it  will  be 

This  number  cannot  be  quite  accurate,  for  the  coefficient  —  differs 

somewhat  in  different  gases.  And  when  pipes  were  sounded  with 
different  gases,  and  the  number  of  vibrations  of  the  notes  multiplied 
with  twice  the  length  of  the  pipe,  numbers  were  obtained  which  differed 
from  those  calculated  by  the  above  formula.  When,  however,  the  calcu- 
lation was  made,  introducing  for  each  gas  the  specia    value  of  — ,  the 

theoretical  results  agreed  very  well  with  the  observed  ones. 

By  the  above  method  the  following  values  have  been  obtained  : — 

Carbonic  acid 856  ft.  in  a  second. 

Oxygen 1040  „ 

Air 1093  „ 

Carbonic  oxide 1106  „ 

Hydrogen         . 4163  „ 


-221]         Velocity  of  Sound  in  Liquids  and  in  Solids.  1 75 

220.  Boppler's  principle. — When  a  sounding  body  approaches  the 
ear,  the  tone  perceived  is  somewhat  higher  than  the  true  one ;  but  if  the 
source  of  sound  recedes  from  the  ear,  the  tone  perceived  is  lower.  The 
truth  of  this,  which  is  known  as  Dopplefs principle,  will  be  apparent  from 
the  following  considerations  : — When  the  source  of  sound  and  the  ear 
are  at  rest,  the  ear  perceives  n  waves  in  a  second ;  but  if  the  ear  ap- 
proaches the  sound,  or  vice  versa,  it  perceives  more  ;  just  as  a  ship 
meets  more  waves  when  it  ploughs  through  them  than  if  it  is  at  rest. 
Conversely,  the  ear  receives  a  smaller  number  when  it  recedes  from  the 
source  of  sound.  The  effect  in  the  first  case  is  as  if  the  sounding  body 
emitted  more  vibrations  in  a  second  than  it  really  does,  and  in  the 
second  case  fewer.  Hence  in  the  first  case  the  note  appears  higher  ;  in 
the  second  case  lower. 

If  the  distance  which  the  ear  traverses  in  a  second  towards  the  source 
of  sound  (supposed  to  be  stationary)  is  s  feet,  and  the  wave  length  of  the 

particular  tone  is  A  feet,  then  there  are  —  waves  in  a  second ;  or  also  —  ,  . 

\  c 

for  X  =  — ,  where  c  is  the  velocity  of  sound  (216).     Hence  the  ear  receives 

not  only  the  11  original  waves,  but  also in   addition.      Therefore   the 

number  of  vibrations  which  the  ear  actually  perceives  is 

,  US  /  J  \ 

c  c 

for  an  ear  which  approaches  a  tone  ;  and  by  similar  reasoning  it  is 

,  lis  ,        s  ^ 

n'  =  n  —  -^  -  n  (i  —  _) 
c  c 

for  an  ear  receding  from  a  tone. 

To  test  Doppler's  theory  Buys  Ballot  stationed  trumpeters  on  the 
Utrecht  railway,  and  also  upon  locomotives,  and  had  the  height  of  the 
approaching  or  receding  tones  compared  with  stationary  ones  by  musicians. 
He  thus  found  both  the  principle  and  the  formula  fully  confirmed. 

221.  Velocity  of  sound  in  liquids  and  in  solids.— The  velocity  of 
sound  in  water  was  investigated  in  1827  by  Colladon  and  Sturm.  They 
moored  two  boats  at  a  known  distance  in  the  lake  of  Geneva.  The  first 
supported  a  bell  immersed  in  water,  and  a  bent  lever  provided  at  one  end 
with  a  hammer  which  struck  the  bell,  and  at  the  other  with  a  lighted  wick, ' 
so  arranged  that  it  ignited  some  powder  the  moment  the  hammer  struck 
the  bell.  To  the  second  boat  was  affixed  an  ear-trumpet,  the  bell  of 
which  was  in  water,  while  the  mouth  was  applied  to  the  ear  of  the 
observer,  so  that  he  could  measure  the  time  between  the  flash  of  light 
and  the  arrival  of  sound  by  the  water.  By  this  method  the  velocity  was 
found  to  be  4708  feet  in  a  second  at  the  temperature  8'i°,  or  four  times 
as  great  as  in  air. 

The  velocity  of  sound,  which  is  different  in  different  liquids,  can  be 
calculated  by  a  formula  analogous  to  that  given  above  (219)  as  applicable 


176  Acoustics.  [221- 

to  gases.  In  this  way  are  obtained  the  number  given  in  the  following 
table.  As  in  the  case  of  gases,  the  velocity  varies  with  the  temperature, 
which  is  therefore  appended  in  each  case  : — 

River  water  (Seine)         .       '.         .     I3°C.  =  4714  ft.  in  a  second 


J»                      J5                    5>                         •                 • 

•     30 

=  5013 

Artificial  sea-water 

.     20 

=  4761 

Solution  of  common  salt 

.     18 

=  5132 

„        „  chloride  of  calcium 

.     23 

-  6493 

Absolute  alcohol    . 

.     23 

=  3804 

Turpentine     .         .         .         > 

.     24 

=  3976 

Ether 

=  3801 

As  a  general  rule,  this  elasticity  of  solids,  as  compared  with  the  density, 
is  greater  than  that  of  liquids,  and  consequently  the  propagation  of  sound 
is  more  rapid. 

The  difference  is  well  seen  in  an  experiment  by  M.  Biot,  who  found 
that  when  a  bell  was  struck  by  a  hammer,  at  one  end  of  an  iron  tube 
3 1 20  feet  long,  two  sounds  were  distinctly  heard  at  the  other  end.  The 
first  of  these  was  transmitted  by  the  tube  itself  with  a  velocity  x\  and  the 
second  by  the  enclosed  air  with  a  known  velocity  a.  The  interval  between 
the  sounds  was  2-5  seconds.     The  value  of  :r,  obtained  from  the  equation 

3I20_3I20_ 
u  X 

shows  that  the  velocity  of  sound  in  the  tube  is  about  9  times  as  great  as 
that  in  air. 

To  this  class  of  phenomena  belongs  the  fact  that  if  the  ear  is  held 
against  a  rock  in  which  a  blasting  is  being  made  at  a  distance,  two 
distinct  reports  are  heard,  one  transmitted  through  the  rock  to  the  ear, 
and  the  other  transmitted  through  the  air. 

The  velocity  of  sound  in  other  solids  has  also  been  determined  theo- 
retically by  Wertheim,  by  means  of  their  coefficient  of  elasticity. 

The  following  table  gives  the  velocity,  expressed  in  feet  per  second  : — 

Lead  .         .         .      '  . 

Gold  .... 

Silver. 

Copper 

Steel  wire   . 

Iron    .... 

The  velocity  in  the  direction  of  the  fibres  was  greater  than  across  them. 

A  direct  method  of  determining  the  velocity  of  sound  in  solids,  gases, 
and  vapours  will  be  described  further  on. 

222.  Reflection  of  sound.— So  long  as  sonorous  waves  are  not  ob- 
structed in  their  motion,  they  are  propagated  in  the  form  of  concentric 
spheres  ;  but,  when  they  meet  with  an  obstacle,  they  follow  the  general 
law  of  elastic  bodies  ,  that  is,  they  return  upon  themselves,  forming  new 
concentric  waves,  which  seem  to  emanate  from  a  second  centre  on  the 


4030 

Pine  . 

1 0900 

5717 

Oak  . 

.     12622 

8553 

Ash    . 

.     13314 

1 1666 

.  Elm  . 

.     13516 

15470 

Fir     . 

.     15218 

16822 

Aspen 

.         .     16677 

223] 


Echoes  and  Resonances. 


177 


other  side  of  the  obstacle.     This  phenomenon  constitutes  the  reflection 
of  sound. 

Fig.  164  represents  a  series  of  incident  waves  reflected  from  an  ob- 
stacle, PQ.     Taking,  forexample,  the  incident  wave  MCDN,  emitted  from 


the  centre  A,  the  corresponding  reflected  wave  is  represented  by  the  arc, 
CKD,  of  a  circle,  whose  centre  a  is  as  far  beyond  the  obstacle  PQ  as  A 
is  before  it. 

If  any  point,  C,  of  the  reflecting  surface  be  joined  to  the  sonorous 
centre,  and  if  the  perpendicular  CH  be  let  fall  on  the  surface  of  this  body, 
the  angle  ACH  is  called  the  ajigle  of  incidence,  and  the  angle  BCH, 
formed  by  the  prolongation  of  ^C  is  the  angle  of  rejiection. 

The  reflection  of  sound  is  subject  to  the  two  following  laws  : — 

I.  The  angle  of  reflection  is  equal  to  the  afigle  of  incidence. 

II.  The  incident  sonorous  ray  and  the  reflected  ray  are  i7i  the  same 
plave  perpendicular  to  the  reflecting  surface. 

From  these  laws  it  follows  that  the  wave  which  in  the  figure  is  pro- 
pagated in  the  direction  AC,  takes  the  direction  CB  after  reflection,  so 
that  an  observer  placed  at  B  hears,  besides  the  sound  proceeding  from 
the  point  A,  a  second  sound,  which  appears  to  come  from  C. 

The  laws  of  the  reflection  of  sound  are  the  same  as  those  for  light  and 
radiant  heat,  and  may  be  demonstrated  by  similar  experiments.  One  of 
the  simplest  of  these  is  made  with  conjugate  mirrors  (see  chapter  on 
Radiant  Heat)  ;  if  in  the  focus  of  one  of  these  mirrors  a  watch  is  placed 
the  ear  placed  in  the  focus  of  the  second  mirror  hears  the  ticking  very 
distinctly,  even  when  the  mirrors  are  at  a  distance  of  12  or  13  yards. 

223.  Echoes  and  resonances. — An  echo  is  the  repetition  of  a  sound 
in  the  air,  caused  by  its  reflection  from  some  obstacle. 

A  very  sharp  quick  sound  can  produce  an  echo  when  the  reflecting 
surface  is  55  feet  distant,  but  for  articulate  sounds  at  least  double  that 
distance  is  necessary,  for  it  may  be  easily  shown  that  no  one  can  pro- 
nounce or  hear  distinctly  more  than  five  syllables  in  a  second.  Now,  as 
the  velocity  of  sound  at  ordinary  temperatures  may  be  taken  at  11 25  feet 
in  a  second,  in  a  fifth  of  that  time  sound  would  travel  225  feet.     If  the 

I  3 


178  Acoustics.  [223- 

reflecting  surface  is  112*5  feet  distant  in  going  and  returning,  sound  would 
travel  through  225  feet.  The  time  which  elapses  between  the  articu- 
lated and  the  reflected  sound  would,  therefore,  be  a  fifth  of  a  secondj  the 
two  sounds  would  not  interfere,  and  the  reflected  sound  would  be  dis- 
tinctly heard.  A  person  speaking  with  a  loud  voice  in  front  of  a  reflector, 
at  a  distance  of  112-5  f^^t»  can  only  distinguish  the  last  reflected  syllable  : 
such  an  echo  is  said  to  be  monosyllabic.  If  the  reflector  were  at  a  dis- 
tance of  two  or  three  times  112-5  ^^^^y  the  echo  would  be  dissyllabic, 
trisyllabic,  and  so  on. 

When  the  distance  of  the  reflecting  surface  is  less  than  112-5  f^^^  ^^^ 
direct  and  the  reflected  sound  are  confounded.  They  cannot  be  heard 
separately  but  the  sound  is  strengthened.  This  is  what  is  called  reso- 
naiice,  and  is  often  observed  in  large  rooms.  Bare  walls  are  very  reso- 
nant ;  but  tapestry  and  hangings,  which  are  bad  reflectors,  deaden  the 
sound- 

Multiple  echoes  are  those  which  repeat  the  same  sound  several  times  : 
this  is  the  case  when  two  opposite  surfaces  (for  example,  two  parallel 
walls)  successively  reflect  sound.  There  are  echoes  which  repeat  the 
same  sound  20  or  30  times.  Ah  echo  in  the  chateau  of  Simonetta,  in 
Italy,  repeats  a  sound  30  times.  At  Woodstock  there  is  one  which 
repeats  from  17  to  20  syllables. 

As  the  laws  of  reflection  of  sound  are  the  same  as  those  of  light 
and  heat,  curved  surfaces  produce  acoustic  foci  like  the  luminous  and 
calorific  foci  produced  by  concave  reflectors.  If  a  person  standing  under 
the  arch  of  a  bridge  speaks  with  his  face  turned  towards  one  of  the  piers, 
the  sound  is  reproduced  near  the  other  pier  with  such  distinctness  that 
a  conversation  can  be  kept  up  in  a  low  tone,  which  is  not  heard  by  any 
one  standing  in  the  intermediate  spaces. 

There  is  a  square  room  with  an  elliptical  ceiling,  on  the  ground  floor  ot 
the  Conservatoire  des  Arts  et  Metiers,  in  Paris,  which  presents  this 
phenomenon  in  a  remarkable  degree  when  persons  stand  in  the  two  foci 
of  the  ellipse. 

It  is  not  merely  by  solid  surfaces,  such  as  walls,  rocks,  ship's  sails, 
etc.,  that  sound  is  reflected.  It  is  also  reflected  by  clouds,  and  it  has  even 
been  shown  by  direct  experiment  that  a  sound  in  passing  from  a  gaseous 
medium  of  one  density  into  another  is  reflected  at  the  surface  as  it  would 
be  against  a  sohd  surface. 

Whispering  galleries  are  formed  of  smooth  walls  having  a  continuous 
curved  form.  The  mouth  of  the  speaker  is  presented  at  one  point,  and 
the  ear  of  the  hearer  at  another  and  distant  point.  In  this  case,  the 
sound  is  successively  reflected  from  one  point  to  the  other  until  it  reaches 
the  ear. 

Different  parts  of  the  earth's  surface  are  unequally  heated  by  the  sun, 
owing  to  the  shadows  of  trees,  evaporation  of  water,  and  other  causes,  so 
that  in  the  atmosphere  there  are  numerous  ascending  and  descending 
currents  of  air  of  different  density.  Whenever  a  sonorous  wave  passes 
from  a  medium  of  one  density  into  another  it  undergoes  partial  reflection,, 
which,  though  riot  strong  enough  to  form  an  echo,  distinctly  weakens 


HNEk 


-224]  Refraction  of  Sound.  179 

the  direct  sound.  This  is  doubtless  the  reason,  as  Humboldt  remarks, 
why  sound  travels  further  at  night  than  at  daytime  ;  even  in  the  South 
American  forests,  where  the  animals,  which  are  silent  by  day,  fill  the 
atmosphere  in  the  night  with  thousands  of  confused  sounds. 

It  has  generally  been  considered  that  fog  in  the  atmosphere  is  a  great 
deadener  of  sound,  it  being  a  mixture  of  air  and  globules,  of  water,  at 
each  of  the  innumerable  surfaces  of  contact  a  portion  of  the  vibration  is 
lost.  The  evidence  as  to  the  influence  of  this  property  is  conflicting ;  recent 
researches  of  Tyndall  show  that  a  white  fog,  or  snow,  or  hail,  are  not  im- 
portant obstacles  to  the  transmission  of  sound,  but  that  aqueous  vapour  is. 
Experiments  made  on  a  large  scale,  in  order  to  ascertain '  the  best 
form  of  fog-signals,  gave  some  remarkable  results. 

On  some  days  which  optically  were  quite  clear,  certain  sounds  could  not 
be  heard  at  a  distance  far  inferior  to  that  at  which  they  could  be  heard  even 
during  a  thick  haze.  Tyndall  ascribes  this  result  to  the  presence  in  the 
atmosphere  of  aqueous  vapour ;  which  forms  in  the  air  innumerable  stride 
that  do  not  interfere  with  its  optical  clearness,  but  render  it  acoustically 
turbid. 

These  conclusions  first  drawn  from  observations  have  been  verified 
by  laboratory  experiments.  Tyndall  has  shown  tliat  a  medium  consisting 
of  alternate  layers  of  a  light  and  heavy  gas  deadens  sound,  and  also  that 
a  medium  consisting  of  alternate  strata  of  heated  and  ordinary  air  exerts 
a  similar  influence.  The  same  is  the  case  with  an  atmosphere  containing 
the  vapours  of  volatile  liquids.  So  long  as  the  continuity  of  air  is  pre- 
served, sound  has  great  power  of  passing  through  the  interstices  of  solids  ; 
thus  it  will  pass  through  twelve  folds  of  a  dry  silk  handkerchief,  but  is 
stopped  by  a  single  layer  if  it  is  wetted. 

224.  Refraction  of  sound. — It  will  be  found  in  the  sequel  that  refrac- 
tion is  the  change  of  direction  which  light  and  heat  experience  on  passing 
from  one  medium  to  another,  Sondhauss  has  found  that  sonorous  waves 
are  refracted  like  light  and  heat.  He  constructed  gas  lenses,  by  filHng 
spherical  or  lenticular  collodion  envelopes  with  carbonic  acid.  With 
envelopes  of  paper  or  of  goldbeater's  skin  the  refraction  of  sound  is  not 
perceptible. 

Sondhauss  cut  equal  segments  out  of  a  large  collodion  balloon,  and 
fastened  them  on  the  two  sides  of  a  sheet  iron  ring  a  foot  in  diameter,  so 
as  to  form  a  hollow  biconvex  lens  about  4  inches  thick  in  the  centre. 
This  was  filled  with  carbonic  acid,  and  a  watch  was  placed  in  the  direc- 
tion of  the  axis  :  the  point  was  then  sought,  on  the  other  side  of  the  lens 
at  which  the  sound  was  most  distinctly  heard.  It  was  found  that  when 
the  ear  was  removed  from  the  axis,  the  sound  was  scarcely  perceptible  ; 
but  that  at  a  certain  point  on  the  axial  line  it  was  very  distinctly  heard. 
Consequently,  the  sonorous  waves  in  passing  from  the  lens  had  converged 
towards  the  axis,  their  direction  had  been  changed  ;  in  other  words,  they 
had  been  refracted. 

The  refraction  of  sound  may  be  easily  demonstrated  by  means  of  one 
of  the  very  thin  india-rubber  balloons  used  as  children's  toys,  inflated  by 


i8o 


Acoustics. 


[224- 


carbonic  acid.  If  the  balloon  be  filled  with  hydrogen,  no  focus  is  detected  ; 
it  acts  like  a  convex  lens,  and  the  divergence  of  the  rays  is  increased 
instead  of  their  being  converged  to  the  ear. 

225.  Speaking:  trumpet.  Ear  trumpet. — These  instruments  are 
based  both  on  the  reflection  of  sound  and  on  its  conductibility  in  tubes. 

The  speaking  trumpet,  as  its  name  implies,  is  used  to  render  the  voice 
audible  at  great  distances.  It  consists  of  a  slightly  conical  tin  or  brass 
tube  (fig.  165),  very  much  wider  at  one  end  (which  is  called  the  bell),  and 


Fig.  165. 

provided  with  a  mouthpiece  at  the  other.  The  larger  the  dimensions  of 
this  instrument  the  greater  is  the  distance  at  which  the  voice  is  heard. 
Its  action  is  usually  ascribed  to  the  successive  reflections  of  sonorous 
waves  from  the  sides  of  the  tube,  by  which  the  waves  tend  more  and 
more  to  pass  in  a  direction  parallel  to  the  axis  of  the  instrument.  It  has, 
however,  been  objected  to  this  explanation,  that  the  sounds  emitted  by 
the  speaking  trumpet  are  not  stronger  solely  in  the  direction  of  the  axis, 
but  in  all  directions,  that  the  bell  would  not  tend  to  produce  parallelism 
in  the  sonorous  wave,  whereas  it  certainly  exerts  considerable  influence 
in  strengthening  the  sound.  It  must  be  said  that  no  satisfactory  explana- 
tion has  been  n-iven  of  the  effect  of  the  bell. 

The  ear  trumpet  is  used  by  persons  who  are  hard  of  hearing.  It  is 
essentially  an  inverted  speaking  trumpet,  and  consists  of  a  conical  metallic 
tube,  one  of  whose  extremities,  terminating  in  a  bell,  receives  the  sound, 
while  the  other  end  is  introduced  into  the  ear.  This  instrument  is  the 
reverse  of  the  speaking  trumpet.  The  bell  serves  as  a  mouthpiece  ;  that 
is,  it  receives  the  sound  coming  from  the  mouth  of  the  person  who 
speaks.  These  sounds  are  transmitted  by  a  series  of  reflections  to  the 
interior  of  the  trumpet,  so  that  the  waves  which  would  become  greatly 
developed,  are  concentrated  on  the  auditory  apparatus,  and  produce  a  far 
greater  effect  than  divergent  waves  would  have  done. 


FJg.  166,  Fig.  167. 

226.  Stetboscope. — One  of  the  most  useful  applications  of  acoustical 
principles  is  the  stethoscope.     Figs.  166,  167  represent  an  improved  form 


V 


-227]        Measurement  of  the  Number  of  Vibrations. 


i8i 


of  this  instrument  devised  by  Konig.  Two  sheets  of  caoutchouc,  c  and  a^ 
are  fixed  to  the  circular  edge  of  a  hollow  metal  hemisphere  ;  the  edge  is 
provided  with  a  stopcock,  so  that  the  plates  can  be  inflated,  and  then 
present  the  appearance  of  a  double  convex  lens  as  represented  in  section 
in  fig.  1 66.  To  a  tubulure  on  the  hemisphere  is  fixed  a  caoutchouc  tube 
terminated  by  horn  or  ivory,  o^  which  is  placed  in  the  ear  (fig.  167). 

When  the  membrane  of  the  stethoscope  is  applied  to  the  chest  of  a  sick 
person  the  beating  of  the  heart  and  the  sounds  of  respiration  are  trans- 
mitted to  the  air  in  the  chamber  CA,  and  from  thence  to  the  ear  by 
means  of  the  flexible  tube.  If  several  tubes  are  fixed  to  the  instrument 
as  many  observers  may  simultaneously  auscultate  the  same  patient. 


CHAPTER   II. 

MEASUREMENT  OF  THE   NUMBER  OF  VIBRATIONS. 

227.  Savart's  apparatus. — Savarfs  tocthed  wheels  so  called  from  the 
name  of  its  inventor,  is  an  apparatus  by  which  the  absolute  number  of 
vibrations  corresponding  to  a  given  note  can  be  determined.  It  consists 
of  a  sohd  oak  frame  in  which  there  are  two  wheels,  A  and  B  (fig.   168); 


e 


Ik 


Fig.  i68j 

the  larger  wheel.  A,  is  connected  with  tlr?tDothed  wheel  by  means  of  a 
strap  and  a  multiplying  wheel,  thereby  causing  the  toothed  wheel  to 
revolve  with  great  velocity  ;  a  card,  E,  is  fixed  on  the  frame,  and,  in 
revolving,  the  toothed  wheel  strikes  against  it,  and  causes  it  to  vibrate. 
The  card  being  struck  by  each  tooth,  makes  as  many  vibrations  as  there 
are  teeth.  At  the  side  of  the  apparatus  there  is  an  indicator,  H,  which 
gives  the  number  of  revolutions  of  the  wheel,  and  consequently  the 
number  of  vibrations  in  a  given  time. 

When  the  wheel  is  moved  slowly,  the  separate  shocks  against  the 
card  are  distinctly  heard  ;  but  if  the  velocity  is  gradually  increased,  the 


l82 


Acoustics. 


[227- 


sound  becomes  higher  and  higher.  Having  obtained  the  sound  whose 
number  of  vibrations  is  to  be  determined,  the  revolution  of  the  wheel  is 
continued  with  the  same  velocity  for  a  certain  number  of  seconds.  The 
number  of  turns  of  the  toothed  wheel  B  is  then  read  off  on  the  indicator, 
and  this  multiplied  by  the  number  of  teeth  in  the  wheel  gives  the  total 
number  of  vibrations.  Dividing  this  by  the  corresponding  number  of 
seconds,  the  quotient  gives  the  number  of  vibrations  per  second  for  the 
given  sound. 

228.  Syren. — The  syren  is  an  apparatus  which,  like  Savart's  wheel,  is 
used  to  measure  the  number  of  vibrations  of  a  body  in  a  given  time.  The 
name  '  syren '  was  given  to  it  by  its  inventor,  Cagniard  Latour,  because  it 
yields  sounds  under  water. 

It  is  made  entirely  of  brass.  Fig.  169  represents  it  fixed  on  the  table 
of  a  bellows,  by  which  a  continuous  current  of  air  can  be  sent  through  it. 
Figs.  170  and  171  show  the  internal  details.     The  lower  part  consists  of 


Fig.  169. 


Fig.  171. 


a  cylindrical  box,  O,  closed  by  a  fixed  plate,  B.  On  this  plate  a  vertical 
rod,  T,  rests,  to  which  is  fixed  a  disc,  A,  moving  with  the  rod.  In  the 
plate  B  there  are  equidistant  circular  holes,  and  in  the  disc  A  are  an 
equal  number  of  holes  of  the  same  size,  and  the  same  distance  from  the 
centre  as  those  of  the  plate.  These  holes  are  not  perpendicular  to  the 
disc  ;  they  are  all  inclined  to  the  same  extent  in  the  same  direction  in  the 
plate,  and  are  inclined  to  the  same  extent  in  the  opposite  direction  in  the 
disc,  so  that  when  they  are  opposite  each  other  they  have  the  appearance 
represented  in  mu,  fig.  171.  Consequently,  when  a  current  of  air  from 
the  bellows  reaches  the  hole  m,  it  strikes  obliquely  against  the  sides  of 
the  hole  n,  and  imparts  to  the  disc  A  a  rotatory  motion  in  the  direction 
nA. 

For  the  sake  of  simplicity,  let  us  first  suppose  that  in  the  movable 
disc  A  there  are  eighteen  holes,  and  in  the  fixed  plate  B  only  one,  which 


-229]        Measurement  of  the  Number  of  Vibrations.  183 

faces  one  of  the  upper  holes.— The  wind  from  the  bellows  striking 
against  the  sides  of  the  latter,  the  movable  disc  begins  to  rotate,  and 
the  space  between  two  of  its  consecutive  holes  closes  the  hole  in  the 
lower  plate.  But  as  the  disc  continues  to  turn  from  its  acquired  velocity, 
two  holes  are  again  opposite  each  other,  a  new  impulse  is  produced, 
and  so  on.  During  a  complete  revolution  of  the  disc  the  lower  hole  is 
eighteen  times  open  and  eighteen  times  closed.  A  series  of  effluxes  and 
stoppages  is  thus  produced,  which  makes  the  air  vibrate,  and  ultimately 
produces  a  sound  when  the  successive  impulses  are  sufficiently  rapid.  If 
the  fixed  plate,  like  the  moving  disc,  had  eighteen  holes,  each  hole  would 
separately  produce  the  same  effect  as  a  separate  one,  the  sound  would  be 
eighteen  times  as  intense,  but  the  number  of  vibrations  would  not  be  in- 
creased. 

In  order  to  know  the  number  of  vibrations  corresponding  to  the  sound 
produced,  it  is  necessary  to  know  the  number  of  revolutions  of  the  disc 
A  in  a  second.  For  this  purpose  an  endless  screw  on  the  rod  T  transmits 
the  motion  to  a  wheel,  a,  with  100  teeth.  On  this  wheel,  which  moves 
by  one  tooth  for  every  turn  of  the  disc,  there  is  a  catch,  P,  which  at  each 
complete  revolution  moves  one  tooth  of  a  second  wheel,  b  (fig.  170). 
On  the  axis  of  these  wheels  there  are  two  needles,  which  move  round 
dials  represented  in  fig.  169.  One  of  these  indices  gives  the  number  of 
turns  of  the  disc  A,  the  other  the  number  of  hundreds  of  turns.  By  means 
of  two  screws,  D  and  C,  the  wheel  a  can  be  uncoupled  from  the  endless 
screw. 

Since  the  sound  rises  in  proportion  to  the  velocity  of  the  disc  A,  the 
wind  is  forced  until  the  desired  sound  is  produced.  The  same  current  is 
kept  up  for  a  certain  time,  two  minutes  for  example,  and  the  number  of 
turns  read  off.  This  number  multiplied  by  18,  and  divided  by  120,  indi- 
cates the  number  of  vibrations  in  a  second. 

With  the  same  velocity  the  syren  gives  the  same  sound  in  air  as  in 
water  ;  the  same  is  the  case  with  all  gases  ;  and  it  appears,  therefore,  that 
any  given  sound  depends  on  the  number  of  vibrations,  and  not  on  the 
nature  of  the  sounding  body. 

The  buzzing  and  humming  noise  of  certain  insects  is  not  vocal,  but  is 
produced  by  very  rapid  flapping  of  the  wings  against  the  air  or  the  body. 
The  syren  has  been  ingeniously  applied  to  count  the  velocity  of  the  undu- 
lations thus  produced,  which  is  effected  by  bringing  it  into  unison  with  the 
sound.  It  has  thus  been  found  that  the  wings  of  a  gnat  flap  at  the  rate  of 
15,000  times  in  a  second. 

229.  Bellows. — In  acoustics  a  bdlows  is  an  apparatus  by  which  wind 
instruments,  such  as  the  syren  and  organ  pipes,  are  worked.  Between 
the  four  legs  of  a  table  there  is  a  pair  of  bellows,  S  (fig.  172),  which  is 
worked  by  means  of  a  pedal,  P.  D  is  a  reservoir  of  flexible  leather,  in 
which  is  stored  the  air  forced  in  by  the  bellows.  If  this  reservoir  is 
pressed  by  means  of  weights  on  a  rod,  T,  moved  by  the  hand,  the  air  is 
driven  through  a  pipe,  E,  into  a  chest,  C,  fixed  on  the  table.  In  this 
chest  there  are  small  holes  closed  by  leather  valves,  which  can  be  opened 


1 84 


Acoustics. 


{229^ 


by  pressing  on  keys  in  front  ot  the  box.     The  syren  or  sounding  pipe  is 
placed  in  one  of  these  holes. 


Fig.  172. 

230.  Ziimit  of  perceptible  sounds. — Before  Savart's  researches, 
physicists  assumed  that  the  ear  could  not  perceive  a  sound  when  the 
number  of  vibrations  was  below  16  for  deep  sounds,  or  above  9,000  for 
acute  sounds.  But  he  showed  that  these  limits  were  too  close,  and 
that  the  faculty  of  perceiving  sounds  depends  rather  on  their  intensity 
than  on  their  height ;  so  that  when  extremely  acute  sounds  are  not  heard, 
it  arises  from  the  fact  that  they  have  not  been  produced  with  sufficient 
intensity  to  affect  the  organ  of  hearing. 

By  increasing  the  diameter  of  the  toothed  wheel,  and  consequently  the 
amplitude  and  intensity  of  the  vibrations,  Savart  pushed  the  limit  of  acute 
sounds  to  24,000  vibrations  in  a  second. 

For  deep  sounds,  he  substituted  for  the  toothed  wheel  an  iron  bar 
about  two  feet  long,  which  revolved  on  a  horizontal  axis  between  two 
thin  wooden  plates,  about  0*08  of  an  inch  from  the  bar.  As  often  as  the 
bar  passed,  a  grave  sound  was  produced,  due  to  the  displacement  of  the 
air.  As  the  motion  became  accelerated,  the  sound  became  continuous, 
very  grave  and  deafening.  By  this  means  Savart  found,  that  with  7  to  8 
vibrations  in  a  second,  the  ear  perceived  a  distinct  but  very  deep  sound. 

M.  Despretz,  however,  who  has  investigated  the  same  subject,  disputes 
Savart's  results  as  to  the  limits  of  deep  sounds,  and  holds  that  no  sound  is 


-231]        Measurement  of  the  Number  of  Vibrations.  185 

audible  that  is  made  by  less  than  16  vibrations  per  second.  Helmholtz 
holds  that  the  perception  of  a  sound  begins  at  30  vibrations,  and  only  has 
a  definite  musical  value  when  the  number  is  more  than  40.  Below  30 
the  impression  of  a  number  of  separate  beats  is  produced.  On  the  other 
hand,  acute  sounds  are  audible  up  to  those  corresponding  to  38,000  vibra- 
tions in  a  second. 

The  discordant  results  obtained  by  these  and  other  observers  for  the 
limit  of  audibility  of  higher  notes,  are  no  doubt  due  to  the  circumstance 
that  different  observers  have  different  capacities  for  the  perception  of 
sounds. 

231.  Bubaxnel's  graphic  method. — When  the  syren  or  Savart's  wheel 
is  used  to  determine  the  exact  number  of  vibrations  corresponding  to  a 
given  sound,  it  is  necessary  to  bring  the  sound  which  they  produce  into 
unison  with  the  given  sound,  and  this  cannot  be  done  exactly  unless  the 
experimenter  have  a  practised  ear.  M.  Duhamel's  graphic  method  is  very 
simple  and  exact,  and  free  from  this  difficulty.  It  consists  in  fixing  a  fine 
point  to  the  body  emitting  the  sound,  and  causing  it  to  trace  the  vibrations 
on  a  properly  prepared  surface. 

The  apparatus  consists  of  a  wood  or  metal  cylinder.  A,  fig.  173,  fixed 


Fig.  1 73. 

to  a  vertical  axis,  O,  and  turned  by  a  handle.  The  lower  part  of  the  axis  is 
a  screw  working  in  a  fixed  nut,  so  that,  according  as  the  handle  is  turned 
from  left  to  right,  or  from  right  to  left,  the  cylinder  is  raised  or  depressed. 
Round  the  cyHnder  is  rolled  a  sheet  of  paper  covered  with  an  inadhesive 
film  of  lampblack.      On  this  film  the  vibrations  register  themselves. 


1 86  Acoustics.  [231- 

This  is  effected  as  follows  :  Suppose  the  body  emitting  the  note  to  be  a 
steel  rod.  It  is  held  firmly  at  one  end,  and  carries  at  the  other  a  fine 
point  which  grazes  the  surfaces  of  the  cylinder.  If  the  rod  is  made  to 
vibrate  and  the  cylinder  is  at  rest,  the  point  would  describe  a  short  line  ; 
but  if  the  cylinder  is  turned,  the  point  produces  an  iindulati?ig  trace, 
containing  as  many  undulations  as  the  point  has  made  vibrations.  Con- 
sequently the  number  of  vibrations  can  be  counted.  It  remains  only  to 
determine  the  time  in  which  the  vibrations  were  made. 

There  are  several  ways  of  doing  this.  The  simplest  is  to  compare  the 
curve  traced  by  the  vibrating  rod  with  that  traced  by  a  tuning-fork 
(237)5  which  gives  a  known  number  of  vibrations  per  second — for  example, 
500.  One  prong  of  the  fork  is  furnished  with  a  point,  which  is  placed 
in  contact  with  the  lampblack.  The  fork  and  the  rod  are  then  set 
vibrating  together,  and  each  produces  its  own  undulating  trace.  When 
the  paper  is  unrolled,  it  is  easy  by  counting  the  number  of  vibrations 
each  has  made  in  the  same  distance  to  determine  the  number  of 
vibrations  made  per  second  by  the  elastic  rod.  Suppose,  for  instance, 
that  the  tuning-fork  made  150  vibrations,  while  the  rod  made  165 
vibrations.  Now  we  already  know  that  the  tuning-fork  makes  one 
vibration  in  the  j^oo  part  of  a  second,  and  therefore  150  vibrations  in  §|§ 
of  a  second.      But   in  the  same  time  the  rod   makes  165  vibrations; 

therefore  it  makes  one  vibration  in  the ^ — ^-  of  a  second,  and  hence 

500  X  165 

it  makes  per  second  5QO  ^  LJ  or  550  vibrations.  • 

150 


CHAPTER   III. 

THE   PHYSICAL  THEORY  OF   MUSIC. 


232.  Properties  of  musical  tones. — A  simple  musical  tone  results 
from  a  continuous  rapid  isochronous  vibration,  provided  the  number  of 
the  vibrations  falls  within  the  very  wide  limits  mentioned  in  the  last 
chapter  (230).     Musical  tones  are  in  most  cases  compound.     The  dis- 

_,-^ ttnction  between  a  simple  and  a  compound  musical  tone  will  be  explained 

later  in  the  chapter.  The  tone  yielded  by  a  tuning-fork  furnished  with 
a  proper  resonance  box  is  simple  ;  that  yielded  by  a  wide-stopped  organ 
pipe,  or  by  a  flute,  is  nearly  simple  ;  that  yielded  by  a  musical  string  is 
compound. 

Musical  tones  have  three  leading  qualities,  namely, /zV^/^,  intensity, 
and  timbre  or  colour. 

i.  The  pitch  of  a  musical  tone  is  determined  by  the  number  of  vibra- 
tions per  second  yielded  by  the  body  producing  the  tone. 

ii.  The  intensity  of  the  tone  depends  on  the  extent  of  the  vibrations. 
It  is  greater  when  the  extent  is  greater,  and  less  when  it  is  less.     It  is,  in 


-234]  Physical  Theory  of  Music,  187 

fact,  nearly  or  exactly  proportional  to  the  square  of  the  extent  or  amplitude 
of  the  vibrations  which  produce  the  tone. 

iii.  The  timb?'e  is  that  peculiar  quality  of  tone  which  distinguishes  a 
note  when  sounded  on  one  instrument  from  the  same  note  when  sounded 
on  another.  Thus  when  the  C  of  the  treble  stave  is  sounded  on  a 
violin,  and  on  a  flute,  the  two  notes  will  have  the  same  pitch,  that  is, 
are  produced  by  the  same  number  of  vibrations  per  second,  and  they  may 
have  the  same  intensity,  and  yet  the  two  tones  will  have  very  distinct 
qualities,  that  is,  their  timbre  is  different.  The  cause  of  the  peculiar 
timbre  of  tones  will  be  considered  later  in  the  chapter. 

233.  Musical  intervals. — Let  us  suppose  that  a  musical  tone,  which 
for  the  sake  of  future  reference  we  will  denote  by  the  letter  C,  is  pro- 
duced by  m  vibrations  per  second  ;  and  let  us  further  suppose  that  any 
other  musical  tone,  X,  is  produced  by  71  vibrations  per  second,  ti  being 
greater  than  m ;  then  the  interval  from  the  note  C  to  the  note  X  is  the 
ratio  71  ;  /;?,  the  interval  between  two  notes  being  obtained  by  division^ 
not  by  subtraction.  Although  two  or  more  tones  may  be  separately 
musical,  it  by  no  means  follows  that  when  sounded  together  they  produce 
a  pleasurable  sensation.  On  the  contrary,  unless  they  are  concordant^ 
the  result  is  harsh,  and  usually  unpleasing.  We  have  therefore  to 
enquire  what  notes  are  fit  to  be  sounded  together.  Now  when  musical 
tones  are  compared,  it  is  found  that  if  they  are  separated  by  an  interval 
of  2  :  I,  4  :  I,  etc.,  they  so  closely  resemble  one  another  that  they  may 
for  most  purposes  of  music  be  considered  as  the  same  tone.  Thus,  sup- 
pose c  to  stand  for  a  musical  note  produced  by  2ni  vibrations  per  second, 
then  C  and  c  so  closely  resemble  one  another  as  to  be  called  in  music  by 
the  same  name.  The  interval  from  C  to  <f  is  called  an  octave,  and  c  is 
said  to  be  an  octave  above  C,  and  conversely  C  an  octave  below  c.  If  we 
now  consider  musical  sounds  that  do  not  differ  by  an  octave,  it  is  found 
that  if  we  take  three  notes,  X,  Y,  and  Z,  resulting  respectively  from  p,  a, 
and  r  vibrations  per  second,  these  three  notes  when  sounded  together  will 
be  concordant  if  the  ratio  oi  p  '.  q  \  r  equals  4:5:6.  Three  such  notes 
form  a  harinonic  triad,  and  if  sounded  with  a  fourth  note,  which  is  the 
octave  of  X,  constitute  what  is  called  in  music  a  major  chord.  Any  of 
the  notes  of  a  chord  may  be  altered  by  one  or  more  octaves  without 
changing  its  distinctive  character;  for  instance,  C,  E,  G,  and  ^  are  a  chord, 
and  C,  c,  e,  g,  form  the  same  chord. 

If,  however,  the  ratio/  :  q  :  r  equals  10  :  12  :  15,  the  three  sounds  are 
slightly  dissonant,  but  not  so  much  so  as  to  disqualify  them  from  pro- 
ducing a  pleasing  sensation,  at  least  under  certain  circumstances.  When 
these  three  notes  and  the  octave  to  the  lower  are  sounded  together  they 
constitute  what  in  music  is  called  a  minor  chord. 

234.  Tbe  musical  scale. — The  series  of  sounds  which  connects  a 
given  note  C,  with  its  octave,  c,  is  called  the  diatonic  scale  or  gamut. 
The  notes  composing  it  are  denoted  by.  the  letters  C,  D,  E,  F,  G,  A,  B. 
The  scale  is  then  continued  by  taking  the  octaves  of  these  notes,  namely, 
<r,  d,  e,f,  g,  a,  b,  and  again  the  octaves  of  these  last,  and  so  on. 

The  notes  are  also  denoted  by  names,  viz.,  do,  or  ut,  re,  mi,  fa,  sol,  la,  si^ 


1 88  Acoustics.  [234- 

do.  The  relations  existing  between  the  notes  are  these  : — C,  E,  G,  form 
a  major  triad,  G,  B,  d,  form  a  major  triad,  and  F,  A,  c,  form  a  major 
triad.  C,  G,  and  F  have,  for  this  reason,  special  names,  being  called 
respectively  the  tonic,  doininant,  and  sub-dojninant,  and  the  three  triads 
the  tonic,  dominant,  and  sub-dominant  triads  or  chords  respectively. 
Consequently  the  numerical  relations  between  the  notes  of  the  scale  will 
be  given  by  the  three  proportions — 

C  :  E  :  G::4  :  5  :  6 
G  :  B  :  2D::4:  5:6 
F  :  A  :  2C::4  :  5  :  6 

Hence  if  in  denotes  the  number  of  double  vibrations  corresponding  to 
the  note  C,  the  number  of  vibrations  corresponding  to  the  remaining 
notes  will  be  given  by  the  following  table — 

do        re        mi      Ja       sol       la        si       do 
CDEFGAB^ 
7n        ^m       \m      pn      pn      |w      ^pn     2m 

The  intervals  between  the  successive  notes  being  respectively — 
C  to  D     D  to  E     E  to  F     F  to  G     G  to  A    A  to  B     B  to  c 


and^l 

because  it  is  about  half  as  great  as  the  interval  of  a  tone.  The  two  tones 
however  are  not  identical,  but  differ  by  an  interval  of  f^,  which  is  called  a 
comma.  Two  notes  which  differ  by  a  comma  can  be  readily  distinguished 
by  an  educated  ear.  The  interval  between  the  tonic  and  any  note  is  de- 
nominated by  the  position  of  the  latter  note  in  the  scale  ;  thus  the  interval 
from  C  to  G  is  a  fifth.  The  scale  we  have  now  considered  is  called  the 
major  scale,  as  being  formed  of  major  triads.  If  the  minor  triad  were 
substituted  for  the  major,  a  scale  would  be  formed  that  could  be  strictly 
called  a  minor  scale.  As  scales  are  usually  written,  however,  the 
ascending  scale  is  so  formed  that  the  tonic  bears  a  minor  triad,  the 
dominant  and  self-dominant  bear  major  triads,  while  in  the  descending 
scale  they  all  bear  minor  triads.  Practically,  in  musical  composition,  the 
dominant  triad  is  always  major.  If  the  ratios  given  above  are  examined, 
it  will  be  found  that  in  the  major  scale  the  interval  from  C  to  E  equals  |, 
while  in  the  minor  scale  it  equals.  \.  The  former  interval  is  called  a 
major  third,  the  latter  a  minor  third.  Hence  the  major  third  exceeds  the 
minor  third  by  an  interval  of  ||.  This  interval  is  called  a  semitone,  though 
very  different  from  the  interval  above  called  by  that  name. 

A  complete  discussion  of  the  number  of  notes,  and  the  intervals  between 
them,  will  be  found  in  an  article  by  Mr.  Ellis,  in  vol.  xiii.  of  the  Proceed- 
ings of  the  Royal  Society  (p.  93),  '  On  a  perfect  Musical  Scale.' 

235.  On  semitones  and  on  scales  with  different  key-notes. — It  will 
be  seen  from  the  last  article  that  the  term  '  semitone'  does  not  denote 
a  constant  interval,  being  in  one  case  equivalent  to  \%  and  in  another  to 
If.     It  is  found  convenient  for  the  purposes  of  music  to  introduce  notes 


-236]  '    Musical  Temperament.  189 

intermediate  to  the  seven  notes  of  the  gamut  ;  this  is  done  by  increasing 
or  diminishing  those  notes  by  an  interval  of  |f.  When  a  note  (say  C)  is 
increased  by  this  interval,  it  is  said  to  be  sharpened,  and  is  denoted  by  the 
symbol  CJI ,  called  '  C  sharp  '  ;  that  is,  CjJ  -^-  C  =  ||.  When  it  is  decreased 
by  the  same  interval,  it  is  said  to  hcjlattened,  and  is  represented  thus — 
B  b ,  called  '  B  flat ' ;  that  is,  B  -^  B  b  =  If.  If  the  effect  of  this  be  examined, 
it  will  be  found  that  the  number  of  notes  in  the  scale  from  C  up  to  c 
has  been  increased  from  seven  to  twenty-one  notes,  all  of  which  can  be 
easily  distinguished  by  the  ear.     Thus  reckoning  C  to  equal  i,  we  have — 

C         Cjt  Db         D         DH  Eb         E     etc. 


etc. 


Hitherto  we  have  made  the  note  C  the  tonic  or  key  note.  Any  other 
of  the  twenty-one  distinct  notes  above  mentioned,  e.g.  G,  or  F,  or  CH  ,  etc., 
may  be  made  the  key  note,  and  a  scale  of  notes  constructed  with  refer- 
ence to  it.  This  will  be  found  to  give  rise  in  each  case  to  a  series  of  notes, 
some  of  which  are  identical  with  those  contained  in  the  series  of  which 
C  is  the  key  note,  but  most  of  them  different.  And  of  course  the  same 
would  be  tnie  for  the  minor  scale  as  well  as  for  the  major  scale,  and 
indeed  for  other  scales  which  may  be  constructed  by  means  of  the  funda- 
mental triads. 

236.  On  musical  temperament. — The  number  of  notes  that  arise  from 
the  construction  of  the  scales  described  in  the  last  article  is  so  great  as 
to  prove  quite  unmanageable  in  the  practice  of  music  :  and  particularly 
for  music  designed  for  instruments  with  fixed  notes,  such  as  the  piano- 
forte. Accordingly,  it  becomes  practically  important  to  reduce  the 
ntuTiber  of  notes,  which  is  done  by  slightly  altering  their  just  proportions. 
This  process  is  called  teinperainent.  By  tempering  the  notes,  however, 
more  or  less  dissonance  is  introduced,  and  accordingly  several  different 
systems  of  temperament  have  been  devised  for  rendering  this  dissonance 
as  slight  as  possible.  The  system  usually  adopted  is  called  the  system 
of  equal  tetJiperament.  It  consists  in  the  substitution  between  C  and 
c  of  eleven  notes  at  equal  intervals,  each  interval  being,  of  course,  the 
twelfth  root  of  2,  or  1-05946.  By  this  means  the  distinction  be- 
tween the  semitones  is  abolished,  so  that,  for  example,  CJf  and  D^ 
become  the  same  note.  The  scale  of  twelve  notes  thus  formed  is 
called  the  chromatic  scale.  It  of  course  follows  that  major  triads  become 
slightly  dissonant.  Thus,  in  the  diatonic  scale,  if  we  reckon  C  to  be  i,  E 
is  denoted  by  1-25000,  and  G  by  1-50000.  On  the  system  of  equal  tem- 
perament, if  C  is  denoted  by  i,  E  is  denoted  by  1-25992  and  G  by 
1-49831. 

If  individual  intervals  are  made  pure  while  the  errors  are  distributed 
over  the  others,  such  a  system  is  called  that  of  unequal  tonperameni. 
Such  a  one  is  Kirnberger's  in  which  nine  of  the  tones  are  pure. 

Although  the  system  of  equal  temperament  has  the  advantage  of 
affording  with  as  small  a  number  of  notes  as  possible,  the  greatest 
variety  of  tones,  yet  it  has  the  disadvantage  that  no  chord  of  equally- 
tempered  instruments,  such  as  the  piano,  is  quite  pure.     And  as  musical 


190 


Acoustics. 


[236- 


education  mostly  has  its  basis  on  the  piano,  even  singers  and  instrumen- 
talists usually  give  equally-tempered  intervals.  Only  in  the  case  of 
string  quartet  players,  who  have  freed  themselves  from  school  rules,  and 
in  that  of  vocal  quartet  singers,  who  sing  much  without  accompaniment, 
does  the  natural  pure  temperament  assert  itself,  and  thus  produce  the 
highest  effect. 

237.  The  num'ber  of  vibrations  producing:  each  note.  The  tuning-- 
fork.— Hitherto  we  have  denoted  the  number  of  vibrations  corresponding 
to  the  note  C  by  w,  and  have  not  assigned  any  numerical  value  to  that 
symbol.  In  the  theory  of  music  it  is  frequently  assumed  that  the  middle  C 
corresponds  to  256  double  vibrations  in  a  second.  This  is  the  note 
which,  on  a  pianoforte  of  seven  octaves,  is  produced  by  the  white  key  on 
the  left  of  the  two  black  keys  close  to  the  centre  of  the  keyboard.  This 
number  is  convenient  as  being  continuously  divisible  by  2.  It  is,  however, 
arbitrary.  An  instrument  is  in  tune  provided  the  intervals  between  the 
notes  are  correct,  when  c  is  yielded  by  any  number  of  vibrations  per 
second  not  differing  much  from  256.  Moreover,  two  instruments  are  in 
tune  with  one  another  if,  being  separately  in  tune,  they  have  any  one 
note,  for  instance,  C,  yielded  by  the  same  number  of  vibrations.  Con- 
sequently, if  two  instruments  have  one  note  in  common,  they  can  then  be 
brought  into  tune  jointly  by  having  their  remaining  notes  separately  ad- 
justed with  reference  to  the  fundamental  note.     A  tuning-fork  or  diapason 

is  an  instrument  yielding  a  constant  sound, 
and  is  used  as  a  standard  for  tuning  musical 
instruments.  It  consists  of  an  elastic  steel 
rod,  bent  as  represented  in  fig.  174.  It  is 
made  to  vibrate  either  by  drawing  a  bow 
across  the  ends,  or  by  striking  one  of  the 
legs  against  a  hard  body,  or  by  rapidly  sep- 
arating the  two  legs  by  means  of  a  steel 
rod,  as  shown  in  the  figure.  The  vibration 
produces  a  note  which  is  always  the  same 
for  the  same  tuning-fork.  The  note  is 
strengthened  by  fixing  the  tuning-fork  on  a 
box  open  at  one  end,  called  a  7'esonance  box. 
The  standard  tuning-fork  in  any  country 
represents  its  accepted  concert  pitch. 

It  has  been  remarked  for  some  years  that 
not  only  has  the  pitch  of  the  tuning  fork 
been  getting  higher  in  the  large  theatres  of 
Europe,  but  also  that  it  is  not  the  same  in 
London,  Paris,  Berlin,  Vienna,  Milan,  etc. 
This  is  a  source  of  great  inconvenience  both 
to  composers  and  singers,  and  a  commission  was  appointed  in  1859  to  es- 
tablish in  France  a  tuning-fork  of  uniform  pitch,  and  to  prepare  a 
standard  which  would  serve  as  an  invariable  type,  In  accordance  with 
the  recommendations  of  that  body,  a  7io?-inal  iiLning-foi'k  has  been  estab- 
lished, which  is  compulsory  on  all  musical  establishments  in  France,  and 


Fig.  174. 


-238]  Musical  Notation.  191 

a  standard  has  been  deposited  in  the  Conservatory  of  Music  in  Paris.  It 
performs  437 "5  double  vibrations  per  second,  and  gives  the  standard  note 
a  or  la,  or  the  a  in  the  treble  stave  (238).  Consequently,  with  reference  to 
this  standard,  the  middle  c  or  do  would  result  from  261  double  vibrations 
per  second. 

In  England  a  committee  appointed  by  the  Society  of  Arts,  recom- 
mended that  a  standard  tuning-fork  should  be  one  constructed  to  yield 
528  double  vibrations  in  a  second  and  that  this  should  represent  d  in  the 
ireble  stave.  This  number  has  the  advantage  of  being  divisible  by  2 
down  to  33,  and  is  in  fact  the  same  as  the  normal  tuning-fork  adopted  in 
Stuttgardt  in  1834,  which  makes  440  vibrations  in  the  second,  and  like 
the  French  one  corresponds  to  a  in  the  same  stave. 

238.  Musical  notation.  XMCusical  rang-e. — It  is  convenient  to  have 
some  means  of  at  once  naming  any  particular  note  in  the  whole  range  of 
musical  sounds  other  than  by  stating  its  number  of  vibrations.  Perhaps  a 
convenient  practice  is  to  call  the  octave,  of  which  the  C  is  produced 
by  an  eight  foot  organ  pipe,  by  the  capital  letters  C,  D,  E,  F,  G,  A,  B  ; 
the  next  higher  octave  by  the  corresponding  small  letters,  <:,</,  ^, y^  ^'•j  «,  b^ 
and  to  designate  the  octaves  higher  than  this  by  the  index  placed  over 
the  letter  thus,  c',  d',  e',f',g\  a',  b\  and  the  higher  series  in  a  similar 
manner.  The  same  principle  may  be  applied  to  the  notes  below  C  thus 
thjg  octave  below  C  is  C^,  and  the  next  lower  one  C^^. 
/   Thus  we  have  the  series 

C„  C.Cct/  d"  c'"  c'\ 

In  musical  writing  the  notes  are  expressed  by  signs  which  indicate  the 
length  of  time  during  which  the  note  is  to  be  played  or  sung,  and  are 
written  on  a  series  of  lines  called  a  stave.     Thus 


i^= 


-qrz:z=z=li 


:S==ti=z=i:P==r= 


c  d  e  f  g  a  b  d 

stands  for  the  octave  in  the  treble  clef ;  of  which  the  top  note  is  the 
standard  c'  and  the  bottom  is  the  middle  c.  Where  the  five  lines  are 
insufficient  they  are  continued  both  above  and  below  the  stave  by  what  are 
called  ledger  lines.  In  order  to  avoid  confusion,  a  bass  clef  is  used  for  the 

lower  notes  ;  and  it  may  be  remarked  that    ^==q=   ^^^d  §=E^ 

stand  for  the  same  note  (237)  which  is  the  middle  c. 

The  deepest  note  of  orchestral  instruments  is  the  E^  of  the  double 
bass  which  makes  41 1  vibrations,  taking  the  keynote  as  making  440 
vibrations  in  a  minute.  Some  organs  and  grand  pianofortes  go  as  low  as 
C^  with  33  vibrations  in  a  minute,  some  grand  pianos  even  as  low  as  A , 
with  27^  vibrations.  But  the  musical  character  of  all  these  notes  below 
E^  is  imperfect,  for  we  are  near  the  limit  at  which  the  ear  can  combine 
the  separate  vibrations  to  a  musical  note  (230).  These  notes  can  only  be 
used  musically  with  their  next  higher  octave,  to  which  they  impart  a 
character  of  depth  and  richness. 


192  Acoustics.  [238- 

In  the  other  direction,  pianofortes  go  to  d""  with  3520  or  even  c^  with 
4,224  vibrations  in  a  second.  The  highest  note  of  the  orchestra  is  pro- 
bably the  d^  of  the  piccolo  flute  which  makes  4752  vibrations.  And  al- 
though the  ear  can  distinguish  sounds  which  are  still  higher,  they  have 
no  longer  a  pleasurable  character.  And  while  the  notes  which  are  distin- 
guishable by  the  ear,  range  between  16  and  38,000  vibrations,  or  11 
octaves  ;  those  which  are  musically  available  range  from  about  40  to  4000 
vibrations  or  within  7  octaves. 

239.  "Wave  leng-tb  of  a  g-iven  note. — Knowing  the  number  of  vibra- 
tions which  a  sounding  body  makes  in  a  second,  the  corresponding  wave 
length  is  easily  calculated.  For  since  sound  travels  at  about  11 20  feet 
in  a  second,  if  a  body  only  made  one  vibration  in  a  second  its  wave 
length  would  be  11 20  feet  :  if  it  made  two,  the  wave  length  would  be 
half  of  1 120  feet ;  if  it  made  three,  the  third,  and  so  on — that  is,  that  the 
wave  length  of  any  note  is  the  quotient  obtained  by  dividing  the  velocity 
of  sound  by  the  number  of  vibrations  ;  and  this  whatever  the  height  of  the 
sound,  since  the  velocity  is  the  same  for  high  and  low  notes. 

Hence,  calling  v  the  velocity  of  sound,  /  the  wave  length,  n  the  number 

of  vibrations  in  a  second,  we  have  v  =  In,  from  which  n  =  -- ,  that  is,  that 

sx     /     the  number  of  vibrations  is  inversely  as  the  wave  length. 
N/  240.  On  compound  musical  tones   and   harmonics.  —  When  any 

/\   given  note  (say  C)  is   sounded  on  most  musical  instruments,  not  that 
/      \tone  alone  is  produced,  but  a  series  of  tones,  each  being  of  less  intensity 

/  than  the  one  preceding  it.     If  C,  which  may  be  called   the  primary 

tone,  is  denoted  by  unity,  the  whole  series  is  given  by  the  numbers 
I,  2,3,4,  5,6,  7,  etc.;  in  other  words,  first  the  primary  C  is  sounded, 
then  its  octave  becomes  audible,  then  the  fifth  to  that  octave,  then  the 
second  octave,  then  the  third,  fifth,  and  a  note  between  the  sixth  and 
.seventh  to  the  second  octave,  and  so  on.  These  secondary  tones  are 
called  the  harmonics  of  the  prin-ary  tone.  Though  feeble  in  comparison 
with  the  primary  tone,  they  may,  with  a  little  practice,  be  heard,  when 
the  primary  tone  is  produced  on  most  musical  instruments  ;  when,  for 
instance,  one  of  the  lower  notes  is  sounded  on  the  pianoforte. 

241.  Kelmholtz's  analysis  of  sound. — For  the  purpose  of  experi- 
mentally proving  the  presence  of  the  harmonics  as  distinct  tones.  Pro- 
fessor Helmholtz  devised  an  instrument  which  he  called  ?i  resonance  globe. 
The  principle  involved  in  its  construction  is  this  :  A  volume  of  air 
contained  in  an  open  vessel,  for  example  a  bottle,  when  caused  to  vibrate, 
tends  to  yield  a  certain  note,  and  consequently  when  that  note  is  sounded 
in  its  neighbourhood,  to  strengthen  it  (214).  A  resonance  globe,  fig.  175, 
is  a  glass  globe  furnished  with  two  openings,  one  of  which,  «,  is  turned 
towards  the  origin  of  the  sound,  and  the  other,  h,  by  means  of  an  india- 
rubber  tube,  is  applied  to  the  ear.  If  the  tone  proper  to  the  resonance 
globe  exists  among  the  harmonics  of  the  compound  tone  that  is  sounded 
it  is  strengthened  by  the  globe,  and  thereby  rendered  distinctly  audible 
Further,  other  things  being  th^  same,  the  note  proper  to  a  given  globe 
depends  on  the  diameter  of  the  globe  and  that  of  the  uncovered  opening. 


-243] 


SyntJiesis  of  Soiinds. 


193 


Consequently,  by  means  of  a  series  of  such  globes,  the  whole  series  of 
harmonics  in  a  given  compound  tone  can  be  rendered  distinctly  audible, 
and  their  existence  put  beyond  a  doubt. 


Fig.  175- 


Fig.  176. 


Konig,  the  eminent  acoustical  instrument  maker,  has  made  an  impor- 
tant modification  in  the  resonance  globe  to  which  he  has  given  the  form 
represented  in  fig.  176.  The  resonator  is  cylindrical,  and  the  end  which 
receives  the  sound  can  be  drawn  out,  so  that  the  volume  may  be  increased 
at  pleasure.  As  the  sound  thereby  becomes  deeper,  the  same  resonator 
may  be  tuned  to  a  variety  of  notes.  On  the  tubulure  fits  a  caoutchouc 
tube  by  which  the  vibrations  may  be  transmitted  in  any  direction. 

242.  Kdnig;'s  apparatns  for  the  analysis  of  sound. — As  the  suc- 
cessive apphcation  to  the  ear  of  various   resonators  is    both  slow  and 

tedious,  Konig  has  devised  a  remarkable  apparatus  in  which  a  series 
>f  resonators  act  on  manometric  flames  (262)  ;  the  sounds  thus  become 
visible,  and  may  be  shown  to  a  large  auditory. 

It  consists  of  an  iron  frame  (fig.  177)  on  which  are  fixed  in  two  parallel 
lines  fourteen  resonators  tuned  so  as  to  give  the  notes  from  F^  to  c^^,  that 
is  to  say,  four  octaves  and  a  half ;  or  notes  of  which  the  highest  give  the 
lower  harmonics  of  the  primary.  On  the  right  is  a  chamber,  C,  which  is 
supplied  with  coal  gas  by  the  caoutchouc  tube,  D,  and  on  which  are 
placed  eight  gas  jets,  each  provided  with  a  manometric  capsule  (251,  263). 
Each  jet  is  connected  with  the  chamber  C  by  a  special  caoutchouc  tube, 
while  behind  the  apparatus  a  second  tube  connects  the  same  jet  to  one  of 
the  resonators.  On  the  right  of  the  jets  is  a  system  of  rotating  mirrors 
identical  with  that  described. 

These  details  being  understood,  suppose  the  largest  resonator  on  the 
right  tuned  to  resound  with  the  note  i,  and  seven  others  with  the  harmonics 
of  this  note.  Let  the  sound  i  be  produced  in  part  of  this  apparatus  ;  if  it 
is  simple,  the  lower  resonator  alone  answers,  and  the  corresponding  flame 
is  alone  dentated  ;  but  if  the  fundamental  note  is  accompanied  by  one  or 
more  of  its  harmonics,  the  corresponding  resonators  speak  at  the  same 
time,  which  is  recognised  by  the  dentation  of  their  flames  ;  and  thus  the 
constituents  of  each  sound  may  be  detected. 

243.  Synthesis  of  sounds. — Not  only  has  Helmholtz  succeeded  in 
decomposing  sounds  into  their  constituents  ;  he  has  verified  the  result  of 
his  analysis  by  performing  the  reverse  operation,  the  synthesis  ;  that  is, 
he  has  reproduced  a  given  sound  by  combining  the  individual  sounds  of 

K 


194 


Acoustics. 


[243- 


which  his  resonators  had  shown  that  it  was  composed.  The  apparatus 
which  he  used  for  this  purpose  consists  of  eleven  tuning-forks,  the  first  of 
which  yields  the  fundamental  note  of  256  vibrations,  or  C,  nine  others 
its  harmonics,  while  the  eleventh  serves  as  make  and  break  to  cause  the 


Fig.  177. 

diapasons  to  vibrate  by  means  of  electro-magnets.  Each  diapason  has  a 
special  electro-magnet,  arid  moreover  a  resonator,  which  strengthens  it. 

All  these  diapasons  and  their  accessories  are  arranged  in  parallel  lines 
of  five  (fig.  178),  the  first  comprising  the  fundamental  note  and  its  uneven 
harmonics,  3,  5,  7,  and  9  ;  the  second  the  even  harmonics,  2,  4,  6,  8  and 
10  ;  beyond,  there  is  the  diapason  break  K  arranged  horizontally.  One  of 
its  limbs  is  provided  with  a  platinum  point  which  grazes  the  surface  of 
mercury  contained  in  a  small  cup,  the  bottom  of  which  is  connected,  by 
a  copper  wire,  with  an  electro-magnet  placed  in  front  of  the  diapason. 

The  apparatus  being  thus  arranged,  a  wire  from  a  voltaic  battery  is 
connected  with  the  binding  screw,  c,  and  this  with  the  electro-magnet,  E  ; 
which  in  turn  is  connected  with  those  of  the  nine  following  diapasons. 


-243] 


Synthesis  of  Sounds. 


195 


and  then  with  the  diapason  K  itself.  So  long  as  the  diapason  does  not 
vibrate,  the  current  does  not  pass,  for  the  platinum  point  does  not  dip  in  the^, 
mercury  cup  which  is  connected  with  the  other  pole  of  the  battery.  But 
when  the  diapason  is  made  to  vibrate  by  means  of  a  bow,  the  current 
passes.  Owing  to  their  elasticity,  the  limbs  of  the  tuning-fork  soon 
revert  to  their  original  position,  the  point  is  no  longer  in  the  mercury,  the 
current  is  broken,  and  so  on  at  each  double  vibration  of  the  diapason. 
This  intermittence  of  the  current  being  transmitted  to  all  the  other 
electro-magnets,  they  are  alternately  active  and  inactive.  Hence  they 
communicate  to  all  the  diapasons  by  their  attraction  the  same  number  of 
vibrations.     This  is  the  case  with  the  diapason  i,  which  is  tuned  in  unison 


Fig.  178. 

with  the  diapason  break  ;  but  the  diapason  3  being  tuned  to  make  three 
times  as  many  vibrations,  makes  three  vibrations  at  each  break  of  the 
current  ;  that  is  to  say,  the  electro-magnet  only  attracts  it  at  every  third 
vibration  ;  in  like  manner,  diapason  b  only  receives  a  fresh  impulse  every 
five  vibrations,  and  so  on. 

The  following  is  the  working  of  the  apparatus.  The  resonator  of  each 
diapason  is  closed  by  a  clapper  O  (fig.  179),  so  that  the  sounds  made  by 
the  diapasons  are  scarcely  perceptible  when  the  clappers  are  lowered. 
Each  of  these  is  fixed  to  the  end  of  a  bent  lever,  the  shorter  arm  of  which 
is  worked  by  a  cord  a,  which  is  connected  with  one  of  the  keys  of  a  key- 
board placed  in  front  of  the  apparatus  (fig.  178).  When  a  key  is 
depressed,  the  cord  m.oves  the  lever,  which  raises  the  clapper,  and  the 
resonator  then  acts  by  strengthening  its  diapason.  Hence  by  depressing 
any  keys,  we  may  add  to  the  fundamental  sounds  any  of  the  nine  primary 


196 


Acoustics. 


[243 


harmonics,  and  thus  reproduce  the  sounds,  the  composition  of  which  has 
been  determined  by  analysis.  Thus  by  depressing  all  the  keys  at  once 
we  obtain  the  sound  of  an  open  pipe  in  unison  with  the  deepest  diapason. 
By  depressing  the  key  of  the  fundamental  notes  and  those  of  its  uneven 
harmonics,  we  obtain  the  sound  of  a  closed  pipe. 


244.  Results  of  Helmboltz's  researches. — By  both  his  analytical  and 
synthetical  investigations  into  sounds  of  the  most  kinds,  those  from 
various  musical  instruments,  the  human  voice,  and  even  noises,  Helm- 
holtz  has  fully  succeeded  in  explaining  the  different  timbre  or  quality  of 
these  sounds.  It  is  due  to  the  different  intensities  of  the  harmonics 
which  accompany  the  primary  tones  of  those  sounds.  The  leading 
results  of  these  researches  into  the  colour  of  sounds  may  be  thus  stated  : 

i.  Simple  tones,  as  those  produced  by  a  tuning-fork  with  a  resonance 
box,  and  by  wide  covered  pipes,  are  soft  and  agreeable  without  any  rough- 
ness, but  weak,  and  in  the  deeper  notes  dull. 

ii.  Musical  sounds  accompanied  by  a  series  of  harmonics,  say  up  to  the 
sixth,  in  moderate  strength  are  full  and  musical.  In  comparison  with 
simple  tones  they  are  grander,  richer,  and  more  sonorous.  Such  are  the 
sounds  of  open  organ  pipes,  of  the  pianoforte,  etc. 

iii.  If  only  the  uneven  harmonics  are  present,  as  in  the  case  of  narrow 
covered  pipes,  of  pianoforte  strings  struck  in  the  middle,  clarionets,  etc. 
the  sound  becomes  indistinct  :  and  when  a  greater  number  of  harmonics 
are  audible,  the  .sound  acquires  a  nasal  character. 

iv.  If  the  harmonics  beyond  the  sixth  and  seventh  are  very  distinct, 
the  sound  becomes  sharp  and  rough.  If  less  strong,  the  harmonics  are 
not  prejudicial  to  the  musical  usefulness  of  the  notes.  On  the  contrary, 
they  are  useful  as  imparting  character  and  expression  to  the  music.  Of 
this  kind  are  most  stringed  instruments,  and  most  pipes  furnished  with 
tongues,  etc.  Sounds  in  which  harmonics  are  particularly  strong  acquire 
thereby  a  peculiarly  penetrating  character ;  such  are  those  yielded  by 
brass  instruments. 


-246]  Physical  Theory  of  Music.  1 97 

V.  To  form  a  given  vowel  sound  one  or  more  characteristic  notes  which 
are  always  the  same  must  be  added.     These  change  with  the  syllable 
pronounced,  but  depend  neither  on  the  height  of  the  note,  nor  on  the" 
person  who  emits  them. 

A  popular  but  adequate  account  of  Helmholtz's  principal  results  will  be 
found  in  Helmholtz's  '  Popular  Scientific  Lectures/  Longman's,  1873. 

245.  Froduction  and  perception  of  sounds. — Vocal  sounds  originate 
in  the  larynx  in  consequence  of  air  being  forced  through  a  slit  formed  of 
two  membranes  called  the  vocal  chords.  These  can  be  tightened  or 
relaxed  by  means  of  certain  muscles,  and  thus  high  or  low  notes  can  be 
produced.  The  notes  produced  by  men  are  deeper  than  those  of  women 
or  boys,  because  in  them  the  larynx  is  longer  and  the  vocal  chords  larger 
and  thicker  ;  hence,  though  equally  elastic,  they  vibrate  less  swiftly. 
Chest  notes  are  due  to  the  fact  that  the  whole  membrane  vibrates, 
while  the  falsetto  is  produced  by  a  vibration  of  the  extreme  edges  only. 
The  ordinary  compass  of  the  voice  is  within  two  octaves,  though  this  is 
exceeded  by  some  celebrated  singers.     Catalani,  for  instance,  is  said  to 

^ave  had  a  range  of  3^  octaves. 

/       The  wave  length  of  the  sounds  emitted  by  a  man's  voice  in  ordinary 
/  conversation  is  from  8  feet  to  12  feet  and  that  of  women's  voice  is  from  2 
sV     feet  to  4  feet  in  a  second. 

1^ — ^^  The  sound  of  the  human  voice  is  very  complex  and  rich  in  harmonics, 

/         for  the  mouth  and  the  various  cavities  opening  into  the  mouth   act  as 

resonators  ;  as  the  note  changes  with  their  extent,  with  the  degree  to 

which  the  mouth  is  opened  and  the  shape  given  to  it,  certain  harmonics 

are  strengthened  or  not,  and  thus  the  voice  acquires  different  timbre. 

Without  giving  an  account  of  the  anatomy  of  the  ear  we  may  state 
succinctly  how  Helmholtz  explains  the  perception  by  the  ear  of  the  most 
complicated  sounds. 

The  recent  observations  of  M.  Corti  have  shown  that  the  inner 
membrane  of  the  cochlea  is  lined  with  about  3,000  extremely  minute 
fibres  which  are  the  termination  of  the  acoustic  nerve.  Each  of  these, 
which  are  called  CortVs  Jibres,  seems  to  be  tuned  for  a  particular  note  as 
if  it  were  a  small  resonator.  It  thus  only  vibrates  in  unison  with  this 
note,  and  is  deaf  for  all  others.  Hence  each  simple  note  only  causes 
one  fibre  to  vibrate,  while  compound  notes  cause  several :  just  as  when 
we  sing  with  a  piano,  only  the  fundamental  note  and  its  harmonics 
vibrate.  'Hence,  however  complex  external  sounds  may  be,  these 
microscopic  fibres  can  analyse  it  and  reveal  the  constituents  of  which  it 
is  formed. 

246.  Beats. — When  two  simple  tones  are  sounded  together,  it  is  'in 
many  cases  found  that  they  alternately  strengthen  and  weaken  one  an- 
other. When  this  is  so,  they  are  said  to  beat  with  one  another.  This  may 
be  explained  as  follows  :  Suppose  AB,  in  fig.  180,  to  be  a  row  of  particles 
transmitting  the  sound  :  suppose  the  vibrations  producing  the  one  tone  to 
be  indicated  by  the  continuous  curved  line  ;  then,  on  the  one  hand,  the 
ordinates  of  the  different  points  of  AB  give  the  velocities  with  which 
those  points  are  simultaneoiisly  moving,  and  on  the  other  hand,  each  point 


198  Acotistics.  [246- 

vvill  have  successively  the  different  velocities  represented  by  the  successive 
ordinates.  In  hke  manner  let  the  dotted  line  show  the  vibrations  which 
produce  the  second  tone.  And,  for  the  sake  of  distinctness,  suppose  the 
number  of  vibrations  in  a  second  producing  the  former  tone  to  be  to  that 
producing  the  latter  in  the  ratio  of  3  :  2.  Now  let  us  consider  any  point 
which  when  at  rest  occupies  the  position  N  ;  draw  the  ordinate  cutting 
the  former  curve  in  P  and  the  latter  in  O.  If  the  tones  were  sounded 
separately,  the  velocity  of  N  at  a  given  distance  produced  by  the  former 
tone  would  be  PN,  and  that  of  N  at  the  same  instant  produced  by  the 
latter  tone  would  be  ON.  Consequently,  as  they  are  sounded  together,  the 
actual  velocity  of  N  at  the  given  instant  is  the  sum  of  these,  or  PN  +  QN. 
If  at  the  same  instant  we  consider  the  point  n,  its  velocity  will  consist 
of  pn  and  nq  jointly,  but  as  these  are  in  opposite  directions,  its  actual 
amount  will  he  pn  —  nq.  Hence  the  actual  velocity  resulting  from  the 
coexistence  of  the  two  tones  will  be  indicated  by  the  curve  in  fig.  181, 

Fig.  180. 


^.4:^^^    A 


whose  ordinates  equal  the  (algebraical)  sum  of  the  corresponding  oj^i- 
nates  of  the  two  curves  in  fig.  180;  that  is,  if  AN,  A«,  .  .  .  represent 
equal  distances  in  both  figures,  the  curve  is  described  by  taking  RN  equal 
to  PN  +  QN,  rn  equal  to  pn  —  qn,  and  so  on.  This  curve  shows  by  its 
successive  ordinates  the  simultaneous  velocities  of  the  different  particles 
of  AB,  and  the  successive  velocities  communicated  to  the  drum  of  the 
ear.  An  inspection  of  the  figure  will  show  that  the  velocities  are  first 
great,  then  small,  then  great,  and  so  on,  the  drum  being  first  moved 
rapidly  for  a  short  time,  then  for  a  short  time  nearly  brought  to  rest,  and 
so  on.  In  short,  the  effect  of  the  beating  of  tones  on  the  air  as  compared 
with  that  of  a  continuous  tone  is  strictly  analogous  to  the  effect  produced 
on  the  eye  by  a  flickering  as  compared  with  a  steady  light. 

It  may  be  proved  that  when  two  simple  tones  are  produced  by  m  and 
n  double  vibrations  per  second,  they  produce  ;//—;/  beats  per  second  ; 
thus,  if  C  is  produced  by  128,  and  D  by  144  double  vibrations  per  second, 
they  will  on  being  sounded  together  produce  16  beats  per  second.  It 
has  been  ascertained  that  the  beats  produced  by  two  tones  are  not  audible 
unless  the  ratio  m  :  n\s  less  than  the  ratio  6  :  5.  Hence,  in  the  case 
represented  by  fig.  181,  though  the  alternations  of  intensity  exist,  they 
would  not  be  audible.  Also,  if  the  tones  have  very  different  intensities, 
the  intensity  of  the  beat  is  very  much  disguised. 

It  is  found  that  when  beats  are  fewer  than  10  per  second  or  more  than 
70  per  second  they  are  disagreeable,  but  not  to  the  extent  of  producing 


-248]  Physical  Theory  of  Music.  1 99 

discord.  Beats  from  10  to  70  per  second  may  be  regarded  as  the  source 
of  all  discord  in  music,  the  maximum  of  dissonance  being  attained  when 
about  30  beats  are  produced  in  a  second.  For  example,  if  c  and  B  are 
sounded  together,  the  effect  is  very  discordant,  the  interval  between  those 
notes  being  16  :  15,  so  that  the  beats  are  audible,  and  the  number  of 
beats  per  second  being  16.  On  the  other  hand,  if  C,  E,  and  G  are  sounded 
together  there  is  no  dissonance,  but  if  C,  E,  G,  B  are  sounded  together 
the  discord  is  very  marked,  since  C  produces  c,  which  is  discordant  with 
B.  It  will  be  remarked  that  C,  E,  G  is  a  major  triad,  while  E,  G,  B  is  a 
minor  triad. 

A  compound  musical  tone,  being  composed  of  simple  tones  represented 
by  1,2,  3,  4,  5,  6,  7,  etc.,  does  not  give  rise  to  any  simple  tones  capable 
of  producing  an  audible  beat  up  to  the  seventh — the  sixth  and  seventh 
are  the  first  that  produce  an  audible  beat.  It  is  for  this  reason  that  there 
is  no  trace  of  roughness  in  a  compound  tone,  unless  the  seventh  harmonic 
be  audible. 

If  we  were  to  represent  graphically  a  compound  tone,  we  should  proceed 
to  construct  a  curve  out  of  simple  tones  of  different  intensities  in  the  same 
manner  as  fig.  181  is  constructed  from  two  simple  tones  of  equal  intensity 
represented  by  fig.  180.  It  is  evident  that  the  resulting  curve  will  take 
different  forms  according  to  the  presence  or  absence  of  different  har- 
monics and  their  different  intensities  ;  in  other  words,  the  colour  of  the 
notes  produced  by  different  instruments  will  depend  upon  the  for7n  of 
the  vibrations  producing  the  sound. 

247.  Combinational  tones. — Besides  the  beats  produced  when  two 
musical  notes  are  sounded  together,  there  is  another  and  distinct  pheno- 
menon, which  may  be  thus  described  :  Suppose  two  simple  tones  to  be 
simultaneously  produced  by  vibrations  of  finite  extent,  and  of  ti  and  m 
vibrations  per  second.  It  has  been  shown  by  Helmholtz  that  they 
generate  a  series  of  other  tones.  The  principal  one  of  these,  which  may 
be  called  the  differential  tone,  is  produced  by  n  —  m  vibrations  per 
second.  Its  intensity  is  generally  very  small,  but  it  is  distinctly  audible 
in  beats.  It  has  been  called  the  grave  harmonic,  as  generally  its 
pitch  is  much  lower  than  that  of  the  notes  by  which  it  is  generated.  It 
has  been  supposed  to  be  caused  by  the  beats  becoming  too  numerous  to 
be  distinguished,  and  coalescing  into  a  continuous  sound,  and  this  sup- 
position was  countenanced  by  the  fact  that  its  pitch  is  the  same  as  the 
beat  number.  The  supposition  is  shown  to  be  erroneous,  first,  by  the 
existence  of  the  differential  tones  for  intervals  that  do  not  beat,  and 
secondly,  by  the  fact  that,  under  certain  circumstances,  both  the  beats 
and  the  differential  tones  may  be  heard  together. 

248.  The  physical  constitution  of  musical  chords. — Let  us  sup- 
pose two  compound  tones  to  be  sounded  together,  say  C  and  G,  then  we 
obtain  two  series  of  tones  each  consisting  of  a  primary  and  its  harmonics 
namely,  denoting  C  by  4,  the  two  series,  4,  8,  12,  16,  .  .  .  and  6,  12,  18, 
24,  etc.  Now,  if  instead  of  producing  the  two  notes  C  and  G,  we  had 
sounded  the  octave  below  C,  we  should  have  produced  the  series,  2,  4, 
6,  8,  10,  12,   14,  16,  18,  etc.      It  is  plain  that  the  two  former  series 


200  Acoustics.  [248- 

when  joined  differ  from  the  last  in  the  following  respects  :  {a)  The 
primary  tone  2  is  omitted,  {b)  In  the  case  of  the  last  series,  the  con- 
secutive tones  continually  decrease  in  intensity,  whereas  in  the  two  former 
series,  4  and  6  are  of  the  same  intensity,  8  is  of  lower  intensity,  but  the 
two  12's  will  strengthen  each  other,  and  so  on.  {c)  Certain  of  the  har- 
monics of  the  primary  3  are  omitted ;  for  example,  10,  14,  etc.,  do  not  occur 
in  either  of  the  two  former  series.  In  spite  of  these  differences,  however, 
the  two  compound  notes  affect  the  ear  in  a  manner  very  closely  re- 
sembling a  single  compound  tone  ;  in  short,  they  coalesce  into  a  single 
tone  with  an  artificial  colour.  It  may  be  added  that  in  the  case  above 
taken  C  and  G  produce  as  a  combination  tone  2  (that  is,  6  —  4),  so  that, 
strictly  speaking,  the  2  is  not  wanted  m  the  series  produced  by  C  and 
G,  only  it  exists  in  very  diminished  intensity.  The  same  explanation  will 
apply  to  all  possible  chords  ;  for.  example,  in  the  case  of  the  major  chord, 
C,  E,  G,  we  have  a  tone  of  artificial  colour  expressed  by  the  series  of 
simple  tones,  4,  5,  6,  8, 10,  12,  15,  16,  18,  etc.,  together  with  the  combination 
tones,  I,  I,  2.  It  will  be  remarked  that  in  the  whole  of  this  series 
there  are  no  dissonant  tones  introduced,  except  15,  16,  and  16,  18,  and 
this  dissonance  will  be  inappreciably  slight,  since  15  is  the  third  harmonic 
of  5,  and  the  16  the  fourth  harmonic  of  4,  so  that  their  intensities  will 
be  different,  as  also  will  be  the  intensities  of  16  and  18.  On  the  other 
hand,  nearly  all  the  tones  which  form  a  natural  compound  tone  are 
present,  namely,  there  are  i,  2,  4,  5,  6,  8,  10,  12,  etc.,  in  place  of  i,  2,  3, 
4,  5,  6,  7,  8,  9,  10,  II,  12,  etc.  In  short,  the  major  triad  differs  only  from 
a  nattirat  compound  tone  in  that  it  consists  of  a  series  of  simple  tones  of 
different  intensities,  and  omits  those  which  by  beating  with  its'  neighbour- 
ing tone  would  produce  dissonance,  for  example,  7,  which  would  beat 
with  6  and  8  ;  9,  which  would  beat  with  8  and  10  ;  and  11,  which  would 
beat  with  10  and  12.  It  is  this  circumstance  which  renders  the  major 
chord  of  such  great  importance  in  harmony.  If  the  constituents  of  the 
minor  chord  are  similarly  discussed,  namely,  three  compound  tones 
whose  primaries  are  proportional  to  10,  12,  15,  it  will  be  found  to  differ 
from  the  major  chord  in  the  following  principal  respects  :  (a)  The 
primary  of  the  natural  tone  to  which  it  approximates  is  very  much  deeper 
than  that  of  the  corresponding  major  chord,  {b)  It  introduces  the  differ- 
ential tones,  2,  3,  5,  which  form  a  major  chord.  Now  it  has  already  been 
remarked  that  when  a  major  and  minor  chord  are  sounded  together,  they 
are  distinctly  dissonant ;  for  example,  when  C,  E,  G,  A,  are  sounded 
together.  Accordingly,  the  fact  of  the  differential  tones  forming  a  major 
chord  shows  that  an  elementary  dissonance  exists  in  every  minor  chord. 


251]  Vibrations  of  Strings.  201 

J 
CHAPTER   \W.\ 

VIBRATIONS   OF   STRETCHED    STRINGS,   AND  ,0F   COLUMNS   OF  AIR. 


I 


meant  the  string  of  a 
.ched  by  a  certain  force, 
The  vibrations  which 
'ongitiiditial,  but  prac- 
■sat  vibrations  may  be 


249.  Vibrations  of  strings. — By  a  string 
musical  instrument,  such  as  a  viohn,  which  is  stj 
and  is  commonly  of  catgut  or  is  a  metallic  wii 
strings  experience  may  be  either  transversat  o\ 
tically  the  former  are  alone  important.  Transi 
produced  by  drawing  a  bow  across  the  string,  as  in  the  case  of  the  violin ; 
or  by  striking  the  string,  as  in  the  case  of  the  pianoforte  ;  or  by  pulling 
it  transversely,  and  then  letting  it  go  suddenly,  as  in  the  case  of  the 
guitar  and  the  harp. 

250.  Sonometer. — The  sonometer  is  an  apparatus  by  which  the  trans- 
verse vibrations  of  strings  may  be  studied.  It  is  also  called  monochord, 
because  it  has  generally  only  one  string.  In  addition  to  the  string,  it 
consists  of  a  thin  wooden  box  to  strengthen  the  sound ;  on  this  there  are 
two  fixed  bridges,  A  and  D  (fig.  182),  over  which  passes  the  string,  which 


Fig.  182. 

is  usually  a  metallic  wire.  This  is  fastened  at  one  end,  and  stretched 
at  the  other  by  a  weight,  P,  which  can  be  increased  at  will.  By  means  of 
a  third  movable  bridge,  B,  the  length  of  that  portion  of  the  wire  which  is 
to  be  put  in  vibration  can  be  altered  at  pleasure. 

251.  Xiaws  of  tlie  transverse  vibrations  of  stringrs. — If  /  be  the 
length  of  a  string,  that  is,  the  vibrating  part  between  two  bridges,  A  and 
B  (fig.  182),  r  the  radius  of  the  string,  d  its  density,  P  the  stretching 
weight,  and  n  the  number  of  vibrations  per  second,  it  is  found  by  calcu- 


lation that 


2rts/ 


^g 


being  the  ratio  of  the  circumference  to  the 


diameter,  g  the  acceleration  of  gravity. 

The  above  formula  expresses  the  following  laws  : — 

I.  The  stretching  weight  or  tension  beiftg  constajtt,  the  number  of 
vibrations  in  a  second  is  inversely  as  the  length. 

II.  The  number  of  vibrations  in  a  second  is  inversely  as  the  diameter 
of  the  string. 

K3 


202  Acoustics.  [251- 

III.  The  number  of  vibrations  in  a  second  is  directly  as  t^ie  square  root 
of  the  stretching  weight  or  tension. 

IV.  The  number  of  vibrations  in  a  second  of  a  string  is  inversely  as  the 
square  root  of  its  density. 

These  laws  are  applied  in  the  construction  of  stringed  instruments,  in 
which  the  length,  diameter,  tension,  and  substance  of  the  strings  are  so 
chosen,  that  given  notes  may  be  produced  from  them. 

252.  Experimental  verification  of  tbe  laws  of  tlie  transverse 
vibration  of  string-s. — Law  of  the  lengths.  In  order  to  prove  this  law, 
we  may  call  to  mind  that  the  relative  numbers  of  vibrations  of  the  notes 
of  the  gamut  are 

CDEFGAB         c 

T  J^liSlls^ 

^843238"' 

If  now  the  entire  length  of  the  sonometer  be  made  to  vibrate,  and  then, 
by  means  of  the  bridge  B,  the  lengths  f ,  |,  f ,  |,  f,  {■.,  |,  which  are  the 
inverse  of  the  above  numbers,  be  successively  made  to  vibrate,  all  the 
notes  of  the  gamut  are  successively  obtained,  which  proves  the  first  law. 

Law  of  the  diameters.  This  law  is  verified  by  stretching  upon  the  sono- 
meter two  cords  of  the  same  material,  the  diameters  of  which  are  as  3  to 
2,  for  instance.  When  these  are  made  to  vibrate,  the  second  cord  gives 
the  fifth  above  the  other  ;  which  shows  that  it  makes  three  vibrations 
while  the  first  makes  two. 

Law  of  the  tensions.  Having  placed  on  the  sonometer  two  identical 
strings,  they  are  stretched  by  weights  which  are  as  4  :  9.  The  second 
now  gives  the  fifth  of  the  first,  from  which  it  is  concluded  that  the 
numbers  of  their  vibrations  are  as  2  :  3,  that  is,  as  the  square  roots  of  the 
tensions.  If  the  two  weights  are  as  16  to  25,  the  major  third  or  |  would 
be  obtained. 

Law  of  the  densities.  Two  strings  of  the  same  radius  but  different 
densities  are  fixed  on  the  sonometer.  Having  been  subjected  to  the 
same  stretching  weight,  the  position  of  the  movable  bridge  on  the  denser 
one  is  altered  until  it  is  in  unison  with  the  other  string.  If  then  d  and  d' 
are  the  densities  of  the  two  strings,  and  /  and  I'  the  lengths  which  vibrate 

in  unison,  we  find  -  ■=."^1—^.     But  as  we  know  from  the  first ^  law  that 
/       \j  d 

^=  ~  ,  we  have  —  =  -'^, ,  which  verifies  this  law. 
/'       n  n       sjd 

253.  iTodes  and  loops.— Let  us  suppose  the  string  AD  (fig.  182)  to 
begin  vibrating,  the  ends  A  and  D  being  fixed,  and  while  it  is  doing  .so. 
let  a  point,  B,  be  brought  to  rest  by  a  stop,  and  let  us  suppose  DB  to  be 
one- third  part  of  AD.  The  part  DB  must  now  vibrate  about  B  and  D 
as  fixed  points  in  the  manner  indicated  by  the  continuous  and  dotted 
lines  ;  now  all  parts  of  the  same  string  tend  to  make  a  vibration  in  the 
same  time  ;  accordingly  the  part  between  A  and  B  will  not  perform  a 
single  vibration,  but  will  divide  into  two  at  the  point  C,  and  vibrate  in 
the  manner  shown  in  the  figure.  If  BD  were  one-fourth  part  of  AD  (fig. 
1 83),  the  part  AD  would  be  subdivided  at  C  and  Q'  into  three  vibrating 
portions  each  equal  to  BD.     The  points  B,  C,  C  are  called  nodes  or  nodal 


255] 


Wind  Instruments. 


203 


points  ;  the  middle  point  of  the  part  of  the  string  between  any  two  conse- 
cutive nodes  is  called  a  loop  or  a  ventral  segment.  It  will  be  remarked 
that  the  ratio  of  BD  :  BA  must  be  that  of  some  two  whole  numbers,  for 
example,  i  :  2,  i  :  3,  2  :  3,  etc.,  otherwise  the  nodes  cannot  be  formed, 
since  the  two  portions  of  the  string  cannot  then  be  made  to  vibrate  in  the 
same  time,  and  the  vibrations  will  interfere  with  and  soon  destroy  one 
another. 

If  now  we  refer  to  fig.  183,  the  existence  of  the  node  at  C  can  be  easily 
proved  by  bending  some  Hght  pieces  of  paper,  and  placing  them  on  the 

Fig.  183. 


Fig.  184. 


String.  Say  three  pieces,  one  at  C  and  the  others  respectively  midway 
between  B  and  C,  and  between  C  and  A.  The  one  at  C  experiences  only 
a  very  slight  motion,  and  remains  in  its  place,  thereby  proving  the  exist- 
ence of  a  node  at  C  ;  the  other  two  are  violently  shaken,  and  in  most 
cases  thrown  off  the  string. 

When  a  musical  string  vibrates  between  fixed  points  A  and  B,  its 
motion  is  not  quite  so  simple  as  might  be  inferred  from  the  above 
description.  In  point  of  fact,  partial  vibrations  are  soon  produced,  and 
superimposed  upon  the  primary  vibrations.  The  partial  vibrations  cor- 
respond to  the  half,  third,  fourth,  etc.  parts  of  the  string.  It  is  by  these 
partial  vibrations  that  the  harm.onics  are  produced  which  accompany  the 
primary  note  due  to  the  primary  vibrations. 

254.  iVind  instruments. — In  the  cases  hitherto  considered  the  sound 
results  from  the  vibrations  of  solid  bodies,  and  the  air  only  serves  as  a 
vehicle  for  transmitting  them.  In  wind  instruments  on  the  contrary, 
when  the  sides  of  the  tube  are  of  adequate  thickness,  the  enclosed  column 
of  air  is  the  sonorous  body.  In  fact,  the  substance  of  the  tubes  is  without 
influence  on  the  primary  tone;  with  equal  dimensions  it  is  the  same 
whether  the  tubes  are  of  glass,  of  wood,  or  of  metal.  These  different  ma- 
terials simply  do  no  more  than  give  rise  to  different  harmonics,  and  impart 
a  different  quality  to  the  compound  tone  produced. 

In  reference  to  the  manner  in  which  the  air  in  tubes  is  made  to  vibrate 
wind  instruments  are  divided  into  7noutk  instruments  and  reed  instru- 
ments. 

255.  Mouth  instruments.— In  mouth  instruments  all  parts  of  the 
mouthpiece  are  fixed.     Fig.  185  represents  the  mouthpiece  of  an  organ 


204 


Acoustics. 


[255^ 


Fig.  1 86. 


pipe,  and  fig.  i86  that  of  a  whistle,  or  of  a  flageolet.  In  both  figures,  the 
aperture  ib  is  called  the  mouth  ;  it  is  here  that  air  enters  the  pipe :  b  and 
o  are  the  lips,  the  upper  one  of  which  is  bevelled. 
The  mouthpiece  is  fixed  at  one  end  of  a  tube, 
the  other  end  of  which  may  be  either  opened  or 
closed.  In  fig.  185  the  tube  can  be  fitted  on  a 
wind-chest  by  means  of  the  foot  P. 

When  a  rapid  current  of  air  enters  by  the 
mouth,  it  strikes  against  the  upper  lip,  and  a 
shock  is  produced  which  causes  the  air  to  issue 
from  bo  in  an  intermittent  manner.  In  this  way, 
pulsations  are  produced  which,  transmitted  to 
the  air  in  the  pipe,  make  it  vibrate,  and  a  sound 
is  the  result.  In  order  that  a  pure  note  may 
be  produced,  there  must  be  a  certain  relation 
between  the  form  of  the  lips  and  the  magnitude 
of  the  mouth ;  the  tube  also  ought  to  have  a 
great  length  in  comparison  with  its  diameter. 
The  number  of  vibrations  depends  in  general  on 
the  dimensions  of  the  pipe,  and  the  velocity  of  the  current  of  air. 

256.  Reed  instruments. — In  reed  instruments  a  simple  elastic  tongue 

sets  the  air  in  vibration.  The 
tongue,  which  is  either  of 
metal  or  of  wood,  is  moved 
by  a  current  of  air.  The 
mouthpieces  of  the  oboe,  the 
bassoon,  the  clarionet,  the 
child's  trumpet,  are  different 
applications  of  the  reed, 
which,  it  may  be  remarked, 
is  seen  in  its  simplest  form  in 
the  Jew's  harp.  Some  organ 
pipes  are  reed  pipes,  others 
are  mouth  pipes. 

Fig.  187  represents  a 
model  of  a  reed  pipe  as  com- 
monly shown  in  lectures.  It 
is  fixed  on  the  wind-chest  O 
of  a  bellows,  and  the  vibra- 
tions of  the  reed  can  be  seen 
through  a  piece  of  glass,  E, 
fitting  into  the  sides.  A 
wooden  horn,  H,  strengthens 
the  sound. 

Fig.  137.  Fig.  188.         Fig.  189.  Y\g.  188  shows  the  reed, 

out  of  the  pipe.  It  consists  of  four  pieces:  ist,  a  rectangular  wooden 
tube  closed  below  and  open  above  at  0  ;  2nd,  a  copper  plate  cc  forming 
one  side  of  the  tube,  and  in   which  there   is   a  longitudinal  aperture. 


-258]  Mouth  and  Reed  Instruments.  205 

through  which  air  passes  from  the  tube  MN  to  the  orifice  o  ;  3rd,  a  thin 
elastic  plate,  i,  called  the  tongue^  which  is  fixed  at  its  upper  end,  and 
which  grazes  the  edge  of  the  longitudinal  aperture,  nearly  closing  it  ; 
4th,  a  curved  wire,  r,  which  presses  against  the  tongue,  and  can  be  moved 
up  and  down.  It  thus  regulates  the  length  of  the  tongue,  and  deter- 
mines the  pitch  of  the  note.  It  is  by  this  wire  that  reed  pipes  are  tuned. 
The  reed  being  replaced  in  the  pipe  MN,  when  a  current  of  air  enters 
by  the  foot  P,  the  tongue  is  compressed,  it  bends  inwards,  and  affords  a 
passage  to  air,  which  escapes  by  the  orifice  o.  But,  being  elastic,  the 
tongue  regains  its  original  position,  and  performing  a  series  of  oscillations 
successively  opens  and  closes  the  orifice.  In  this  way  sonorous  waves 
result  and  produce  a  note,  whose  pitch  increases  with  the  velocity  of  the 
current. 

In  this  reed  the  tongue  vibrates  alternately  before  and  behind  the  aper- 
ture, and  just  escapes  grazing  the  edges,  as  is  seen  in  the  harmonium,  con- 
certina, etc.  ;  such  a  reed  is  called  2.  free  reed.  But  there  are  other  reeds 
called  beatifig  reeds,  in  which  the  tongue,  which  is  larger  than  the  orifice, 
strikes  against  the  edges  at  each  oscillation.  The  reed  of  the  clarionet, 
represented  in  fig.  189,  is  an  example  of  this  ;  it  is  kept  in  its  place  by 
the  pressure  of  the  lips.  The  reeds  of  the  hautboy  and  bassoon  are  also 
of  this  kind. 

257.  Of  the  tones  produced  by  the  same  pipe. — Daniel  Bernouilli 
discovered  that  the  same  organ  pipe  can  be  made  to  yield  a  succession  of 
tones  by  properly  varying  the  force  of  the  current  of  air.  The  results  he 
arrived  at  may  be  thus  stated  : — = 

i.  If  the  pipe  is  open  at  the  end  opposite  to  the  mouthpiece,  then,  de- 
noting the  primary  tone  by  I,  we  can,  by  gradually  increasing  the  force 
of  the  current  of  air,  obtain  successively  the  tones  2,  3,  4,  5,  etc.,  that  is 
to  say,  the  harmonics  of  the  primary  tone. 

ii.  If  the  pipe  is  closed  at  the  end  opposite  to  the  mouthpiece,  then, 
denoting  the  primary  tone  by  l,  we  can,  by  gradually  increasing  the  force 
of  the  current  of  air,  obtain  successively  the  tones  3,  5,  7,  etc.,  that  is  to 
say,  the  uneven  harinonics  of  the  primary  tone. 

It  must  be  added  that  if  a  closed  and  an  open  pipe  are  to  yield  the 
same  primary  tone,  the  closed  pipe  must  be  half  the  length  of  the  open 
pipe,  if  in  other  respects  they  are  the  same. 

In  any  case  it  is  impossible  to  produce  from  the  given  pipe  a  tone  not 
included  in  the  above  series  respectively. 

^     Although  the  above  laws  are  enunciated  with  reference  to  an  organ 
^ipe,  they  are  of  course  true  of  any  other  pipe  of  uniform  section. 

^58.  On  the  nodes  and  loops  of  an  orgran  pipe. — The  vibrations  of 
the  air  producing  a  musical  tone  take  place  in  a  direction  parallel  to  the 
axis  of  the  pipe — not  transversely  as  in  the  case  of  the  portions  of  a 
vibrating  spring.  In  the  former  case,  however,  as  well  as  in  the  latter, 
the  phenomena  of  nodes  and  loops  may  be  produced.  But  now  by  a  7iode 
must  be  understood  a  section  of  the  column  of  air  contained  in  the  pipe, 
where  the  particles  remain  at  rest,  but  where  there  are  rapid  alternations 
of  condensation  and  rarefaction.     By  a  loop  or  ventral  segment  must  be 


206 


Acoustics. 


[258- 


iinderstood  a  section  of  the  column  of  air  contained  in  the  pipe  where  the 
vibrations  of  the  particles  of  air  have  the  greatest  amplitudes,  and  where 
there  is  no  change  of  density.  The  sections  of  the  column  of  air  are,  of 
course,  made  at  right  angles  to  its  axis.  When  the  column  of  air  is 
divided  into  several  vibrating  portions,  it  is  found  that  the  distance 
between  any  two  consecutive  loops  is  constant,  and  that  it  is  bisected  by 
a  node.  We  can  now  consider  separately  the  cases  of  the  open  and  closed 
pipes. 

i.  In  the  case  of  a  stopped  pipe,  the  bottom  is  always  a  node,  for  the 
layer  of  air  in  contact  with  it  is  necessarily  at  rest,  and  only  undergoes 
variations  in  density.  At  the  mouthpiece,  on  the  contrary,  where  the  air 
has  a  constant  density,  that  of  the  atmosphere,  and  the  vibration  is  at  its 
maximum,  there  is  always  a  loop.     In  any  stopped  pipe  there  is  at  least 


f 


¥  ¥ 


u 

V 

N 
V 
N 
V 

/ 


Fig.  190.         Fig.  i9i.         Fig.  192. 


Fig.  193.        Fig.  194-        Fig.  195 


one  node  and  one  loop  (fig.  190)  ;  the  pipe  then  yields  its  fundamental 
note,  and  the  distance  VN  from  the  loop  to  the  node  is  equal  to  half  a 
condensed  or  rarefied  wave  length. 

If  the  current  of  air  be  forced,  the  mouthpiece  always  remains  a  loop, 
and  the  bottom  a  node,  the  column  divides  into  three  equal  parts  (fig.  191) 
and  an  intermediate  node  and  loop  are  formed.  The  sound  produced  is 
the  first  harmonic.  When  the  second  harmonic  (5)  is  produced,  there 
are  two  intermediate  nodes  and  two  loops,  and  the  tube  is  then  sub- 
divided into  five  equal  parts  (fig.  192),  and  so  on. 

ii.  In  the  case  of  the  open  pipe,  whatever  tone  it  produces,  there  must 
be  a  loop  at  each  end,  since  the  enclosed  column  of  air  is  in  contact  with 
the  external  air  at  those  points.  When  the  primary  tone  is  produced, 
there  will  be  a  loop  at  each  end,  and  a  node  at  the  middle  section  of  the 
pipe,  the  nodes  and  loops  dividing  the  column  into  tivo  equal  parts 
(fig.  193).     When  the  first  harmonic  (2)  is  produced,  there  will  be  a  loop 


-258] 


Nodes  and  Loops  of  an  Organ  Pip£. 


207 


at  each  end,  and  a  loop  in  the  middle,  the  column  being  divided  'mXofoiir 
equal  parts  by  the  alternate  loops  and  nodes  (fig.  194).  When  the  second 
harmonic  (3)  is  produced,  the  column  of  air  will  be  divided  into  six  equal 
parts  by  the  alternate  nodes  and  loops,  and  so  on  (fig.  195).  It  will  be 
remarked  that  the  successive  modes  of  division  of  the  vibrating  column 
are  the  only  ones  compatible  with  the  alternate  recurrence  at  equal  in- 
tervals of  nodes  and  loops,  and  with  the  occurrence  of  a  loop  at  each  end 
of  the  pipe. 

There  are  several  experiments  by  which  the  existence  of  nodes  and 
loops  can  be  shown. 


o 


{d)  If  a  fine  membrane  is  stretched  over  a  pasteboard  ring,  and  has 
sprinkled  on  it  some  fine  sand,  it  can  be  gradually  let  down  a  tube,  as 
shown  in  fig.  198.  Now  suppose  the  tube  to  be  producing  a  musical 
note.  As  the  membrane  descends,  it  will  be  set  in  vibration  by  the 
vibrating  air.  But  when  it  reaches  a  node  it  will  cease  to  vibrate,  for 
there  the  air  is- at  rest.  Consequently  the  grains  of  sand,  too,  will  be  at  rest, 
and  their  quiescence  will  indicate  the  position  of  the  node.     On  the  other 


2o8 


Acoustics. 


[258 


hand,  when  the  membrane  reaches  a  loop,  that  is,  a  point  where  the  am- 
phtude  of  the  vibrations  of  the  air  attains  a  maximum,  it  will  be  violently 
agitated,  as  will  be  shown  by  the  agitation  of  the  grains  of  sand.  And 
thus  the  positions  of  the  loops  can  be  rendered  manifest. 

{b)  Again,  suppose  a  pipe  to  be  constructed  "Avith  holes  bored  in  one  of 
its  sides,  and  these  covered  by  little  doors  which  can  be  opened  and 
shut,  as  shown  m  fig.  196.  Let  us  suppose  the  little  doors  to  be  shut  and 
the  pipe  to  be  caused  to  produce  such  a  tone  that  the  nodes  are  at  N  and 
N'  and  the  loops  at  V,  Y',  Y^\  At  the  latter  points  the  density  is  that  of 
the  external  air,  and  consequently  if  the  door  at  V  is  opened  no  change 
is  produced  in  the  note.  At  the  former  points  N  and  N'  there  are  alter- 
nately condensation  and  rarefaction  taking  place.  If  now  the  door  at 
N'  is  opened,  this  alternation  of  density  is  no  longer  possible,  for  the 
density  at  this  open  point  must  be  the  same  as  that  of  the  external  air, 
and  consequently  N^  becomes  a  loop  and  a  note  yielded  by  the  tube  is 
changed.  The  change  of  notes  produced  by  changing  the  fingering  of 
the  flute  is,  of  course,  one  form  of  this  experi- 
ment. 

{c)  Suppose  A,  in  fig.  197,  to  be  a  pipe 
emitting  a  certain  note,  and  suppose  P  to  be  a 
plug,  fitting  the  tube,  fastened  to  the  end  of  a 
long  rod  by  which  it  can  be  forced  down  the 
tube.  Now  when  the  plug  is  inserted,  whatever 
be  its  position,  there  will  be  a  node  in  contact 
with  it.  Consequently,  as  it  is  gradually  forced 
down,  the  note  yielded  by  the  pipe  will  keep  on 

r^.      ..  changing.     But  every  time  it  reaches  a  position 

fe;,f-^]       which  was  occupied  by  a  node  before  its  inser- 
I  tion,  the  note  becomes  the  same  as  the  note 

BiiAiiiiMii  originally  yielded.  For  now  the  column  of  air 
vibrates  in  exactly  the  same  manner  as  it  did 
before  the  plug  was  put  in. 

{a)  Y\g.  1 99  shows  another  mode  of  illustrating 
the  same  point,  which  is  identical  in  principle 
with  Konig's  manometric  flames.  The  figure 
represents  an  organ  pipe,  on  one  side  of  which 
is  a  chest,  P,  filled  with  coal  gas,  by  means  of 
the  tube  S.  The  gas  from  the  chest  comes  out 
in  three  jets,  A,  B,  C,  and  is  then  ignited. 
The  manner  in  which  the  gas  passes  from 
the  chest  to  the  point  of  ignition  is  shown 
'^'  '^^'  in  the   smallest   figure,  which   is   an  enlarged 

section  of  A.  A  circular  hole  is  bored  in  the  side  of  the  pipe  and  covered 
with  a  membrane,  r.  A  piece  of  wood  is  fitted  into  the  hole  so  as  to 
leave  a  small  space  between  it  and  the  membrane.  The  gas  passes  from 
the  chest,  in  the  direction  indicated  by  the  arrow,  into  the  space  between 
the  membrane  and  the  piece  of  wood,  and  so  out  of  the  tube  7?i,  at  the 
mouth  of  which  it  is  ignited.     Now  suppose  the  pipe  to  be  caused  to 


II      fl 


260]  Nodes  and  Loops  of  mi  Organ  Pipe.  209 

yield  its  primary  note,  then  as  it  is  an  uncovered  pipe  there  ought  to  be 
a  node  at  B,  its  middle  point.  Consequently  there  ought  to  be  rapid 
changes  of  density  at  B  ;  these  would  cause  the  membrane  r  to  vibrate,^ 
and  thereby  blow  out  the  flame  w,  and  this  is  what  actually  happens. 
If  by  increasing  the  force  of  the  wind  the  octave  to  the  primary  note  is 
produced,  B  will  be  a  loop,  and  A  and  C  nodes.  Consequently  the  flames 
at  A  and  C  will  now  be  extinguished,  as  is,  in  point  of  fact,  the  case. 
But  at  B,  there  being  no  change  of  density,  the  membrane  is  unmoved, 
and  the  flame  continues  to  burn  steadily. 

By  each  and  all  of  these  experiments  it  is  shown  that  in  a  given  pipe, 
whether  open  or  closed,  there  are  always  a  certain  number  of  nodes,  and 
midway  between  any  two  consecutive  nodes  there  is  always  a  loop  or 
ventral  segment. 

259.  Forznulse  relative  to  tbe  number  of  vibrations  produced  by 
a  musical  pipe. — It  follows  from  what  has  been  said  that  the  column  of 
air  in  stopped  pipes  is  always  divided  by  the  nodes  and  loops  into  an 
uneven  number  of  parts  which  are  equal  to  each  other,  and  each  of  which 
is  a  quarter  of  a  complete  vibration  (figs.  190,  191,  and  192)  while  in  an 
open  pipe  it  is  divided  into  an  even  number  of  such  parts  (figs.  193,  194, 
195).  If  L  be  the  length  of  the  pipe,  /  the  wave  length  of  the  sound 
which  it  emits,  and/  any  whole  number,  then  for  stopped  pipes  we  have 

L  =  (2/  +  i)  -  ;  and  for  open  pipes  L  =  2/  -  =^  .    Replacing  in  each  of 
4  42 

these  formulas  /  by  its  value  -  (237),  we  haveL  =  (2/  +1)  —  and  L  = 

n  4.n       y , 

?—  ;  from  which  for  stopped  pipes  we  have  n  =  I  p  -^  ^v  ^^^  ^^^  open 

7.n  rr  tr  r  4L  ' 

ones  Ji=  ^ — 
2  L 

If,  in  the  first  formula,  we  give  to  p  the  successive  values  o,  i,  2,  3,  4, 

etc.,  we  have  ;^  =  -^,    ?^,  i-^  ;   that  is  the  fundamental   sound  and 
4L     4L     4L 

all  its  uneven  harmonics  ;  and  in  the  formula  for  the  open  pipe  we  get 

similarly —,^' ^, etc.,  that  is  the  fundamental  note  and  all  its  har- 

2  L  2  L  2  L 
monies  even  and  uneven. 

260.  Explanation  of  tbe  existence  of  nodes  and  loops  In  a  musical 
pipe.— The  existence  of  nodes  and  loops  is  to  be  explained  by  the  co- 

A . , -^^C — ^S^i^ ^-^— -^ ff 


existence  in  the  same  pipe  of  two  equal  waves  travelling  m  contrary 
directions. 

Let  A  be  a  point  from  which  a  series  of  waves  sets  out  towards  B,  and 


210  A  coiistics.  [260- 

let  the  length  of  these  waves,  whether  of  condensation  or  rarefaction,  be 
AC,  CD,  DB.  And  let  B  be  the  point  from  which  the  series  of  exactly 
equal  waves  sets  out  towards  A.  It  must  be  borne  in  mind  that  in  the 
case  of  a  wave  of  condensation  originating  at  A,  the  particles  move  in  the 
direction  A  to  B,  but  in  a  wave  of  condensation  originating  at  B  they 
move  in  the  direction  B  to  A.  Now  let  us  suppose  that  condensation  at 
C,  caused  by  the  wave  from  A,  begins  at  the  same  instant  that  condensa- 
tion caused  by  the  wave  from  B  begins  at  D.  Consequently,  restricting 
our  attention  to  the  particles  in  the  line  CD,  at  any  instant  the  velocities 
of  the  particles  in  CD  due  to  the  former  w^ave  will  be  represented  by  the 
ordinates  of  the  curve  SPRT,  while  those  due  to  the  wave  from  B  will 
be  represented  by  the  co-ordinates  of  the  curve  TQrS.  Then,  since  the 
waves  travel  with  the  same  velocity  and  are  at  C  and  D  respectively  at 
the  same  instant,  we  must  have,  for  any  subsequent  instant,  CR  equal  to 
Dr.  If,  therefore,  N  is  the  middle  point  between  C  and  D,  we  must  have 
rN  equal  to  RN,  and  consequently  PN  equal  to  ON,  that  is  to  say,  if  the 
particle  at  N  transmitted  only  one  vibration,  its  motion  at  each  instant 
would  be  in  the  opposite  phase  to  that  of  its  motion  if  it  transmitted  only 
the  other  vibration.  In  other  words,  the  particle  N  will  at  every  instant 
tend  to  be  moved  with  equal  velocity  in  opposite  directions  by  the  two 
waves,  and  therefore  will  be  pennaneritly  at  rest.  That  point  is  therefore 
a  node.  In  like  manner  there  is  a  node  at  N'  midway  between  A  and  C, 
and  also  at  N'^  midway  between  B  and  D.  In  regard  to  the  motion  of 
the  remaining  particles,  it  is  plain  that  their  respective  velocities  will  be 
the  (algebraical)  sum  of  the  velocities  they  would  at  each  instant  receive 
from  the  waves  separately.  Hence  at  the  instant  indicated  by  the  diagram 
they  are  given  by  the  ordinates  of  the  curve  HNK.  This  curve  will 
change  from  instant  to  instant,  and  at  the  end  of  the  time  occupied  by  the 
passage  of  a  wave  of  condensation  (or  of  rarefaction)  from  C  to  D  will 
occupy  the  position  shown  by  the  dotted  line  Ji^k.  Hence  it  is  evident 
that  particles  near  N  have  but  small  changes  of  velocity,  whilst  those 
near  C  and  D  experience  large  changes  of  velocity. 

If  the  curve  HK  were  produced  both  ways,  it  would  always  pass 
through  W  and  N^'  ;  the  part,  however,  between  N  and  N'  would  some- 
times be  on  one  side  and  sometimes  on  the  other  side  of  AB.  Hence  all 
the  particles  between  W  and  N  have,  simultaneously,  first  a  motion  in 
the  direction  A  to  B,  and  then  a  motion  in  the  direction  B  to  A,  those 
particles  near  C  having  the  greatest  amplitude  of  vibrations.  Hence 
near  N  and  W  there  will  be  alternately  the  greatest  condensation  and 
rarefaction. 

This  explanation  apphes  to  the  case  in  which  AB  is  the  axis  of  an  open 
[organ  pipe,  A  being  the  end  where  the  mouthpiece  is  situated.     The 

^aves  from  B  have  their  origin  in  the  reflection  of  the  series  of  waves 
from  A.     In  the  particular  case  considered,  the  note  yielded  by  the  pipe 
that  indicated  by  3,  that  is,  the  fifth  above  the  octave  to  the  primary 

[ote.     A  similar  explanation  can  obviously  be  applied  to  all  other  cases, 
id  whether  the  end  be  opened  or  closed.  But  in  the  latter  case  the  series 
of  waves  from  the  closed  end  must  commence  at  a  point  distant  from  the 


-261]    Ktindfs  Determination  of  the  Velocity  of  Sound.       2 1 1 


mouthpiece  by  a  space  equal  to  one-half,  or  three  halves,  or  five  halves, 
etc.  of  the  length  of  a  wave  of  condensation  or  expansion, 

261.  Kundt's  determination  of  the  velocity  of  sound. — Kundt  has 
devised  a  method  of  determining  the  velocity  of  sound  in  solids  and  in 
gases  which  can  be  easily  performed  by  means  of  simple 
apparatus,  and  is  capable  of  great  accuracy.     A  glass  tube  © 

BB,  about  two  yards  long,  and  two  inches  in  the  clear,  is 
closed  at  one  end  by  a  movable  stopper  b  ;  the  other  end  is 
fitted  with  a  cork  KK,  which  tightly  grasps  a  glass  tube 
AA,  of  smaller  dimensions.  This  is  closed  at  one  end  by  a 
piston  a  which  moves  with  gentle  friction  in  the  outer  tube 
BB.  Then  by  rubbing  the  free  end  of  the  tube  AA  with  a 
wet  cloth,  it  produces  longitudinal  vibrations,  and  these 
transmit  their  motion  to  the  air  in  the  part  ab.  If  the  tube 
ab  contain  some  lycopodium  powder,  this  is  set  in  active  vibra- 
tion and  then  arranges  itself  in  small  patches  in  a  certain 
definite  order  as  represiented  in  the  figure ;  the  nature  and 
arrangement  of  which  depend  on  the  vibrating  part  of  the 
rod  and  the  tube.  When  the  length  of  the  column  of  air  is 
an  exact  multiple  of  the  wave  length  the  heaps  are  not  dis- 
tinct. 

These  heaps  represent  the  nodes,  and  the  mean  distance 
d  between  them  can  be  measured  with  great  accuracy.  This 
distance  represents  the  distance  between  two  nodes,  which  is 
half  a  wave  length  ;  that  is  the  wave  length  of  the  sound  in 
air  is  id.  If  the  rod  has  the  length  s  and  is  grasped  in  the 
middle  by  the  cork  KK,  from  the  law  of  the  longitudinal  vi- 
brations of  rods,  (265)  the  wave  length  of  the  sound  it  then 
emits  is  twice  its  length  or  2  s.  That  is  the  wave  length  of  the 
vibrating  column  of  air  is  to  that  in  the  rod  as  2d  :  is.  As  the 
velocity  of  sound  in  any  body  is  equal  to  the  wave  length  in 
that  body  multiplied  by  the  number  of  vibrations  in  a  second  ; 
and  since  the  number  of  vibrations  is  here  the  same  in  both 
cases,  for  the  tone  is  the  same,  the  velocity  of  sound  in  the 
glass  is  to  the  velocity  of  sound  in  air  as  7.sn  :  idn^  that  is  as 
s  :  d.  Thus  when  the  glass  tube  was  clamped  in  the  middle  by 
KK,  so  that  the  length  ab  was  equal  to  half  the  length  of  the 
tube  Art,  the  number  of  the  ventral  segments  was  eight.  This 
corresponds  to  a  ratio  of  wave  length  of  i  to  16  :  in  other 
words  the  velocity  of  sound  in  glass  is  16  times  that  in  air. 

The  method  is  capable  of  great  extension.  By  means  of 
the  stopcock  different  gases  could  be  introduced  instead  of  air,  and  corre- 
sponding differences  found  for  the  length  of  the  ventral  segments  ;  from 
which,  by  a  simple  calculation  the  corresponding  velocities  were  found. 
Thus  the  velocities  of  sound  in  carbonic  acid,  coal  gas,  and  hydrogen, 
were  found  to  be  respectively  o-8,  i'6,  and  3*56  that  of  air,  or,  nearly  as 
the  inverse  square  of  the  densities. 

So  also  by  varying  the  material  of  the  rod  A  a,  different  velocities 


212 


Acoustics. 


[261- 


are  obtained.     Thus  the  velocity  in  steel  was  found  to  be  15  "24,  and  that 
in  brass  10*87  that  of  air. 

262.  Chemical  harmonicon.— The  air  in  an 
open  tube  may  be  made  to  give  a  sound  by 
means  of  a  luminous  jet  of  hydrogen,  coal  gas, 
etc.  When  a  glass  tube  about  12  inches  long 
is  held  over  a  lighted  jet  of  hydrogen  (fig.  202), 
a  note  is  produced,  which,  if  the  tube  is  in  a 
certain  position,  is  the  fundamental  note  of  the 
tube.  The  sounds,  doubtless,  arise  from  the 
successive  explosions  produced  by  the  periodic 
combinations  of  the  atmospheric  oxygen  with 
the  issuing  jet  of  hydrogen.  The  apparatus  is 
called  the  chemical  harmonicon. 

The  phenomena  of  the  chemical  harmonicon 
and  of  singing  flames  have  been  investigated  by 
Prof.  Tyndal!,  whose  Lectures  on  Soujid  con- 
tain a  number  of  very  beautiful  experiments  on 
this  subject. 

The  note  depends  on  the  size  of  the  flame 
and  the  length  of  the  tube  :  with  along  tube,  by 
varying  the  position  of  the  jet  in  the  tube,  the 
series  of  notes  in  the  ratio  1.2:3:4:5  is 
obtained. 

If,  while  the  tube  emits  a  certain  sound,  the 
voice  or  the  (syren  229)  be  gradually  raised  to 
the  same  height,  as  soon  as  the  note  is  nearly  in  unison  with  the  har- 
monicon, the  flame  becomes  agitated,  jumps  up  and  down,  and  is  finally 
steady  when  the  two  sounds  are  in  unison.  If  the  tone  of  the  syren  is 
gradually  heightened,  the  pulsations  again  commence  ;  they  are  the 
optical  expressions  of  the  beats  (246)  which  occur  near  perfect  unison. 

If,  while  the  jet  burns  in  the  tube  and  produces  a  note,  the  position 
of  the  tube  is  slightly  altered,  a  point  is  reached  at  which  no  sound  is 
heard.  If  now  the  voice,  or  the  syren,  or  the  tuning-fork,  be  pitched  at 
the  note  produced  by  the  jet,  it  begins  to  sing,  and  continues  to  sing  even 
after  the  syren  is  silent.  A  mere  noise,  or  shouting  at  an  incorrect  pitch, 
affects  the  flame,  but  does  not  cause  it  to  sing. 

263.  stringred  instruinents< — Stringed  musical  instruments  depend 
on  the  production  of  transverse  vibrations.  In  some,  such  as  the  piano, 
the  sounds  are  constant,  and  each  note  requires  a  separate  string  ;  in 
others,  such  as  the  violin  and  guitar,  the  sounds  are  varied  by  the  finger- 
ing, and  can  be  produced  by  fewer  strings. 

In  the  piano  the  vibrations  of  the  strings  are  produced  by  the  stroke 
of  the  hammer,  which  is  moved  by  a  series  of  bent  levers  communicating 
with  the  keys.  The  sound  is  strengthened  by  the  vibrations  of  the  air  in 
the  sounding  board  on  which  the  strings  are  stretched.  Whenever  a  key 
is  struck,  a  damper  is  raised  which  falls  when  the  finger  is  removed  from 
the  key  and  stops  the  vibrations  of  the  corresponding  strings.     By  means 


Fig.  202. 


-264]  Wwd  InsU'uments.  2 1 3 

of  a  pedal  all  the  dampers  can  be  simultaneously  raised,  and  the  vibra- 
tions then  last  for  some  time. 

The  harp  is  a  sort  of  transition  from  the  instruments  with  constant  to 
those  with  variable  sounds.  Its  strings  correspond  to  the  natural  notes 
of  the  scale  :  by  means  of  the  pedals  the  lengths  of  the  vibrating  parts 
can  be  changed,  so  as  to  produce  sharps  and  flats.  The  sound  is 
strengthened  by  the  sounding  box,  and  by  the  vibrations  of  all  the 
strings  harmonic  with  those  played. 

In  the  violin  and  guitar  each  string  can  give  a  great  number  of  sounds 
according  to  the  length  of  the  vibrating  part,  which  is  determined  by  the 
pressure  of  the  fingers  of  the  left  hand  while  the  right  hand  plays  the  bow, 
or  the  strings  themselves.  In  both  these  instruments  the  vibrations  are 
communicated  to  the  upper  face  of  the  sounding  box,  by  means  of  the 
bridge  over  which  the  strings  pass.  These  vibrations  are  communicated 
from  the  upper  to  the  lower  face  of  the  box,  either  by  the  sides  or  by  an 
intermediate  piece  called  the  sound  post.  The  air  in  the  interior  is  set  in 
vibration  by  both  faces,  and  the  strengthening  of  the  sound  is  produced 
by  all  these  simultaneous  vibrations.  The  value  of  the  instrument  con- 
sists in  the  perfection  with  which  all  possible  sounds  are  intensified, 
which  depends  essentially  on  the  quality  of  the  wood,  and  the  relative 
arrangement  of  the  parts. 

264.  IVind  instruments. — All  wind  instruments  may  be  referred  to 
the  different  types  of  sounding  tubes  which  have  been  described.  In 
some,  such  as  the  organ,  the  notes  2.xq  fixed,  and  require  a  separate  pipe 
for  each  note  ;  in  others  the  notes  are  variable,  and  are  produced  by 
only  one  tube  :  the  flute,  horn,  etc.  are  of  this  class. 

In  the  organ  the  pipes  are  of  various  kinds,  namely,  mouth  pipes,  open 
and  stopped,  and  reed  pipes  with  apertures  of  various  shapes.  By  means 
of  stops  the  organist  can  produce  any  note  by  both  kinds  of  pipe. 

In  th^fiute,  the  mouthpiece  consists  of  a  simple  lateral  circular  aper- 
ture ;  the  current  of  air  is  directed  by  means  of  the  lips,  so  that  it  grazes 
the  edge  of  the  aperture.  The  holes  at  different  distances  are  closed 
either  by  the  fingers  or  by  keys  ;  when  one  of  the  holes  is  opened,  a  loop 
is  produced  in  the  corresponding  layer  of  air,  which  modifies  the  distri- 
bution of  nodes  and  loops  in  the  interior,  and  thus  alters  the  note.  The 
whistling  of  a  key  is  similarly  produced. 

The  pandtTaji  pipe  consists  of  tubes  of  different  sizes  corresponding 
to  the  different  notes  of  the  gamut. 

In  the  trumpet,  the  horn,  the  trombone,  cornet-h-piston,  and  ophicleide, 
the  lips  form  the  reed,  and  vibrate  in  the  mouthpiece.  In  the  horn, 
different  notes  are  produced  by  altering  the  distance  of  the  lips.  In  the 
trombone,  one  part  of  the  tube  slides  within  the  other,  and  the  performer 
can  alter  at  will  the  length  of  the  tube,  and  thus  produce  higher  or  lower 
notes.  In  the  cornet-a-piston  the  tube  forms  several  convolutions  ; 
pistons  placed  at  different  distances  can,  when  played,  cut  off  communi- 
cation with  other  parj;s  of  the  tube,  and  thus  alter  the  length  of  the 
vibrating  column  of  air. 


\/ 


214 


A  coiistics. 


[265- 


CHAPTER   V. 


VIBRATIONS   OF  RODS,   PLATES,  AND  MEMBRANES. 

265.  Vibrations  of  rods. — Rods  and  narrow  plates  of  wood,  of  glass, 
and  especially  of  tempered  steel,  vibrate  in  virtue  .of  their  elasticity  ;  like 
strings  they  have  two  kinds  of  vibrations,  longitudinal  and  transverse. 
The  latter  are  produced  by  fixing  the  rods  at  one  end,  and  passing  a  bow 
over  the  free  part..  Longitudinal  vibrations  are  produced  by  fixing  the 
rod  at  any  part,  and  rubbing  it  in  the  direction  of  its  length  with  a  piece 
of  cloth  sprinkled  with  resin.  But  in  the  latter  case  the  sound  is  only 
produced  when  the  point  of  the  rod  at  which  it  has  been  fixed  is  some 
aliquot  part  of  its  length,  as  a  half,  a  third,  or  a  quarter. 

It  is  shown  by  calculation  that  the  nuniber  of  transverse  vibrations 
made  in  a  given  time  by  rods  and  thin  plates  of  the  same  kind  is  directly 
as  their  thickness,  and  inversely  as  the  square  of  their  length.  The  width 
of  the  plate  does  not  affect  the  number  of  vibrations.  A  wide  plate,  how- 
ever, requires  a  greater  force  to  set  it  in  motion  than  a  narrow  one.     It  is, 

of  course,  understood  that  one  end 
of  the  vibrating  plate  is  held  firmly. 
The  laws  of  the  longitudinal  vi- 
brations of  strings,  are   expressed 

in  the  formula  ;z  =  _i      /^^   in 

2.rl  V  -nd 
which  «,  r,  /,  d,  and  g,  have  all  the 
same  meaning  as  in  the  formula 
for  the  transverse  vibrations,  while 
O  is  the  coefficient  of  elasticity  of 
the  string,  the  number  which  ex- 
presses the  weight  by  which  the  cord 
must  be  stretched  in  order  to  elongate 
by  its  own  length. 

Fig.  203  represents  an  instru- 
ment invented  by  Marloye,  and 
known  as  Marloye's  harp,  based  on 
the  longitudinal  vibration  of  rods. 
It  consists  of  a  solid  wooden 
pedestal  in  which  are  fixed  twenty 
thin  deal  rods,  some  coloured  and 
others  white.  They  are  of  such  a 
length  that  the  white  rods  give  the 
diatonic  scale,  while  the  coloured 
Y\a-  203  °^^^  Si'^^  th^  semitones,  and  com- 

plete the  chromatic  scale.  The  in- 
strument is  played  by  rubbing  the  rods  in  the  direction  of  their  length 
between  the  finger  and  thumb,  which  have  been  previously  covered 


-266] 


Vibrations  of  Rods  and  Plates. 


215 


with  powdered  resin.  The  notes  produced  resemble  t"hose  of  a  pan- 
daean  pipe. 

The  timing-fork,  the  triangle,  and  musical  boxes  are  examples  of  the 
transverse  vibrations  of  rods.  In  musical  boxes  small  plates  of  steel 
of  different  dimensions  are  fixed  on  a  rod,  like  the  teeth  of  a  comb.  A 
cylinder  whose  axis  is  parallel  to  this  rod,  and  whose  surface  is  studded 
with  steel  teeth,  arranged  in  a  certain  order,  is  placed  near  the  plates. 
By  means  of  a  clockwork  motion,  the  cylinder  rotates,  and  the  teeth 
striking  the  steel  plate  set  them  in  vibration,  producing  a  tune,  which 
depends  on  the  arrangement  of  the  teeth  on  the  cylinder. 

If  a  given  rod  be  clamped  either  in  the  middle,  or  at  both  ends,  the 
wave  length  of  the  note  produced  by  making  it  vibrate  longitudinally,  is 
double  its  own  length,  and  if  it  be  clamped  at  one  end  only  and  made 
to  vibrate  longitudinally,  the  wave  length  of  the  sound  is  four  times  its 
own  length. 

Thus  the  former  case  is  analogous  to  an  open  pipe,  and  the  latter  to  a 
stopped  pipe  in  respect  of  the  sounds  produced. 

266.  Vibrations  of  plates. — In  order  to  make  a  plate  vibrate,  it  is 
fixed  in  the  centre  (fig.  204),  and  a  bow  rapidly  drawn  across  one  of  the 


Fig.  205. 


edges  ;  or  else  it  is  fixed  at  any  point  of  its  surface,  and  caused  to  vibrate 
by  rapidly  drawing  a  string  covered  with  resin  against  the  edges  of  a 
central  hole  (fig.  205). 

Vibrating  plates  contain  nodal  lines  (253),  which  vary  in  number  and 
position  according  to  the  form  of  the  plates,  their  elasticity,  the  mode  of 
excitation,  and  the  number  of  vibrations.  These  nodal  lines  may  be 
made  visible  by  covering  the  plate  with  fine  sand  before  it  is  made  to 
vibrate.  As  soon  as  the  vibrations  commence,  the  sand  leaves  the 
vibrating  parts,  and  accumulates  on  the  nodal  lines,  as  seen  in  figs.  204 
and  205. 

The  position  of  the  nodal  lines  may  be  determined  by  touching  the 


2i6  Acoustics.  [267- 

points  at  which  it  is  desired  to  produce  them.  Their  number  increases 
with  the  number  of  vibrations,  that  is,  as  the  note  given  by  the  plates  is 
higher.  The  nodal  lines  always  possess  great  symmetry  of  form,  and  the 
same  form  is  always  produced  on  the  same  plate  under  the  same  con- 
ditions.    They  were  discovered  by  Chladni. 

The  vibrations  of  plates  are  governed  by  the  following  law  : — /;/  plates 
of  the  same  kind  and  shape ^  and  giving  the  same  system  of  nodal  lines, 
the  ntwiber  of  vibrations  per  second  is  directly  as  the  thickftess  of  the 
plates,  and  inversely  as  their  area. 

Go7igs  and  cymbals  are  examples  of  instruments  in  which  sounds  are 
produced  by  the  vibration  of  metallic  plates.  The  glass  harmotiicon 
depends  on  the  vibrations  of  glass  plates. 

267.  Vibrations  of  xuembranes, — In  consequence  of  their  inflexibility 
membranes  cannot  vibrate  unless  they  are  stretched,  like  the  skin  of  a 
drum.  The  sound  they  give  is  more  acute  in  proportion  as  they  are 
smaller  and  more  tightly  stretched.  To  obtain  vibrating  membranes, 
Savart  fastened  gold-beater's  skin  on  wooden  frames. 


Fig.  206. 

In  the  drum,  the  skins  are  stretched  on  the  ends  of  a  cylindrical  box. 
When  one  end  is  struck,  if  communicates  its  vibrations  to  the  internal 
column  of  air,  and  the  sound  is  thus  considerably  strengthened.  The  cords 
stretched  against  the  lower  skin  strike  against  it  when  it  vibrates,  and 
produce  the  sound  characteristic  of  the  drum. 

Membranes  either  vibrate  by  direct  percussion,  as  in  the  drum,  or  they 
rhay  be  set  in  vibration  by  the  vibrations  of  the  air,  as  Savart  has  observed, 
provided  these  vibrations  are  sufficiently  intense.  Fig.  206  shows  a  mem- 
brane vibrating  under  the  influence  of  the  vibrations  in  the  air  caused  by 
a  sounding  bell.  Fine  sand  strewn  on  the  membrane  shows  the  formation 
of  nodal  lines  just  as  upon  plates. 

There  are  numerous  instances  in  which  solid  bodies  are  set  in  vibration 
by  the  vibrations  of  the  air.  The  condition  most  favourable  for  the  pro- 
duction of  this  phenomenon  is,  that  the  body  to  be  set  in  vibration  is  under 
such  conditions  that  it  can  readily  produce  vibrations  of  the  same  dura- 
tion as  those  transmitted  to  it  by  the  air.  The  following  are  some  of  these 
phenomena  : 

If  two  violoncello  strings  tuned  in  unison  are  stretched  on  the  same 


-268]  Methods  of  Studying  Vibratory  Motions.  2 1 7 

sound-box,  as  soon  as  one  of  them  is  sounded,  the  other  is  set  in  vibration. 
This  is  also  the  case  if  the  interval  of  the  strings  is  an  octave,  or  a  perfect  _^ 
fifth.     A  violin  string  may  also  be  made  to  vibrate  by  sounding  a  tuning- 
fork. 

Two  large  glasses  are  taken  of  the  same  shape,  and  as  nearly  as  pos- 
sible of  the  same  dimensions  and  weight,  and  are  brought  in  unison  b'y 
pouring  into  them  proper  quantities  of  water.  If  now  one  of  them  is 
sounded,  the  other  begins  to  vibrate,  even  if  it  is  at  some  distance,  but  if 
water  be  added  to  the  latter,  it  ceases  to  vibrate. 

Breguet  found  that  if  two  clocks,  whose  time  was  not  very  different, 
were  fixed  on  the  same  metallic  support,,  they  soon  attained  exactly  the 
same  time. 

Membranes  are  eminently  fitted  for  taking  up  the  vibrations  of  the  air, 
on  account  of  their  small  mass,  their  large  surface,  and  the  readiness  with 
which  they  subdivide.  With  a  pretty  strong  whistle,  nodal  lines  may  be 
produced  in  a  membrane  stretched  on  a  frame,  even  at  the  distant  end  of 
a  large  room. 

The  phenomenon  so  easily  produced  in  easily-moved  bodies  is  also 
found  in  large  and  less  elastic  masses ;  all  the  pillars  and  walls  of  a  church 
vibrate  more  or  less  while  the  bells  are  being  rung. 

'  chAPTER  Vl. 

GRAPHICAL   METHOD   OF  STUDYING  VIBRATORY   MOTIONS. 

268.  AK.  Ziissajous'  xnetbod  of  making-  vibrations  apparent. — The 

method  of  M.  Lissajous  exhibits  the  vibratory  motion  of  bodies  either 
directly  or  by  projection  on  a  screen.  It  has  also  the  great  advantage 
that  the  vibratory  motions  of  two  sounding  bodies  may  be  compared 
without  the  aid  of  the  ear,  so  as  to  obtain  the  exact  relation  between  them. 

This  method,  which  depends  on  the  persistence  of  visual  sensations  on 
the  retina,  consists  in  fixing  a  small  mirror  on  the  vibrating  body,  so  as 
to  vibrate  with  it,  and  impart  to  a  luminous  ray  a  vibratory  motion  similar 
to  its  own. 

M.  Lissajous  uses  tuning-forks,  and  fixes  to  one  of  the  prongs  a  small 
metallic  mirror,  in  (fig.  207),  and  to  the  other  a  counterpoise,  ;/,  which  is 
necessary  to  make  the  tuning-fork  vibrate  regularly  for  a  long  time.  At  a 
few  yards'  distance  from  the  mirror  there  is  a  lamp  surrounded  by  a 
dark  chimney,  in  which  is  a  small  hole,  giving  a  single  luminous  point. 
The  tuning-fork  being  at  rest,  the  eye  is  placed  so  that  the  luminous  point 
is  seen  at  0.  The  tuning-fork  is  then  made  to  vibrate,  and  the  image  elon- 
gates so  as  to  form  a  persistent  image,  oi,  which -diminishes  in  proportion 
as  the  amplitude  of  the  oscillation  decreases.  If,  during  the  oscillation 
of  the  mirror,  it  is  made  to  rotate  by  rotating  the  tuning-fork  on  its  axis, 
a  sinuous  line,  oix,  is  produced  instead  of  the  straight  line  oi.  These  dif- 
ferent effects  are  explained  by  the  successive  displacements  of  the  luminous 
pencil,  and  by  the  duration  of  these  luminous  impressions  on  the  eye  after 

L 


2l8 


Acoustics. 


[268- 


the  cause  has  ceased,  a  phenomenon  to  which  we  shall  revert  in  treating 
of  vision. 


'■VXAAJ,  |.- 


rwiViihi 


Fig.  207. 


N   LAMBERT 


Fig.  208, 


If,  instead  of  viewing  these  effects  directly,  they  are  projected  on  the 
screen,  the  experiment  is  arranged  as  shown  in  fig.  208,  the  pencil  reflected 


-270]         Optical  Combination  of  Vibratory  Motions,  219 

from  the  vibrating  mirror  is  reflected  a  second  time  from  a  fixed  mirror, 
rn,  which  sends  it  towards  an  achromatic  lens,  /,  placed  so  as  to  project 
the  images  on  the  screen. 

269.  Combination  of  two  vibratory  motions  in  tbe  same  direction. 

— M.  Lissajous  has  resolved  the  problem  of  the  optical  combination  of 


Fig.  209. 

two  vibratory  motions — vibrating  at  first  in  the  same  direction,  and  then 
at  right  angles  to  each  other. 

Fig.  209  represents  the  experiment  as  arranged  for  combining  two 
parallel  motions.  Two  tuning-forks  provided  with  mirrors  are  so  arranged 
that  the  light  reflected  from  one  of  them  reaches  the  other,  which  is  almost 
parallel  to  it,  and  is  then  sent  towards  a  screen  after  having  passed 
through  a  lens. 

If  now  the  first  tuning-fork  alone  vibrates,  the  image  on  the  screen  is 
the  same  as  in  figure  209  ;  but  if  they  both  vibrate,  supposing  they 
are  in  unison,  the  elongation  increases  or  diminishes  according  as  the 
simultaneous  motions  imparted  to  the  image  by  the  vibrations  of  the 
mirrors  do  or  do  not  coincide. 

If  the  tuning-forks  pass  their  position  of  equilibrium  in  the  same  time, 
and  in  the  same  direction,  the  image  attains  its  maximum  ;  and  the  image 
is  at  its  minimum  when  they  pass  at  the  same  time  but  in  opposite  direc- 
tions. Between  these  two  extreme  cases  the  amplitude  of  the  image 
varies  according  to  the  time  which  elapses  between  the  exact  instant  at 
which  the  tuning-forks  pass  through  their  position  of  rest  respectively. 
The  ratio  of  this  time  to  the  time  of  a  double  vibration  is  called  a  differ- 
ence of  phase  of  the  vibration. 

If  the  tuning-forks  are  exactly  in  unison,  the  luminous  appearance  on 
the  screen  experiences  a  gradual  diminution  of  length  in  proportion  as 
the  amplitude  of  the  vibration  diminishes  ;  but  if  the  pitch  of  one  is  very 
little  altered,  the  magnitude  of  the  image  varies  periodically,  and,  while 
the  beats  resulting  from  the  imperfect  harmony  are  distinctly  heard,  the 
eyes  see  the  concomitant  pulsations  of  the  image. 

270.  Optical  combination  of  two  vibratory  motions  at  rig-bt  ang^les 
to  eacb  other. — The  optical  combination  of  two  rectangular  vibratory 
motions  is  effected  as  shown  in  the  figure  210,  that  is,  by  means  of  two 


220 


A  cons  tics. 


[270- 


tuning-forks,  one  of  which  is  horizontal  and  the  other  vertical,  and  both 
provided  with  mirrors.  If  the  horizontal  fork  first  vibrates  alone,  a  hori- 
zontal luminous  outline  is  seen  on  the  screen,  while  the  vibration  of  the 
other  produces  a  vertical  image.      If  both  tuning-forks  vibrate  simul- 


taneously the  two  motions  combine,  and  the  reflected  pencil  describes  a 
more  or  less  complex  curve,  the  form  of  which  depends  on  the  number  of 
vibrations  of  the  two  tuning-forks  in  a  given  time.  This  curve  gives 
a  valuable  means  of  comparing  the  number  of  vibrations  of  two  sounding 
bodies. 

Fig.  211  show^s  the  luminous  image  on  the  screen  when  the  tuning-forks 
are  in  unison,  that  is,  when  the  number  of  vibrations  is  equal. 


Thefractions  below  each  curve  indicate  the  differences  of  phase  between 
them.  The  initial  form  of  the  curve  is  determined  by  the  difference  of 
phase.  The  curve  retains  exactly  the  same  form  when  the  tuning-forks 
are  in  unison,  provided  that  the  amplitudes  of  the  two  rectangular  vibra- 
tions decrease  in  the  same  ratio. 


271]         Optical  Combination  of  Vibratory  Motions. 


22* 


If  the  tuning-forks  are  not  quite  in  unison,  the  initial  difference  of  phase 
is  not  preserved,  and  the  curve  passes  through  all  its  variations. 

Fig.  212  represents  the  different  appearances  of  the  luminous  image 
when  the  difference  between  the  tuning-forks  is  an  octave  ;  that  is,  when 


Fig.   212. 

the  numbers  of  their  vibrations  are  as  i  :  2  ;  and  fig.  213  gives  the  series 
of  curves  when  the  numbers  of  the  vibrations  are  as  3  :  4. 

It  will  be  seen  that  the  curves  are  more  complex  when  the  ratios  or  the 
numbers  of  vibrations  are  less  simple.     M.  Lissajous  has  examined  these 


curves  theoretically  {Annales  de  Physique  et  de  CJiiiiiie^  1857),  and  has 
calculated  their  general  equations. 

When  these  experiments  are  made  with  a  Duboscq's  photo-electrical 
apparatus  instead  of  an  ordinary  lamp,  the  phenomena  are  remarkably 
brilliant. 

271.  Zieon  Scott's  Phonautogrrapli.— This  beautiful  apparatus  pos- 
■  sesses  the  great  advantage  of  being  able  to  register  not  only  the  vibra- 
tions produced  by  solid  bodies,  but  also  those  produced  by  wind  instru- 
ments, by  the  voice  in  singing,  and  even  by  any  noise  whatsoever,  for 
instance,''that  of  thunder,  or  the  report  of  a  cannon.     It  consists  of  an 


222 


Acoustics » 


[271- 


ellipsoidal  barrel,  AB,  about  a  foot  and  a  half  long  and  a  foot  in  its 
greatest  diameter,  made  of  plaster  of  Paris.  The  end  A  is  open,  but  the 
end  B  is  closed  by  a  solid  bottom,  to  the  middle  of  which  is  fitted  a  brass 
tube,  rt,  bent  at  an  elbow  and  terminated  by  a  ring  on  which  is  fixed  a 
flexible  membrane  which  by  means  of  a  second  ring  can  be  stretched  to 
the  required  amount.  Near  the  centre  of  the  membrane,  fixed  by  sealing- 
wax,  is  a  hog's  bristle  which  acts  as  a  style,  and,  of  course,  shares  the 


Fig.  214. 

movements  of  the  membrane.  In  order  that  the  style  might  not  be  at  a 
node,  M.  Scott  fitted  the  stretching  ring  with  a  moveable  piece,  /,  which 
he  calls  a  subdivider,  and  which,  being  made  to  touch  the  membrane  first 
at  one  point  and  then  at  another,  enables  the  experimenter  to  alter  the 
arrangements  of  the  nodal  lines  at  will.  By  means  of  the  subdivider 
the  point  is  made  to  coincide  with  a  loop,  that  is,  a  point  where  the 
vibrations  of  the  membrane  are  at  a  maximum. 

When  a  sound  is  produced  near  the  apparatus,  the  air  in  the  ellipsoid, 
the  membrane,  and  the  style  will  vibrate  in  unison  with  it,  and  it  only 
remains  to  trace  on  a  sensitive  surface  the  vibrations  of  the  style,  and  to 
fix  them.  For  this  purpose  there  is  placed  in  front  of  the  membrane  a 
copper  cylinder,  C,  turning  round  a  horizontal  axis  by  means  of  a  handle, 
in.  On  the  prolonged  axis  of  the  cylinder  a  screw  is  cut  which  works  in 
a  nut ;  consequently,  when  the  handle  is  turned,  the  cylinder  gradually 
advances  in  the  direction  of  its  axis.  Round  the  cylinder  is  wrapped  a 
sheet  of  paper,  covered  with  a  thin  layer  of  lampblack. 

The  apparatus  is  used  by  bringing  the  prepared  paper  into  contact 


-271] 


The  P hoiiaiitograph. 


223 


with  the  point  of  the  style,  and  then  setting  the  cylinder  in  motion  round 
its  axis.  So  long  as  no  sound  is  heard  the  style  remains  at  rest,  and 
merely  removes  the  lampblack  along  a  Hne  which  is  a  helix  on  the 
cylinder,  but  which  becomes  straight  when  the  paper  is  unwrapp>ed.  But 
when  a  sound  is  heard,  the  membrane  and  the  style  vibrate  in  unison, 
and  the  line  traced  out  is  no  longer  straight,  but  undulates ;  each  undula- 
tion corresponding  to  a  double  vibration  of  the  style^  Co-nsequently,  the 
figures  thus  obtained  faithfully  denote  the  number,  amplitude,  and  iso- 
chronism  of  the  vibrations. 

Fig.  215  shows  the  trace  produced  when  a  simple  note  is  sung,  and 
strengthened  by  means  of  its  upper  octave.  The  latter  note  is  represented 
by  the  curve  of  lesser  amplitude.    Fig.  216  represents  the  sound  produced 


Fig.  215. 


Fig.  216. 


Fig.  217. 


Fig.  21 


jointly  by  two  pipes  whose  notes  differ  by  an  octave.  Fig.  217  in  its 
lower  line  represents  the  rolling  sound  of  the  letter  R  when  pronounced 
with  a  ring  ;  and  fig.  218  on  its  lower  Hne  represents  the  sound  produced 
by  a  tin  plate  when  struck  with  the  finger. 

The  upper  lines  of  figs.  217  and  218  are  the  same,  and  represent  the 
perfectly  isochronous  vibrations  of  a  tuning-fork  placed  near  the  ellipsoid. 
These  lines  were  traced  by  a  fine  point  on  one  branch  of  the  fork,  which 
was  thus  found  to  make  exactly  500  vibrations  per  second.  In  conse- 
quence, each  undulation  of  the  upper  line  corresponds  to  the  s^^th  part  of 
a  second  ;  and  thus  these  lines  become  very  exact  means  of  measuring 
short  intervals  of  time.     For  example,  in  fig.  217,  each  of  the  separate 


224 


Acoustics. 


[271- 


shocks  producing  the  rolling  sound  of  the  letter  R  corresponds  to  about 
1 8  double  vibrations  of  the  tuning-fork,  and  consequently  lasts  about  -^^^ 
or  about  ^-^Xh  of  a  second. 

272.  K6nlg:'s  znanoznetric  flames. — Konig's  method  consists  in  trans- 
mitting the  movement  of  the  sonorous  waves  which  constitute  a  sound  to 
gas  flames,  which,  by  their  pulsations,  indicate  the  nature  of  the  sounds. 
For  this  purpose  a  metallic  capsule,  represented  in  section  at  A,  fig.  219 


Fig.  219. 


is  divided  into  two  compartments  by  a  thin  membrane  of  caoutchouc ;  on 
the  right  of  the  figure  is  a  gas  jet, and  below  it  a  tube  conveying  coal  gas; 
on  the  left  is  a  tubulure,  to  which  may  be  attached  a  caoutchouc  tube. 
The  other  end  of  this  may  be  placed  at  the  node  of  an  organ  pipe  (258) 
or  it  terminates  in  a  mouth-piece,  in  front  of  which  a  given  note  may  be 
sung  ;  this  is  the  arrangement  represented  in  fig.  219. 

When  the  sound  waves  enter  the  capsule  by  the  mouth-piece  and  the 
tube,  the  membrane  yielding  to  the  condensation  and  rarefaction  of  the 
waves,  the  coal  gas  in  the  compartment  on  the  right  is  alternately  con- 
tracted and  expanded,  and  hence  are  produced  alternations  in  the  length 
of  the  flame,  which  are,  however,  scarcely  perceptible  when  the  flame  is 
observed  directly.  But  to  render  them  distinct  they  are  received  on  a 
mirror  with  four  faces,  M,  which  may  be  turned  by  two  cog-wheels  and  a 
handle.  As  long  as  the  flame  burns  steadily  there  appears  in  the  mirror, 
when  turned,  a  continuous  band  of  light.  But  if  the  capsule  is  connected 
with  a  sounding  tube  yielding  the  fundamental  note,  the  image  of  the 


-272] 


Kdnigs  M alio  metric  Flames. 


22 1; 


flame  takes  the  form  represented  in  figure  220,  and  that  of  figure  221  if 
the  sound  yields  the  octave.  If  the  two  sounds  reach  the  capsule  simul- 
taneously the  flame  has  the  appearance  of  fig.  222:  in  that  case,  however 


Fig.  220. 


Fig.  221 


the  tube  leading  to  the  capsule  must  be  connected  by  a  T-pipe  with  two 
sounding  tubes,  one  giving    the  fundamental  note,  and  the  other  the 


Fig.  222. 


Fig.  223. 


octave.     If  one  gives  the  fundamental  note  and  the  other  the  third,  the. 
flame  has  the  appearance  of  figure  223. 


226 


Acoustics. 


[272- 


If  the  vowel  E  be  sung  in  front  of  the  mouth-piece  first  upon  c,  and 
then  upon  c'^  the  turning  mirror  gives  the  flames  represented  in  figs. 

Fig.  224. 


Fig.  225. 

224  and  225  ;  and  by  singing  the  vowel  O  on  the  same  notes  the  figs. 
226  and  227. 

Fig.  226. 


Fig.  227. 


■273]  Heat,  227 


CHAPTER   I. 

PRELIMINARY  IDEAS.      THERMOMETERS. 

273.  Heat.  Hypothesis  as  to  its  nature. — In  ordinary  language  the 
term  heat  is  used  not  only  to  express  a  particular  sensation,  but  also  to 
describe  that  particular  state  or  condition  of  matter  which  produces  this 
sensation.  Besides  producing  this  sensation,  heat  acts  variously  upon 
bodies ;  it  melts  ice,  boils  water,  makes  metals  red-hot,  produces  elec- 
trical currents,  decomposes  compound  bodies,  and  so  forth. 

Two  theories  as  to  the  cause  of  heat  have  been  propounded  ;  these 
are  the  theory  of  emission  and  the  theory  of  undulation. 

On  the  first  theory,  heat  is  caused  by  a  subtle  imponderable  fluid,  which 
surrounds  the  molecules  of  bodies,  and  which  can  pass  from  one  body  to 
another.  These  heat  atmospheres,  which  thus  surround  the  molecules, 
exert  a  repelling  influence  on  each  other,  in  consequence  of  which  heat 
acts  in  opposition  to  the  force  of  cohesion.  The  entrance  of  this  sub- 
stance into  our  bodies  produces  the  sensation  of  warmth,  its  egress  the 
sensation  of  cold. 

On  the  second  hypothesis  the  heat  of  a  body  is  caused  by  an  ex- 
tremely rapid  oscillating  or  vibratory  motion  of  its  molecules  ;  and  the 
hottest  bodies  are  those  in  which  the  vibrations  have  the  greatest  velocity 
and  the  greatest  amplitude.  At  any  given  time  the  whole  of  the  mole- 
cules of  a  body  possess  a  sum  of  vis  viva  which  is  the  heat  they  contain. 
To  increase  their  temperature  is  to  increase  their  vis  viva  ;  to  lower  their 
temperature  is  to  decrease  their  vis  viva.  Hence,  on  this  view,  heat  is 
not  a  substance  but  a  condition  of  7natter,  and  a  condition  which  can  be 
transferred  from  one  body  to  another.  When  a  heated  body  is  placed 
in  contact  with  a  cooler  one  the  former  cedes  more  molecular  motion 
than  it  receives  ;  but  the  loss  of  the  former  is  the  equivalent  of  the  gain 
of  the  latter. 

It  is  also  assumed  that  there  is  an  imponderable  elastic  ether,  which 
pervades  all  matter  and  infinite  space.  A  hot  body  sets  this  in  rapid 
vibration,  and  the  vibrations  of  this  ether  being  communicated  to 
material  objects  set  them  in  more  rapid  vibration,  that  is,  increase  their 


228  On  Heat,  [273- 

temperature.  Here  we  have  an  analogy  with  sound  ;  a  sounding  body 
is  in  a  state  of  vibration,  and  its  vibrations  are  transmitted  by  atmo- 
spheric air  to  the  auditory  apparatus  in  which  is  produced  the  sensation 
of  sound. 

This  hypothesis  as  to  the  nature  of  heat  is  now  admitted  by  the  most 
distinguished  physicists.  It  affords  a  better  explanation  of  all  the  pheno- 
mena of  heat  than  any  other  theory  ;  and  it  reveals  an  intimate  connec- 
tion between  heat  and  light.  It  will  be  subsequently  seen  that  by  the 
friction  of  bodies  against  each  other  an  indefinite  quantity  of  heat  is 
produced.  Experiment  has  shown  that  there  is  an  exact  equivalence 
between  the  motion  thus  destroyed  and  the  heat  produced.  These  and 
many  other  facts  are  utterly  inexplicable  on  the  assumption  that  heat  is 
a  substance,  and  not  a  form  of  motion. 

In  what  follows,  however,  the  phenomena  of  heat  will  be  considered, 
as  far  as  possible,  independently  of  either  hypothesis  ;  but  we  shall  sub- 
sequently return  to  the  reasons  for  the  adoption  of  the  latter  hypothesis. 

Assuming  that  the  heat  of  bodies  is  due  to  the  motion  of  their  particles, 
we  may  admit  the  following  explanation  as  to  the  nature  of  this  motion 
in  the  various  forms  of  matter. 

In  solids  the  molecules  have  a  kind  of  vibratory  motion  about  certain 
fixed  positions.  This  motion  is  probably  very  complex  ;  the  constituents 
of  the  molecule  may  oscillate  about  each  other,  besides  the  oscillation  of 
the  molecule  as  a  whole,  and  this  latter  again  may  be  a  to-and-fro  motion, 
or  it  may  be  a  rotatory  motion  about  the  centre. 

In  the  liquid  state  the  molecules  have  no  fixed  positions.  They  can 
rotate  about  their  centres  of  gravity,  and  the  centre  of  gravity  itself  may 
move.  But  the  repellent  action  of  the  motion,  compared  with  the  mutual 
attraction  of  the  molecules  is  not  sufficient  to  separate  the  molecules 
from  each  other.  A  molecule  no  longer  adheres  to  particular  adjacent 
ones  ;  but  it  does  not  spontaneously  leave  them  except  to  come  into  the 
same  relation  to  fresh  ones  as  to  its  previous  adjacent  ones.  Thus  in  a 
liquid  there  is  a  vibratory,  rotatory,  and  progressive  motion. 

In  \)ciQ gaseous  state  the  molecules  are  entirely  without  the  sphere  of 
their  mutual  attraction.  They  fly  forward  in  straight  lines  according  to 
the  ordinary  laws  of  motion,  until  they  impinge  against  other  molecules, 
or  against  a  fixed  envelope  which  they  cannot  penetrate,  and  then  return 
in  an  opposite  direction,  with,  in  the  main,  their  original  velocity.  The 
perfection  of  the  gaseous  state  implies  that  the  space  actually  occupied 
by  the  molecules  of  the  gas  be  infinitely  small  compared  with  the  entire 
volume  of  the  gas  ;  that  the  time  occupied  by  the  impact  of  a  molecule 
either  against  another  molecule  or  against  the  sides  of  the  vessel  ht  in- 
finitely small  in  comparison  with  the  interval  between  any  two  impacts  ; 
and  that  the  influence  of  molecular  attraction  be  infinitely  small.  When 
these  conditions  are  not  fulfilled  the  gas  partakes  more  or  less  of  the 
nature  of  a  liquid,  and  exhibits  certain  deviations  from  Boyle's  law.  This 
is  the  case  with  all  gases  ;  to  a  very  slight  extent  with  uncondensible 
gases,  but  to  a  far  greater  extent  with  vapours  and  condensible  gases, 
especially  near  their  points  of  liquefaction. 


-275] 


General  Effects  of  Heat. 


229 


274.  General  effects  of  heat. — The  general  effects  of  heat  upon  bodies 
may  be  classed  under  three  heads.  One  portion  is  expended  in  raising, 
the  temperature  of  the  body,  that  is,  in  increasing  the  vis  viva  of  its 
molecules.  In  the  second  place,  the  molecules  of  bodies  have  a  certain 
attraction  for  each  other,  owing  to  which  is  due  their  relative  positions  ; 
hence  a  second  portion  of  heat  is  consumed  in  augmenting  the  ampli- 
tude of  the  oscillations,  by  which  an  increase  of  volume  is  produced,  or 
in  completely  altering  the  relative  positions  of  the  molecules  by  which 
a  change  of  state  is  effected.  These  two  effects  are  classed  as  internal 
"duork.  Thirdly,  since  bodies  are  surrounded  by  atmospheric  air  which 
exerts  a  certain  pressure  on  their  surface,  this  has  to  be  overcome  or 
lifted  through  a  certain  distance.  The  heat  or  work  required  for  this  is 
called  the  external  work. 

If  O  units  of  heat  are  imparted  to  a  body,  and  if  A  be  the  quantity  of 
heat  which  is  equivalent  to  the  unit  of  work  ;  then  if  W  is  the  amount 
of  heat  which  serves  to  increase  the  temperature,  I  that  required  to  alter 
the  position  of  the  molecules,  and  if  L  be  the  equivalent  of  the  external 
work,  then 

Q  =  A(W  +  I  +  L). 

275.  Expansion. — All  bodies  expand  by  the  action  of  heat.  As  a 
general  rule,  gases  are  the  most  expansible,  then  liquids,  and  lastly 
solids. 

In  solids  which  have  definite  figures,  we  can  either  consider  the  expan- 
sion in  one  dimension,  or  the  linear  expansion  ;  in  two  dimensions,  the 
supe7'ficial  expansion  ;  or  in  three  dimensions,  the  (;;//^zV<2/ expansion  or  the 
expansion  of  volume,  although  one  of  these  never  takes  place  without  the 
other.  As  Hquids  and  gases  have  no  definite  figures,  the  expansions  of 
volume  have  in  them  alone  to  be  considered. 

To  show  the  linear  expansion  of  solids,  the  apparatus  represented  in 
fig.  228  may  be  used.     A  metal  rod,  A,  is  fixed  at  one  end  by  a  screw 


Fig.  228. 

B,  while  the  other  end  presses  against  the  short  arm  ot  an  index,  K 
which  moves  on  a  scale.  Below  the  rod  there  is  a  sort  of  cylindrical 
lamp  in  which  alcohol  is  burned.  The  needle  K  is  at  first  at  the  zero 
point,  but  as  the  rod  becomes  heated,  it  expands,  and  moves  the  needle 
alonof  the  scale. 


230 


On  Heat. 


[275- 


The  cubical  expansion  of  solids  is  shown  by  a  Gravesande^s  ring.  It 
consists  of  a  brass  ball  a  (fig.  229),  which  at  the  ordinary  temperature 
passes  freely  through  a  ring,  ;«,  almost  of  the  same  diameter.  But  when 
the  ball  has  been  heated,  it  expands  and  no  longer  passes  through  the 
ring. 

In  order  to  show  the  expansion  of  liquids,  a  large  glass  bulb  provided 
with  a  capillary  stem  is  used  (fig.  230).     If  the  bulb  and  a  part  of  the 


Fig.  229. 


Fig.  230.  Fig.  231 


Stem  contain  some  coloured  liquid,  the  liquid  rapidly  rises  in  the  stem 
when  heat  is  applied,  and  the  expansion  thus  observed  in  far  greater 
than  in  the  case  of  solids. 

The  same  apparatus  may  be  used  for  showing  the  expansion  of  gases. 
Being  filled  with  air,  a  small  thread  of  mercury  is  introduced  into  the 
capillary  tube  to  serve  as  index  (fig.  231).  When  the  globe  is  heated  in 
the  slightest  degree,  even  by  approaching  the  hand,  the  expansion  is  so 
great  that  the  index  is  driven  to  the  end  of  the  tube,  and  is  finally 
expelled.  Hence,  even  for  a  very  small  degree  of  heat,  gases  are  highly 
expansible. 

In  these  different  experiments  the  bodies  contract  on  cooling,  and 
when  they  have  attained  their  former  temperature  they  resume  their 
original  volume.  Certain  metals,  however,  especially  zinc,  form  an  ex- 
ception to  this  rule,  and  it  appears  to  be  also  the  case  with  some  kinds  of 
glass. 

MEASUREMENT  OF  TEMPERATURE.      THERMOMETRY. 

276.  Temperature. — The  temper  attire  or  hotness  of  a  body,  indepen- 
dently of  any  hypothesis  as  to  the  nature  of  heat,  may  be  defined  as  being 


-278]  Thermometers.  231 

the  greater  or  less  extent  to  which  it  tends  to  impart  sensible  heat  to  othen 
bodies.  The  temperature  of  a  body  must  not  be  confounded  with  thfr 
quantity  of  heat  it  possesses  ;  a  body  may  have  a  high  temperature  and 
yet  have  a  very  small  quantity  of  heat,  and  conversely  a  low  temperature 
and  yet  possess  a  large  amount  of  heat.  If  a  cup  of  water  be  taken  from 
a  bucketful,  both  will  indicate  the  same  temperature,  yet  the  quantities 
they  possess  will  be  different.  This  subject  of  the  quantity  of  heat  will 
be  afterwards  more  fully  explained  in  the  chapter  on  Specific  Heat. 

277.  TYiemioTaeteT^.—  Therfnometers  are  instruments  for  measuring 
temperatures.  Owing  to  the  imperfections  of  our  senses  we  are  unable 
to  measure  temperatures  by  the  sensation  of  heat  or  cold  which  they 
produce  in  us,  and  for  this  purpose  recourse  must  be  had  to  the  physical 
action  of  heat  on ,  bodies.  These  actions  are  of  various  kinds,  but  the 
expansion  of  bodies  has  been  selected  as  the  easiest  to  observe.  But 
heat  also  produces  electrical  phenomena  in  bodies  ;  and  on  these  the 
most  delicate  methods  of  observing  temperatures  have  been  based,  as  we 
shall  see  in  a  subsequent  chapter. 

Liquids  are  best  suited  for  the  construction  of  thermometers — the  ex- 
pansion of  solids  being  too  small,  and  that  of  gases  too  great.  Mercury 
and  alcohol  are  the  only  liquids  used — the  former  because  it  only  boils  at 
a  very  high  temperature,  and  the  latter  because  it  does  not  solidify  at  the 
greatest  known  cold. 

The  mercurial  thermometer  is  the  most  extensively  used.  It  consists 
of  a  capillary  glass  tube,  at  the  end  of  which  is  blown  the  bulb,  a  cylin- 
drical or  spherical  reservoir.  Both  the  bulb  and  a  part  of  the  stem  are 
filled  with  mercury,  and  the  expansion  is  measured  by  a  scale  graduated 
either  on. the  stem  itself,  or  on  a  frame  to  which  it  is  attached. 

Besides  the  manufacture  of  the  bulb,  the  construction  of  the  thermo- 
meter comprises  three  operations  :  the  calibration  of  the  tube,  or  its 
division  into  parts  of  equal  capacity,  the  introduction  of  the  mercury  into 
the  reservoir,  and  the  graduation. 

278.  Division  of  the  tube  into  parts  of  equal  capacity. — As  the 
indications  of  the  thermometer  are  only  correct  when  the  divisions  of  the 
scale  correspond  to  equal  expansions  of  the  mercury  in  the  reservoir,  the 
scale  must  be  graduated  so  as  to  indicate  parts  of  equal  capacity  in  the 
tube.  If  the  tube  were  quite  cylindrical,  and  of  the  same  diameter 
throughout,  it  would  only  be  necessary  to  divide  it  into  equal  lengths. 
But  as  the  diameter  of  glass  tubes  is  usually  greater  at  one  end  than 
another,  parts  of  equal  capacity  in  the  tube  are  represented  by  unequal 
lengths  of  the  scale. 

In  order,  therefore,  to  select  a  tube  of  uniform  calibre,  a  thread  of 
mercury  about  an  inch  long  is  introduced  into  the  capillary  tube,  and 
moved  in  different  positions  in  the  tube,  care  being  taken  to  keep  it  at 
the  same  temperature.  If  the  thread  is  of  the  same  length  in  every 
part  of  the  tube,  it  shows  that  the  capacity  is  everywhere  the  same  ;  but 
if  the  thread  occupies  different  lengths  the  tube  is  rejected,  and  another 
one  sought. 


232 


On  Heat. 


[279- 


279.  Filling:  tlie  thermometer.— In  order  to  fill  the  thermometer  with 
mercury,  a  small  funnel,  C  (fig.  232),  is  blown  on  at  the  top,  and  is  filled, 
with  mercury  ;  the  tube  is  then  slightly  inclined, 
and  the  air  in  the  bulb  expanded  by  heating  it 
with  a  spirit  lamp.  The  expanded  air  partially 
escapes  by  the  funrtel,  and  on  cooling,  the  air 
which  remains  contracts,  and  a  portion  of  the 
mercury  passes  into  the  bulb  D.  The  bulb  is 
then  again  warmed,  and  allowed  to  cool,  a  fresh 
quantity  of  mercury  enters,  and  so  on,  until  the 
bulb  and  part  of  the  tube  are  full  of  mercury. 
The  mercury  is  then  heated  to  boihng ;  the 
mercurial  vapours  in  escaping  carry  with  them 
the  air  and  moisture  which  remain  in  the  tube. 
The  tube,  being  full  of  the  expanded  mercury 
and  of  mercurial  vapour,  is  hermetically  sealed 
at  one  end.  When  the  thermometer  is  cold,  the 
mercury  ought  to  fill  the  bulb  and  a  portion  of 
the  stem. 

280.  Graduation  of  the  thermometer. — The 
thermometer  being  filled,  it  requires  to  be  gra- 
duated, that  is,  to  be  provided  with  a  scale  to 
which  variations  of  temperature  can  be  referred. 
And,  first  of  all,  two  points  must  be  fixed  which 
represent  identical  temperatures  and  which  can 
always  be  easily  produced. 

Experiment  has  shown  that  ice  always  melts 
at  the  same  point  whatever  be  the  degree  of  heat,  and  that  distilled  water 
under  the  same  pressure,  and  in  a  vessel  of  the  same  kind,  always  boils 
at  the  same  temperature.  Consequently,  for  the  first  fixed  point,  or  zero, 
the  temperature  of  melting  ice  has  been  taken  ;  and  for  a  second  fixed 
point,  the  temperature  of  boiling  water  in  a  metallic  vessel  under  the 
normal  atmospheric  pressure  of  760  millimetres. 

This  interval  of  temperature,  that  is,  the  range  from  zero  to  the  boiling 
point,  is  taken  as  the  unit  for  comparing  temperatures  ;  just  as  a  certain 
length,  a  foot  or  a  metre  for  instance,  is  used  as  a  basis  for  comparing 
lengths. 

281.  Determination  of  the  fixed  points. — To  obtain  zero,  snow  or 
pounded  ice  is  placed  in  a  vessel,  in  the  bottom  of  which  is  an  aperture 
by  which  water  escapes  (fig.  233).  The  bulb  and  a  part  of  the  stem 
of  the  thermometer  are  immersed  in  this  for  about  a  quarter  of  an  hour, 
and  a  mark  made  at  the  level  of  the  mercury  which  represents  zero. 

The  second  fixed  point  is  determined  by  means  of  the  apparatus  re- 
presented in  the  figures  234  and  235,  of  which  235  represents  a  vertical 
section.  In  both,  the  same  letters  designate  the  same  parts.  The  whole 
of  the  apparatus  is  of  copper.  A  central  tube,  A,  open  at  both  ends,  is 
fixed  on  a  cylindrical  vessel  containing  water  ;  a  second  tube,  B,  con- 
centric with  the  first,  and  surrounding  it,  is  fixed  on  the  same  vessel,  M. 


Fig.  235 


-281] 


Graduation  of  the  Thermometer. 


233 


In  this  second  cylinder,  which  is  closed  at  both  ends,  there  are  three 

tubulures,  a^  E,  D. .  A  cork,  in  which  is  the  thermometer  /,  fits  in  a. 

To    E    a    glass   tube,   containing    mercury,  is 

attached,   which    serves   as   a    manometer  for 

measuring  the   pressure  of  the  vapour  in  the 

apparatus.     D  is  an  escape  tube  for  the  vapotir 

and  condensed  water. 

The  apparatus  is  placed  on  a  furnace  and 
heated  till  the  water  boils ;  the  vapour  produced 
in  M  rises  in  the  tube  A,  and  passing  through 
the  two  tubes  in  the  direction  of  the  arrows, 
escapes  by  the  tubulure  D.  The  thermometer  / 
being  thus  surrounded  with  vapour,  the  mercury 
expands  and  when  it  has  become  stationary,  the 
point  at  which  it  stops  is  marked.  This  is  the 
point  sought  for.  The  object  of  the  second 
case,  B,  is  to  avoid  the  cooling  of  the  central 
tubulure  by  its  contact  with  the  air. 

The  determination  of  the  point  100  (see  next 
article)  would  seem  to  require  that  the  height  ot 
the  barometer  during  the   experiment    should 
be  760  millimetres,  for  when  the  barometric  height  is  greater  or  less  than 
this  quantity,  water  boils  either  above  or  below  100  degrees.     But  the 


Fig.  233. 


\ 


Fig.  234.  Fig.  235 

point  100  may  always  be  exactly  obtained,  by  making  a  correction  in- 
troduced by  M.  Biot.  He  found  that,  for  every  27  millimetres'  difference 
in  height  of  the  barometer,  there  was  a  difference  in  the  boiling  point  of 
I  degree.     If,  for  example,  the  height  of  the  barometer  is  778— that  is 


234 


On  Heat. 


[281- 


I 


1 8  millimetres,  or  two-thirds  of  27,  above  760— water  would  boil  at  100 
degrees  and  two-thirds.  Consequently,  loof  would  have  to  be  marked 
aj  the  point  at  which  the  mercury  stops, 

Gay-Lussac  observed  that  water  boils  at  a  somewhat  higher  tem- 
perature in  a  glass  than  in  a  metal  vessel :  and  as  the  boiling  point  is 
raised  by  any  salts  which  are  dissolved,  it  has  been  assumed  that  it  was 
necessary  to  use  a  metal  vessel  and  distilled  water  in  fixing  the  boiling 
point.  M.  Rudberg  has,  however,  shown  that  these  latter  precautions  are 
superfluous.  The  nature  of  the  vessel,  and  salts  dissolved  in  ordinary 
water,  influence  the  temperature  of  boiling  water,  but  not  that  of  the 
vapour  which  is  formed.  That  is  to  say,  that  if  the  temperature  of  boil- 
ing water  from  any  of  the  above  causes  is  higher  than  100  degrees,  the 
temperature  of  the  vapour  does  not  exceed  100,  provided  the  pressure  is 
not  more  than  760  millimetres.  Consequently,  the  higher  point  may  be 
(g)  determined  in  a  vessel  of  any  material,  provided  the  thermo- 
meter is  quite  surrounded  by  vapour,  and  does  not  dip  in  the 
water. 

Even  with  distilled  water,  the  bulb  of  the  thermometer  must 
not  dip  in  the  liquid  ;  for  it  is  only  the  upper  layer  that  really 
has  the  temperature  of  100  degrees,  since  the  temperature  in- 
creases from  layer  to  layer  towards  the  bottom  in  consequence 
of  the  increased  pressure. 

282.  Construction  of  tbe  scale. — Just  as  the  foot-rule  which 
is  adopted  as  the  unit  of  comparison  for  length  is  divided  into 
a  number  of  equal  divisions  called  inches  for  the  purpose  of 
having  a  smaller  unit  of  comparison,  so  likewise  the  unit  of 
comparison  of  temperatures,  the  range  from  zero  to  the  boiling 
point,  must  be  divided  into  a  number  of  parts  of  equal  capacity 
called  degrees.  There  are  three  modes  in  which  this  is  done. 
On  the  Continent,  and  more  especially  in  France,  this  space  is 
divided  into  100  parts,  and  this  division  is  called  the  Cetitigrade 
or  Celsius  scale;  the  latter  being  the  name  of  the  inventor. 
The  Centigrade  thermometer  is  almost  exclusively  adopted  in 
foreign  scientific  works,  and  as  its  use  is  gradually  extending 
in  this  country,  it  has  been  and  will  be  adopted  in  this  book. 
The  degrees  are  designated  by  a  small  cipher  placed  a  little 
above  on  the  right  of  the  number  which  marks  the  temperature, 
and  to  indicate  temperatures  below  zero  the  mihus  sign  is 
placed  before  them.  Thus,  —15°  signifies  15  degrees  below 
zero. 

In  accurate  thermometers  the  scale  is  marked  on  the  stem 
itself  (fig.  235).  It  cannot  be  displaced,  and  its  length  remains 
fixed,  as  glass  has  very  little  expansibihty.  The  graduation  is 
effected  by  covering  the  stem  with  a  thin  layer  of  wax,  and  then 
marking  the  divisions  of  the  scale,  as  well  as  the  corresponding 
numbers,  with  a  steel  point.  The  thermometer  is  then  exposed  for  about 
ten  minutes  to  the  vapours  of  hydrofluoric  acid,  which  attacks  the  glass 
where  the  wax  has  been  removed.  The  rest  of  the  wax  is  then  removed, 
and  the  stem  is  found  to  be  permanently  etched. 


Fig.  236. 


-282]  Construction  of  the  Therino7neter  Scale.  235 

Besides  the  Centigrade  scale  two  others  are  frequently  used — Fahren- 
heit's scale  and  Reaionur^s  scale. 

In  Reaumur's  scale  the  fixed  points  are  the  same  as  on  the  Centi- 
grade scale,  but  the  distance  between  them  is  divided  into  80  degrees, 
instead  of  into  100,  That  is  to  say,  80  degrees  Reaumur  are  equal  to 
100  degrees  Centigrade  ;  one  degree  Reaumur  is  equal  to  ^^^  or  |  of  a 
degree  Centigrade,  and  one  degree  Centigrade  equals  y^o^o  *^^  I  degrees 
Reaumur.  Consequently,  to  convert  any  number  of  Reaumur's  degrees 
into  Centigrade  degrees  (20  for  example),  it  is  merely  necessary  to  multiply 
them  by  f  (which  gives  25).  Similarly,  Centigrade  degrees  are  converted 
into  Rdaumur  by  multiplying  them  by  f . 

The  thermometric  scale  invented  by  Fahrenheit  in  17 14  is  still  much 
used  in  England,  and  also  in  Holland  and  North  America.  The  higher 
fixed  point  is  like  that  of  the  other  scales,  the  temperature  of  boiling 
water,  but  the  null  point  or  zero  is  the  temperature  obtained  by  mixing 
equal  weights  of  sal-ammoniac  and  snow,  and  the  interval  between  the 
two  points  is  divided  into  212  degrees.  The  zero  was  selected  because 
the  temperature  was  the  lowest  then  known,  and  was  thought  to  repre- 
sent absolute  cold.  When  Fahrenheit's  thermometer  is  placed  in  melting 
ice  it  stands  at  32  degrees,  and,  therefore,  100  degrees  on  the  Centigrade 
scale  are  equal  to  1 80  degrees  on  the  Fahrenheit  scale,  and  thus  i  degree 
Centigrade  is  equal  to  |  of  a  degree  Fahrenheit,  and  inversely  i  degree 
Fahrenheit  is  equal  to  |  of  a  degree  Centigrade. 

If  it  be  required  to  convert  a  certain  number  of  Fahrenheit  degrees  (95 
for  example)  into  Centigrade  degrees,  the  number  32  must  first  be  sub- 
tracted, in  order  that  the  degrees  may  count  from  the  same  part  of  the 
scale.  The  remainder  in  the  example  is  thus  63,  and  as  i  degree  Fah- 
renheit is  equal  to  |  of  a  degree  Centigrade,  63  degrees  are  equal  to 
63  + 1  or  35  degrees  Centigrade. 

If  F  be  the  given  temperature  in  Fahrenheit  degrees  and  C  the  corre- 
sponding temperature  in  Centigrade  degrees,  the  former  may  be  converted 
into  the  latter  by  means  of  the  formula 

(F.  =  32)f  =  C, 

and  conversely.  Centigrade  degrees  may  be  converted  into  Fahrenheit  by 
means  of  the  formula 

fC.  +  32  =  F. 

These  formulas  are  applicable  to  all  temperatures  of  the  two  scales,  pro- 
vided the  signs  are  taken  into  account.  Thus,  to  convert  the  temperature 
of  5  degrees  Fahrenheit  into  Centigrade  degrees,  we  have 

(5-32)1  =  :::^^^  = -15  c. 

In  like  manner  we  have,  for  converting  Reaumur  into  Fahrenheit 
degrees,  the  formula 

|R.  +  33  =  F, 

and   conversely,  for  changing  Fahrenheit    into  Rdaumur    degrees,  the 
formula 

CF.-32)|  =  R. 


236  On  Heat  [283- 

283.  Displacement  of  zero. — Thermometers,  even  when  constructed 
with  the  greatest  care,  are  subject  to  a  source  of  error  which  must  be 
taken  into  account  :  this  is,  that  in  course  of  time  the  zero  tends  to  rise, 
the  displacement  sometimes  extending  to  as  much  as  2  degrees  ;  so  that 
when  the  thermometer  is  immersed  in  melting  ice  it  no  longer  sinks  to  zero. 

This  is  generally  attributed  to  a  diminution  of  the  volume  of  the 
reservoir  and  also  of  the  stem,  occasioned  by  the  pressure  of  the 
atmosphere.  It  is  usual  with  very  delicate  thermometers  to  fill  them 
two  or  three  years  before  they  are  graduated. 

Besides  this  slow  displacement,  there  are  often  variations  in  the 
position  of  the  zero,  when  the  thermometer  has  been  exposed  to  high 
temperatures,  caused  by  the  fact  that  the  bulb  and  stem  do  not  contract 
on  cooling  to  their  original  volume  (275),  and  hence  it  is  necessary  to 
verify  the  position  of  zero  when  a  thermometer  is  used  for  delicate 
determinations. 

Regnault  has  found  that  some  mercurial  thermometers,  which  agree 
at  0°  and  at  100°,  differ  between  these  points,  and  that  these  differences 
frequently  amount  to  several  degrees.  Regnault  thinks  that  this  is  due 
to  the  unequal  expansion  of  different  kinds  of  glass. 

284.  limits  to  tbe  employment  of  mercurial  thermometers. — Of 
all  thermometers  in  which  liquids  are  used,  the  one  with  mercury  is  the 
most  useful,  because  this  liquid  expands  most  regularly,  and  is  easily 
obtained  pure,  and  because  its  expansion  between  —36°  and  100°  is 
7'cgular,  that  is  proportional  to  the  degree  of  heat.  It  also  has  the 
advantage  of  having  a  very  low  specific  heat.  But  for  temperatures 
below  —36°  C.  the  alcohol  thermometer  must  be  used,  for  mercury 
solidifies  at  —40°  C.  Above  100  degrees  the  coefficient  of  expansion 
increases  and  the  indications  of  the  mercurial  thermometers  are  only 
approximate,  the  error  arising  sometimes  to  several  degrees.  Mercurial 
thermometers  also  cannot  be  used  for  temperatures  above  350°,  for  this 
is  the  boiling  point  of  mercury. 

285.  Alcohol  thermometer. — The  alcohol  thermometer  differs  from 
the  mercurial  thermometer  in  being  filled  with  coloured  alcohol.  But  as 
the  expansion  of  liquids  is  less  regular  in  proportion  as  they  are  near  the 
boiling  point,  alcohol  which  boils  at  78°  C,  expands  very  irregularly. 
tTence,  alcohol  thermometers  are  usually  graduated  by  placing  them 
in  baths  at  different  temperatures  together  with  a  standard  mercurial 
thermometer,  and  marking  on  the  alcohol  thermometer  the  temperature 
indicated  by  the  mercurial  thermometer.  In  this  manner  the  alcohol 
thermometer  is  comparable  with  the  mercurial  one  ;  that  is  to  say,  it 
indicates  the  same  temperatures  under  the  same  conditions.  The  alcohol 
thermometer  is  especially  used  for  low  temperatures,  for  it  does  not 
solidify  at  the  greatest  known  cold. 

286.  Conditions  of  the  delicacy  of  a  thermometer. — A  thermometer 
may  be  delicate  in  two  ways: — i,  When  it  indicates  very  small  changes 
of  temperature.  2.  When  it  quickly  assumes  the  temperature  of  the 
surrounding  medium. 

The  first  object  is  attained  by  having  a  very  narrow  capillary  tube  and 


-288] 


Differential  Thermometer. 


237 


a  very  large  bulb  ;  the  expansion  of  the  mercury  on  the  stem  is  then 
limited  to  a  small  number  of  degrees,  the  10  to  20  or  20  to  30  for  instance 
so  that  each  degree  occupies  a  great  length  on  the  stem,  and  can  be  sub- 
divided into  very  small  fractions.  The  second  kind  of  delicacy  is  obtained 
by  making  the  bulb  very  small,  for  then  it  rapidly  assumes  the  tempera- 
ture of  the  liquid  in  which  it  is  placed. 

A  good  mercurial  thermometer  should  answer  to  the  following  tests  : 
When  its  bulb  and  stem,  to  the  top  of  the  column  of  mercury,  are  im- 
mersed in  melting  ice,  the  top  of  the  mercury  should  exactly  indicate  o°C. ; 
and  when  suspended  with  its  bulb  and  scale  immersed  in  the  steam  of 
water  boiling  in  a  metal  vessel  (as  in  fig.  234),  the  barometer  standing  at 
760  mm.,  the  mercury  should  be  stationary  at  100°  C.  When  the  instru- 
ment is  inverted,  the  mercury  should  fill  the  tube,  and  fall  with  a  metallic 
click,  thus  showing  the  complete  exclusion  of  air.  The  value  of  the  de- 
grees should  be  uniform  :  to  ascertain  this,  a  little  cylinder  of  mercury 
may  be  detached  from  the  column  by  a  slight  jerk,  and  on  inclining  the 
tube  it  may  be  made  to  pass  from  one  portion  of  the  bore  to  another.  If 
the  scale  be  properly  graduated,  the  column  will  occupy  an  equal  number 
of  degrees  in  all  parts  of  the  tube. 

287.  Differential  thermometer.— Sir  John  Leslie  constructed  a 
thermometer  for  showing  the  difference  of  temperature  of  two  neigh- 
bouring places,  from  which  it  has  received  the  name  differetitial  ther- 
mometer. 

A  modified  form  of  it  is  that  devised  by  Matthiesson  (fig.  237),  which 
has  the  advantage  of  being  available  for  indicating  the  temperature  of 
liquids.  It  consists  of  a  bent  glass 
tube,  each  end  i  of  which  is  bent 
twice,  and  terminates  in  a  bulb  ; 
the  bulbs  being  pendant  can  be 
readily  immersed  in  a  liquid.  The 
bend  contains  some  coloured  liquid, 
and  in  atube which  connects  the  two 
limbs  is  a  stopcock,  by  which  the 
liquid  in  each  hmb  is  easily  brought 
to  the  same  level.  The  whole  is 
supported  by  a  frame. 

When  one  of  the  bulbs  is  at  a 
higher  temperature  than  the  other, 
the  liquid  in  the  stem  is  depressed, 
and  rises  in  the  other  stem. 

The  instrument  is  now  only 
used  as  a  thermoscope^  that  is  to 
indicate  a  difference  of  temperature 
between  the  two  bulbs  and  not  to 
measure  its  amount. 

288.  Sregruet's  metallic  ther- 
mometer. —  Breguet  invented  a 
thermometer  founded  on  the  unequal  expansion  of  metals,  and  remark- 


238 


On  Heat. 


[288- 


able  for  its  delicacy.  It  consists  of  three  strips  of  platinum,  gold,  and 
silver,  which  are  passed  through  a  rolling  mill  so  as  to  form  a  very  thin 
metallic  ribbon.  This  is  then  coiled  in  a  spiral  form,  as  seen  in  fig.  238, 
and  one  end  being  fixed  to  a  support,  a  light  needle  is  fixed  to  the  other, 
v/hich  is  free  to  move  round  a  graduated  scale. 

Silver,  which  is  the  most  expansible  of  the  metals,  forms  the  internal 
face  of  the  spiral,  and  platinum  the  external.  When  the  temperature 
rises,  the  silver  expands  more  than  gold  or  platinum,  the  spiral  un- 
winds itself,  and  the  needle  moves  from  left  to  right  of  the  above  figure. 

The  contrary  effect  is  produced  when 
the  temperature  sinks.  The  gold  is 
placed  between  the  other  two  metals, 
because  its  expansibility  is  interme- 
diate between  that  of  the  silver  and 
the  platinum.  Were  these  two  metals 
employed  alone,  their  rapid  unequal 
expansion  might  cause  a  fracture. 
Breguet's  thermometer  is  graduated  in 
Centigrade  degrees,  by  comparing  it 
with  a  standard  mercurial  thermo- 
meter. 

289.  Rutberford's  xnaxixuum  and 
xuinimuzu  thermometers.— It  is  ne- 
cessary, in  meteorological  observations, 
to  know  the  highest  temperature  of 
the  day  and  the  lowest  temperature 
of  the  night.  Ordinary  thermometers 
could  only  give  these  indications  by  a  continuous  observation,  which 
would  be  impracticable.  Several  instruments  have  accordingly  been  in- 
vented for  this  purpose,  the  simplest  of  which  is  Rutherford's.  On  a 
rectangular  piece  of  plate-glass  (fig.   239)  two  thermometers  are  fixed, 


Pig.  238. 


^     Fig.  239. 

whose  stems  are  bent  horizontally.  The  one.  A,  is  a  mercurial,  and  the 
other,  B,  an  alcohol  thermometer.  In  A  there  is  a  small  piece  of  iron 
wire,  A,  moving  freely  in  the  tube,  which  serves  as  an  index.  The  ther- 
mometer being  placed  horizontally,  when  the  temperature  rises  the  mer- 


291] 


Different  Remarkable  Temperatures. 


239 


cury  pushes  the  index  before  it.  But  as  soon  as  the  mercury  contracts 
the  index  remains  in  that  part  of  the  tube  to  which  it  has  been  moved, 
for  there  is  no  adhesion  between  the  iron  and  the  mercury.  In  this  way 
the  index  registers  the  highest  temperature  which  has  been  attained  ;  in 
the  figure  this  is  31°.  In  the  minimum  thermometer  there  is  a  small 
hollow  glass  tube  which  serves  as  index.  When  it  is  at  the  end  of  the 
column  of  liquid,  and  the  temperature  falls,  the  column  contracts,  and 
carries  the  index  with  it,  in  consequence  of  adhesion,  until  it  has  reached 
the  greatest  contraction.  When  the  temperature  rises  the  alcohol  ex- 
pands, and  passing  between  the  sides  of  the  tube  and  the  index,  does  not 
displace  B.  The  position  of  the  index  gives  therefore  the  lowest  temper- 
ature which  has  been  reached  :  in  the  figure  this  was  9^  degrees  below 
zero. 

290.  Pyrometers. — The  name  pyrometers  is  given  to  instruments  for 
measuring  temperatures  so  high  that  mercurial  thermometers  could  not 
be  used.  The  older  contrivances  for  this  purpose,  Wedgewood's,  DanielFs 
(which  in  principle  resembled  the  apparatus  in  fig.  228),  Brongniart's,  etc., 
are  gone  entirely  out  of  use.  None  of  them  gives  an  exact  measure  of 
temperature.  The  arrangements  now  used  for  the  purpose  are  either 
based  on  the  expansion  of  gases  and  vapours,  or  on  the  electrical  proper- 
ties of  bodies,  and  will  be  subsequently  described. 

291.  Different  remarkable  temperatures. — The  following  table  gives 
some  of  the  most  remarkable  points  of  temperature.  It  may  be  observed, 
that  it  is  easier  to  produce  very  high  temperatures  than  very  low  de- 
grees of  cold. 

Greatest  artificial  cold  produced  by  a  bath  of  bisulphide  of 

carbon  and  liquid  nitrous  acid —  140°  C. 

Greatest  cold  produced  by  ether  and  liquid  carbonic  acid  —  no 


Greatest  natural  cold  recorded 

Mercury  freezes 

Mixture  of  snow  and  salt  . 

Ice  melts   .... 

Greatest  density  of  water  . 

Mean  temperature  of  London 

Blood  heat 

Water  boils 

Mercury  boils    . 

Red  heat  (just  visible)         (Daniell) 

Silver  melts       .         .         .        „ 

Cast  iron  melts  .         .        „ 

Highest  heat  of  wind  furnace  „ 


in  Arctic  expeditions 


-  49 

-  39'4 

-  20 

o 
+  4 
9'9 
36-6 
100 

350 

526 

1000 

1530 
1800 


240 


On  Heat. 


[292- 


CHAPTER    II. 

EXPANSION   OF   SOLIDS. 

292.  Xtinear  expansion  and  cubical  expansion.  Coefficients  of 
expansion. — It  has  been  already  explained  that  in  solid  bodies  the  ex- 
pansion may  be  according  to  three  dimensions — linear,  superficial,  and 
cubical. 

The  coefficient  of  litiear  expansion  is  the  elongation  of  the  unit  of  length 
of  a  body  when  its  temperature  rises  from  zero  to  one  degree  ;  the  coeffi- 
cient of  superficial  expansion  is  the  increase  of  the  surfsice  in  being  heated 
from  zero  to  i  degree,  and  the  coefficient  of  cubical  expansion  is  the  in- 
crease of  the  unit  of  volume  under  the  same  circumstances. 

These  coefficients  vary  with  different  bodies,  but  for  the  same  body  the 
coefficient  of  cubical  expansion  is  three  times  that  of  the  linear  expansion ^ 
as  is  seen  from  the  following  considerations.  Suppose  a  cube,  the  length 
of  whose  side  is  i  at  zero.  Let  k  be  the  elongation  of  this  side  in  passing 
from  zero  to  i  degree,  its  length  at  i  degree  will  be  i  +  >^,  and  the  volume 
of  the  cube,  which  was  i  at  zero,  will  be  (i  +  k)"^,  or  1  +  3^^  +  3/^^  +  J^.  But 
as  the  elongation  k  is  always  a  very  small  fraction  (see  table,  art.  294),  its 
square  ^^,  and  its  cube  P,  are  so  small  that  they  may  be  neglected,  and 
the  value  at  i  degree  becomes  very  nearly  i  +  3-^.  Consequently,  the  in- 
crease of  volume  is  3/^',  or  thrice  the  coefficient  of  linear  expansion. 

In  the  same  manner  it  may  be  shown  that  the  coefficient  of  superficial 
expansion  is  double  the  coefficient  of  linear  expansion. 

293.  Measurement  of  the  coefficient  of  linear  expansion.  Iiavoisier 
and  liaplace's  method. — The  apparatus  used  by  Lavoisier  and  Laplace 
for  determining  the  coefficients  of  linear  expansion  (fig.  240)  consists  of  a 


Fig.  240. 

brass  trough,  placed  on  a  furnace  between  four  stone  supports.  On  the 
two  supports,  on  the  right  hand,  there  is  a  horizontal  axis,  at  the  end  of 
which  is  a  telescope ;  on  the  middle  of  this  axis,  and  at  right  angles  to  it, 
is  fixed  a  glass  rod,  turning  with  it,  as  does  also  the  telescope.  The  other 
two  supports  are  joined  by  a  cross  piece  of  iron,  to  which  another  glass 
rod  is  fixed,  also  at  right  angles.  The  trough,  which  contains  oil  or  water, 
is  heated  by  a  furnace  not  represented  in  the  figure,  and  the  bar  whose 
expansion  is  to  be  determined  is  placed  in  it. 


-294] 


Expansion  of  Solids. 


241 


Fig.  241  represents  a  section  of  the  apparatus  ;  G  is  the  telescope,  KH 
the  bar,  whose  ends  press  against  the  two  glass  rods  F  and  D.  As  the 
rod  F  is  fixed,  the  bar  can  only  expand  in  the  direction  KH,  and  in 
order  to  eliminate  the  effects  of  friction  it  rests  on  two  glass  rollers. 
Lastly,  the  telescope  has  a  cross-view  in  the  eyepiece,  which,  when  the 


Fig.  241 


telescope  moves,  indicates  the  depression  by  the'corresponding  number  of 
divisions  on  a  vertical  scale  AB,  at  a  distance  of  220  yards. 

The  trough  is  first  filled  with  ice,  and  the  bar  being  at  zero,  the  division 
on  the  scale  AB,  corresponding  to  the  wire  of  the  telescope,  is  read  off. 
The  ice  having  been  removed,  the  trough  is  filled  with  oil  or  water,  which 
is  heated  to  a  given  temperature.  The  bar  then  expands,  and  when  its 
temperature  has  become  stationary,  which  is  determined  by  means  of 
thermometers,  the  division  of  the  scale,  seen  through  the  telescope,  is 
read  off. 

From  these  data  the  elongation  of  the  bar  is  determined  ;  for  since  it 
has  become  longer  by  a  quantity,  CH,  and  the  optical  axis  of  the  tele- 
scope has  become  inclined  in  the  direction  GB,  the  two  triangles,  GHC 
and  ABG,  are  similar,  for  they  have  the  sides  at  right  angles  each  to 

each,  so  that =  .-:— .    In  the  same  way,  if  HC  were  another  elonga- 

AB     AG 


tion,  and  AB'  a  corresponding  deviation,  there  would  still  be 


HC^_GH 
AB'     AG  ' 


from  which  it  follows  that  the  ratio  between  the  elongation  of  the  bar  and 

C  H 
the  deflection  of  the  telescope  is  constant,  for  it  is  always  equal  to  -—,  * 

A  preliminary  measurement  had  shown  that  this  ratio  was  yij'     Con- 

HG  AB 

sequently,   =  =^r  whence  HC=- — ;  that  is,  the  total  elongation  of 

AB       '**'  744 

the  bar  is  obtained  by  dividing  the  length  on  the  scale  traversed  by  the 
cross  wire  by  744.  Dividing  this  elongation  by  the  length  of  the  bar,  and 
then  by  the  temperature  of  the  bath,  the  quotient  is  the  dilatation  for  the 
unit  of  length  and  for  a  single  degree — in  other  words,  the  coefficient  of 
linear  dilatation. 

294.  Roy  and  Ramsden's  method. — Lavoisier  and  Laplace's  method 
is  founded  on  an  artifice  which  is  frequently  adopted  in  physical  deter- 
minations, and  which  consists  in  amplifying  by  a  known  amount  dimen- 
sions which,  in  themselves,  are  too  small  to  be  easily  measured.  Unfor- 
tunately this  plan  is  often  more  fallacious  than  profitable,  for  it  is  first 
necessary  to  determine  the  ratio  of  the  motion  measured  to  that  on  which 


242 


On  Heat. 


[294- 


it  depends.  In  the  present  case  it  is  necessary  to  know  the  lengths  ot 
the  arms  of  the  lever  in  the  apparatus,  But  this  preliminary  operation 
may  introduce  errors  of  such  importance  as  partially  to  counterbalance 
the  advantage  of  great  delicacy.  The  following  method,  which  was  used 
by  General  Roy  in  1787,  and  which  was  devised  by  Ramsden,  depends 
on  another  principle.  It  measures  the  elongations  directly,  and  without 
amphfying  them,  but  it  measures  them  by  means  of  a  micrometer,  which 
indicates  very  small  displacements. 

The  apparatus  (fig.  242)  consists  of  three  parallel  metal  troughs  about 
6  feet  long.     In  the  middle  one  there  is  a  bar  of  the  body  whose  expan- 


Fig.  242. 


sion  is  to  be  determined,  and  in  the  two  others  are  cast-iron  bars  01 
exactly  the  same  length  as  this  bar.  Rods  are  fixed  vertically  on  both 
ends  of  these  three  bars.  On  the  rods  in  the  troughs  A  and  B  there  are 
rings  with  cross-wires  like  those  of  a  telescope.  On  the  rods  in  the  trough 
C  are  small  telescopes  also  provided  with  cross-wires. 

The  trough  being  filled  with  ice,  and  all  three  bars  at  zero,  the  points 
of  intersection  of  the  wires  in  the  disc,  and  of  the  wires  in  the  telescope, 
are  all  in  a  line  at  each  end  of  the  bar.  The  temperature  in  the  middle 
trough  is  then  raised  to  100°  C.  by  means  of  spirit  lamps  placed  beneath 
the  trough  ;  the  bar  expands,  but  as  it  is  in  contact  with  the  end  of  a 
screw,  rt,  fixed  on  the  side,  all  the  elongation  takes  place  in  the  direction 
;/;«,  and  as  the  cross-wire  n  remains  in  position,  the  cross-wir^  in  is 
moved  towards  B  by  a  quantity  equal  to  the  elongation.  But  since  the 
screw  a  is  attached  to  the  bar,  by  turning  it  slowly  from  right  to  left,  the 
bar  is  moved  in  the  direction  inn,  and  the  cross-wire  in  regains  its  original 
position.  To  effect  this,  the  screw  has  been  turned  by  a  quantity 
exactly  equal  to  the  elongation  of  the  bar,  and  as  this  advance  of  the 


-295]  Expansion  of  Solids.  243 

screw  is  readily  deduced  from  the  number  of  turns  of  its  tlwead  (11),  the 
total  expansion  of  the  bar  is  obtained,  which,  divided  by  the  temperature 
of  the  bath,  and  this  quotient  by  the  length  of  the  bar  at  zero,  gives  the 
coefficient  of  linear  expansion. 

Coefficieiits  of  linear  expansion  for  1°  between  0°  and  100°  C. 

White  glass      .     .     .  o-oockx)86j3  Copper 0-000017182 

Platinum       ....  0-000008842  Bronze      .....  0-000018167 

Untempered  steel       .  0-000010788  Brass        0-000018782 

Cast  iron       ....  0-000011250  Silver 0-000019097 

Wrought  iron    .     .     .  0-000012204  Tin 0-000021730 

Tempered  steel      .     .  0-000012395  Lead 0-000028575 

Gold 0-000014660  Zinc 0-000029417 

From  what  has  been  said  about  the  linear  expansion  (292),  the  co- 
efficients of  cubical  expansion  of  solids  are  obtained  by  multiplying  those 
of  linear  expansion  by  three. 

The  coefficients  of  the  expansion  of  the  metals  vary  with  their  physical 
condition,  being  different  for  the  same  metal  according  as  it  has  been 
cast  or  hammered  and  rolled,  hardened  or  annealed.  As  a  general  rule, 
operations  which  increase  the  density  increase  also  the  rate  of  expansion. 
But  even  for  substances  in  apparently  the  same  condition,  different  ob- 
servers have  found  very  unequal  amounts  of  expansions  ;,  this  may  arise 
in  the  case  of  compound  substances,  such  as  glass,  brass,  or  steel,  from  a 
want  of  uniformity  in  chemical  composition,  and  in.  simple  bodies  from 
slight  differences  of  physical  state. 

The  expansion  of  amorphous  solids,  and  of  those-  which  crystallise  in 
the  regular  system,  is  the  same  for  all  dimensions,,  unless  they  are  sub- 
ject to  a  strain  in  some  particular  direction.  A  fragjnent  of  such  a  sub- 
stance varies  in  bulk,  but  retains  the  same  shape.  Crystals  not  belonging 
to  the  regular  system  exhibit,  when  heated,  an.  unequal  expansion  in  the 
direction  of  their  different  axes,  in  consequence,  of  which  the  magnitude 
of  their  angles,  and  therefore  their  form,  is  altered.  In  the  dimetric 
system  the  expansion  is  the  same  in  the  direction  of  the  two  equal  axes, 
but  different  in  the  third.  In  crystals  belonging  to  the  hexagonal  system 
the  expansion  is  the  same  in  the  direction  of  the  three  secondary  axes, 
but  different  from  that  according  to  the  principal  one.  In  the  trimetric 
system  it  is  different  in  all  three  directions. 

To  the  general  law  that  all  bodies  expand  by  heat  there  is  an  impor- 
tant exception  in  the  case  of  iodide  of  silver,  which  contracts  somewhat 
when  heated.  It  has  a  negative  coefficient  of  expansion  the  value  of 
which  is  0-00000139. 

295.  The  coefficients  of  expansion  increase  with  the  temperature. 
— According  to  Dr.  Matthiessen,  who  determined  the  expansion  of  the 
metals  and  alloys  by  weighing  them  in  water  at  different  temperatures, 
the  coefficients  of  expansion  are  not  quite  regular  between  0°  and  100°. 
He  found  the  following  values  for  the  linear  expansion  between  0°  and 
100°:— 

M  2' 


244  On  Heat.  [295- 

Zinc  .     .  .  L,=  Lo  (i +0-00002741  /  + 0-0000000235 /') 

Lead      .  .  L^  =  L^  (i  +  0-00002726  /  +  0-0000000074  i) 

Silver    .  .  Li  =  Lo  (i  +0-00001809  /  + 0-0000000135  f^) 

Copper  .  ,  L,  =  Lq  (i  +  0-00001408  /  +  0-0000000264  f^) 

Gold      .  .  L,  =  Lo  (i +0-00001358 /  +  0-0000000I 12  Z'^) 

The  same  authority  has  found  that  alloys  expand  very  nearly  according 
to  the  following  law  : — '  The  coefficients  of  expansion  of  an  alloy  are  equal 
to  the  mean  of  the  coefficients  of  expansion  of  the  volumes  of  the  metals 
composing  it.' 

296.  Formulae  relative  to  the  expansion  of  solids. — Let  /  be  the 
length  of  a  bar  at  zero,  /'  its  length  at  the  temperature  f  C,  and  «  its 
coefficient  of  linear  expansion.  The  tables  usually  give  the  expansion 
for  1°  between  0°  and  100°,  as  in  article  294,  or  for  100°  ;  in  this  latter 
case  n  is  obtained  by  dividing  the  number  by  100. 

The  relation  existing'between  the  above  quantities  is  expressed  by  a 
few  simple  formulas. 

The  elongation  corresponding  to  /°  is  /  times  a  or  nt  for  a  single  unit 
of  length,  or  oil  for  /  units.  The  length  of  the  bar  which  is  /  at  zero  is 
/+  atl  at  /",  consequently, 

r^l+atl=l{l+at) 

This  formula  gives  the  length  of  a  body  I'  at  /°,  knowing  its  length  /at 
zero,  and  the  coefficient  of  expansion  a  ;  and  by  simple  algebraical  trans- 
formations, we  can  obtain  from  it  formula:  for  the  length  at  zero,  knowing 
the  length  /'  at  t°,  and  also  for  finding  a  the  coefficient  of  linear  expan- 
sion, knowing  the  lengths  /'  and  /  at  i°  and  zero  respectively. 

It  is  obvious  that  the  formulae  for  cubical  expansion  are  entirely  analo- 
gous to  the  preceding. 

The  following  are  examples  of  the  application  of  these  formulas  : — 

A  metal  bar  has  a  length  /'  at  i'°,  what  will  be  its  length  /  at  /°  ? 

From  the  above  formula  we  first  get  the  length  of  the  given  bar  at 

zero,  which  is ;  by  means  of  the  same  formula  we  pass  from  zero  to 

I  +  at 

f°  in  multiplying  by  i  +  at',  which  gives  for  the  desired  length  the 
formula 

1+at 

The  density  of  a  body  being  d  at  zero,  required  its  density  d'  at  t°. 

If  I  be  the  volume  of  the  body  at  zero,  and  D  its  coefficient  of  cubical 

expansion,  the  volume  at  t  will  be  i  +  D/,  and  as  the  density  of  a  body 

is  in  inverse  ratio  of  the  volume  which  the  body  assumes  in  expanding, 

we  get  the  inverse  proportion, 

d'  :  d=\    :    i  +  D/, 

d'         \  ^'        d 

^ . ;  or  d 


d      i  +  D^'  i  +  D/ 

Consequently,  when  a  body  is  heated  from  o  to  /°,  its  density,  and 
therefore  its  weight  for  an  equal  volume,  is  inversely  as  the  binomial  ex- 
pression, I  +  D/. 


-297] 


Application  of  the  Expansion  of  Solids. 


J45 


297.  Applications  of  tbe  expansion  of  solids.— In  the  arts  we  meet 
with  numerous  examples  of  the  influence  of  expansion,  (i.)  The  bars  of 
furnaces  must  not  be  fitted  tightly  at  their  extremities,  but  must,  at  least, 
be  free  at  one  end,  otherwise,  in  expanding,  they  would  split  the  masonry. 
(ii.)  In  making  railways  a  small  space  is  left  between  the  successive  rails, 
for  if  they  touched,  the  force  of  expansion  would  cause  them  to  curve 
or  would  break  the  chairs,  (iii.)  Water  pipes  are  fitted  to  one  another  by 
means  of  telescopic  joints,  which  allow  room  for  expansion,  (iv.)  If  a 
glass  is  heated  or  cooled  too  rapidly  it  cracks  ;  this  arises  from  the  fact 
that  glass  is  a  bad  conductor  of  heat,  the  sides  become  unequally 
heated,  and  consequently  unequally  expanded,  which  causes  a  fracture. 

"When  bodies  have  been  heated  to  a  high  temperature,  the  force  pro- 
duced by  their  contraction  on  cooling  is  very  considerable  ;  it  is  equal  to 
the  force  which  is  needed  to  compress  or  expand  the  material  to  the 
same  extent  by  mechanical  means.  Ac- 
cording to  Barlow  a  bar  of  malleable 
iron  a  square  inch  in  section  is  stretched 
10000^^  of  its  length  by  a  weight  of  a  ton  ; 
the  same  increase  is  experienced  by  about 
9°  C.  A  difference  of  45°  C.  between  the 
cold  of  winter  and  the  heat  of  summer  is 
not  unfrequently  experienced  in  this 
country.  In  that  range,  a  wrought  iron 
bar  ten  inches  long  will  vary  in  length  by 
^^gth  of  an  inch  and  will  exert  a  strain,  if 
its  ends  are  securely  fastened,  of  fifty 
tons.  It  has  been  calculated  from  Joule's 
data  that  the  force  exerted  by  heat  in  ex- 
panding a  pound  of  iron  between  0°  and 
100°  during  which  it  increases  about  olo^^ 
of  its  bulk,  is  equal  to  16,000 foot  pounds; 
that  is,  it  could  raise  a  weight  of  7  tons 
through  a  height  of  one  foot. 

(i.)  An  application  of  this  contractile 
force  is  seen  in  the  mode  of  securing  the 
tires  on  wheels.  The  tire  being  made  red 
hot,  and  thus  considerably  expanded,  is 
placed  on  the  circumference  of  the  wheel 
and  then  cooled.  The  tire,  when  cold,  em- 
braces the  wheel  with  such  force  as  not 
only  to  secure  itself  on  the  rim,  but  also  to 
press  home  the  joints  of  the  spokes  into 
the  felloes  and  nave,  (ii.)  Another  inter- 
esting application  was  made  in  the  case 
of  a  gallery  at  the  Conservatoire  des  Arts 
et  Metiers  in  Paris,  the  walls  of  which  had  begun  to  bulge  outwards. 
Iron  bars  were  passed  across  the  building  and  screwed  into  plates  on  the 
outside  of  the  walls.     Each  alternate  bar  was  then  heated  by  means  of 


rig-  243- 


246 


On  Heat. 


[297 


o 


^ 


lamps,  and  when  the  bar  had  expanded  it  was  screwed  up.  The  bars 
being  then  allowed  to  cool  contracted,  and  in  so  doing  drew  the  walls 
together.     The  same  operation  was  performed  on  the  other  bars. 

298.  Compensation  pendulum. — An  important  application  of  the 
expansion  of  metals  has  been  made  in  the  cofupensation pendulum.  This  is 
a  pendulum  in  which  the  elongation,  when  the  teipperature  rises,  is  so 
compensated  that  the  distance  between  the  centre  of  suspension  and  the 
centre  of  oscillation  (76)  remains  constant,  which,  from  the  laws  of  the 
pendulum  ^^'j),  is  necessary  for  isochronous  oscillations,  and  in  order  that 
the  pendulum  may  be  used  as  a  regulator  of  clocks. 

In  fig.  243,  which  represents  the  gridiron  pendulum,  one  of  the  com- 
monest forms  of  compensation  pendulum,  the  ball,  L,  instead  of  being 
supported  by  a  single  rod,  is  supported  by  a  framework,  consisting  of 
alternate  rods  of  steel  and  brass.  In  the  figure,  the  shaded  rods  represent 
steel  ;  including  a  small  steel  rod,  b^  which  supports  the  whole  of  the 
apparatus,  there  are  six  of  them.  The  rest  of  the  rods,  four  in  number, 
are  of  brass.  The  rod  /,  which  supports  the  ball,  is  fixed  at  its  upper  end 
to  a  horizontal  cross-piece  ;  at  its  lower  end  it  is  free,  and  passes  through 
the  two  circular  holes  in  the  lower  horizontal  cross-pieces. 

Now  it  is  easy  to  see  from  the  manner  in  which  the  vertical  rods  are 
fixed  to  the  cross-pieces,  that  the  elongation  of  the  steel  rods  can  only 
take  place  in  a  downward  direction,  and  that  of  the  brass  rods  in  an  up- 
ward direction.  Consequently  in  order  that  the  pendulum  may  remain  of 
the  same  length,  it  is  necessary  that  the  elongation  of  the  brass  rods  shall 
tend  to  make  the  ball  rise  by  exactly  the  same  quantity  that  the  elonga- 
tion of  the  steel  rod  tends  to  lower  it  :  a  result  which  is  attained  when  the 
sum  of  the  lengths  of  the  steel  rods  A  is  to  the  sum  of  the  lengths  of  the 
brass  rods  B  in  the  inverse  ratio  of  the  coefficients  of  expansion  of  steel 
and  brass,  a  and  b,  that  is,  in  the  proportion  A  :  B  =  ^  :  «. 

The  elongation  of  the  rod  may  also  be  compensated  for  by  means  of 
coviperisating  strips.  These  consist  of  two  blades  of  copper  and  iron 
soldered  together  and  fixed  to  the  pendulum  rod,  as  represented  in  fig. 
244.      The  copper  blade,  which  is  more  expansible,  is  below  the  iron. 


.^ 


V. 


Fig.  244. 


Fig.  245. 


Fig.  246. 


When  the  temperature  sinks,  the  pendulum  rod  becomes  shorter,  and  the 
ball  rises.  But  at  the  same  time  the  compensating  strips  become  curved, 
as  seen  in  fig.  245,  in  consequence  of  the  copper  contracting  more  than 


-299]  Expansion  of  Liquids.  247 

the  iron,  and  two  metallic  balls  at  their  extremities  become  lower.  If  they 
have  the  proper  size  in  reference  to  the  pendulum  ball,  the  parts  which 
tend  to  approach  the  centre  of  suspension  compensate  those  which  tend 
to  remove  from  it,  and  the  centre  of  oscillation  is  not  displaced.  If  the 
temperature  rises  the  pendulum  ball  descends,  but  at  the  same  time  the 
small  balls  ascend,  as  shown  in  fig.  246,  so  that  there  is  always  compen- 
sation. 

One  of  the  most  simple  compensating  pendulums  is  the  mercury  peit- 
dulu77i,  invented  by  an  English  watchmaker,  Graham.  The  ball  of  the 
pendulum,  instead  of  being  solid,  consists  of  a  glass  cylinder,  containing 
pure  mercury,  which  is  placed  in  a  sort  of  stirrup,  supported  by  a  steel 
rod.  when  the  temperature  rises  the  rod  and  stirrup  become  longer,  and 
thus  lower  the  centre  of  gravity  ;  but  at  the  same  time  the  mercury  ex- 
pands, and,  rising  in  the  cylinder,  produces  an  inverse  effect,  and  as  mer- 
cury is  much  more  expansible  than  steel,  a  compensation  may  be  effected 
without  making  the  mercurial  vessel  of  undue  dimensions. 

The  same  principle  is  applied  in  the  compensating  balances  of  chrono- 
meters. The  motion  here  is  regulated  by  a  balance  or  wheel,  furnished 
with  a  spiral  spring,  and  the  time  of  the  chronometer  depends  on  the 
force  of  the  spring,  the  mass  of  the  balance,  and  on  its  circumference. 
Now  when  the  temperature  rises  the  circumference  increases,  and  the 
chronometer  goes  slower ;  and  to  prevent  this,  part  of  the  mass  must  be 
brought  nearer  the  axis.  On  the  circumference  of  the  balance  compen- 
sating strips  are  fixed,  of  which  the  more  expansible  metal  is  on  the 
outside,  and  at  the  end  of  these  are  small  masses  of  metal  which  play 
the  same  part  as  the  balls  in  the  above  case.  When  the  radius  is 
expanded  by  heat,  the  small  masses  are  brought  nearer  the  centre  in  con- 
sequence of  the  curvature  of  the  strips  ;  and  as  they  can  be  fixed  in  any 
position,  they  are  easily  arranged  so  as  to  compensate  for  the  expansion 
of  the  balance. 


CHAPTER  III. 

EXPANSION   OF   LIQUIDS. 


299.  Apparent  and  real  expansion. — If  a  flask  of  thin  glass,  provided 
with  a  capillary  stem,  the  flask  and  part  of  the  stem  being  filled  with 
some  coloured  liquid,  be  immersed  in  hot  water,  fig.  247,  the  column  of 
liquid  in  the  stem  at  first  sinks  from  b  to  a,  but  then  immediately  after 
rises,  and  continues  to  do  so  until  the  liquid  inside  has  the  same  tempe- 
rature as  the  hot  water.  This  first  sinking  of  the  liquid  is  not  due  to  its 
contraction  ;  it  arises  from  the  expansion  of  the  glass,  which  becomes 
heated  before  the  heat  can  reach  the  liquid  ;  but  the  expansion  of  the 
liquid  soon  exceeds  that  of  the  glass,  and  the  liquid  ascends. 

Hence  in  the  case  of  liquids  we  must  distinguish  between  the  appar- 
ent and  the  real  or  absolute  expansion.  The  apparent  expansion  is  that 
which  is  actually  observed  when  liquids  contained  in  vessels  are  heated  : 


248 


On  Heat. 


[299 


Fig.  247. 


the  absolute  expansion  is  that  which  would  be  observed  if  the  vessel  did 
not  expand  ;  or,  as  this  is  never  the  case,  it  is  the  apparent  expansion 

corrected  for  the  simultaneous  expansion 
of  the  containing  vessel. 

As  has  been  already  stated,  the  cubical 
expansion  of  liquids  is  alone  considered  ; 
and  as  in  the  case  of  solids,  the  coefficient 
of  expatisio7t  of  a  liquid  is  the  increase  of 
the  unit  of  volume  for  a  single  degree,  but 
a  distinction  is  here  made  between  the 
coefficient  of  absolute  expansion  and  the 
coefficient  oj  appareftt  expajision.  Of  the 
many  methods  which  have  been  employed 
for  determining  these  two  coefficients,  we 
shall  describe  that  of  Dulong  and  Petit. 

300.  Coefficient  of  the  absolute  ex- 
pansion of  mercury. — In  order  to  deter- 
mine the  coefficient  of  obsolute  expansion 
of  mercury,  the  influence  of  the  envelope 
must  be  eliminated.  Dulong  and  Petit's 
method  depends'on  the  hydrostatical  prin- 
ciple that,  in  two  communicating  vessels,  the  heights  of  two  columns  of 
liquid  in  equilibrium  are  inversely  as  their  densities  (104),  a  principle  in- 
dependent of  the  diameters  of  the  vessels,  and  therefore  of  their  expansions. 
The  apparatus  consists  of  two  glass  tubes,  A  and  B  (fig.  248),  joined  by 
a  capillary  tube,  and  kept  vertical  on  an  iron  support,  KM,  the  horizon- 
tality  of  which  is  adjusted  by  means  of  two  levelling  screws  and  two  spirit 
levels,  m  and  n.  Each  of  the  tubes  is  surrounded  by  a  metal  case,  of 
which  the  smaller,  D,  is  filled  with  ice  ;  the  other,  E,  containing  oil,  can 
be  heated  by  the  furnace,  which  is  represented  in  section  so  as  to  show 
the  case.  Mercury  is  poured  into  the  tubes  A  and  B  ;  it  remains  at  the 
same  level  in  both  as  long  as  they  are  at  the  same  temperature,  but  rises 
in  B  in  proportion  as  it  is  heated,  and  expands. 

Let  h  and  d  be  the  height  and  density  of  the  mercury  in  the  leg  A,  at 
the  temperature  zero,  and  h'  and  d!  the  same  quantities  in  the  leg  B.  From 
the  hydrostatical  principle  previously  cited  we  have  had  hd=h'd' .     Now 

from  the  problem  in  article  296,  d'  =  - — =^,  D  being  the  coefficient  of  ab- 
solute expansion  of  mercury  ;  substituting  this  value  of  d'  in  the  equation, 

we  have — -  =}id.  from  which  we  get  D  = — ~  -. 

i  +  D/        '  ^  ht 

The  coefficient  of  absolute  expansion  of  mercury  is  obtained  from  this 

formula,  knowing  the  heights  h'  and  h,  and  the  temperature  /  of  the  bath 

in  which  the  tube  B  is  immersed.     In   Dulong  and  Petit's  experiment 

this  temperature  was  measured  by  a  weight  thermometer,  P   (302),  the 

mercury  of  which  overflowed  into  the  basin,  C,  and  by  means  of  an  air 

thermometer,  T  (311)  ;  the  heights  h'  and  h  were  measured  by  a  catheto- 

meter,  K  (85). 


301] 


Expansion  of  Liquids. 


249 


Dulong  and  Petit  found  by  this  method  that  the  coefficient  of  absolute 
expansion  of  mercury,  between  0°  and  100°  C.  is  ^^.  But  they  found 
that  the  coefficient  increased  with  the  temperature.  Between  100°  and 
200°  it  is  5/25,  and  betwen  200°  and  300°  it  is  ~-^.  The  same  observa- 
tion has  been  made  in  reference  to  other  Hquids,  showing  that  their  ex- 


Fig.  248. 

pansion  is  not  regular.  It  has  beea  found  that  this  expansion  is  less 
regular  in  proportion  as  liquids  are  near  a  change  in  their  state  of  aggre- 
gation, that  is,  approach  their  freezing  or  boiling  points.  Dulong  and 
Petit  found  that  the  expansion  of  mercury  between  — 36°  and  100°  is  prac- 
tically quite  uniform. 

Regnault,  who  has  determined  this  important  physical  constant,  has 
found  that  the  mean  coefficient  between  0°  and  100°  is  55^^85  between  100° 
and  200°,  53^^,  and  between  200°  and  300°,  t^^^^. 

301.  Coefficient  of  tbe  apparent  expansion  of  mercury. — The  co- 
efficient of  apparent  expansion 
of  a  liquid  varies  with  the  na- 
ture of  the  envelope.  That  of 
mercury  in  glass  was  deter- 
mined by  means  of  the  appa- 
ratus represented  in  figure  249. 

It  consists  of  a  glass  cyhnder  ^  ^is-:^^:,^^^^^^^ 

to  which  is  joined  a  bent  capil-  Pj^  ,^ 

lary  glass  tube,  open  at  the  end. 

The  apparatus  is  weighed  first  empty,  and  then  when  filled  with  mer- 
cury at  zero  ;  the  difference  gives  the  weight  of  the  mercury,  P.  It  is 
then  raised  to  a  known  temperature,  / ;  the  mercury  expands,  a  certain 

M3 


250 


Oh  Heat. 


[301- 


^- 


^ 


quantity  passes  out,  which  is  received  in  the  capsule  and  weighed.  If 
the  weight  of  this  mercury  be  p,  that  of  the  mercury  remaining  in  the  ap- 
paratus will  be  P— ^ 

When  the  temperature  is  again  zero,  the  mercury  in  cooling  produces 
an  empty  space  in  the  vessel,  which  represents  the  contraction  of  the 
weight  of  mercury  P  —p,  from  f  to  zero,  or,  what  is  the  same  thing,  the 
expansion  of  the  same  weight  from  o  to  t°,  that  is,  the  weight  p  repre- 
sents the  expansion  of  the  weight  P  — /,  for  f.  If  this  weight  expands 
n  glass  by  a  quantity  p  for  f^  a  single  unit  of  weight  would  expand 

^      for  /°'and  ^^— ^-  for    a    single  degree  ;  consequently,    for   D', 
(P  -p)  (P  -p)t 

the  coefficient  of  apparent  expansion  of  mercury  in  glass,  we  have 
D'  = ?- .  Dulong  and  Petit  found  the  coefficient  of  apparent  expan- 
sion of  mercury  in  glass  to  be  g^^^. 

302.  VTeigrbt  thermometer. — The  apparatus  represented  in  fig.  249  is 
called  the  weight  thentiometer,  because  the  temperature  can  be  deduced 
from  the  weight  of  mercury  which  overflows. 

The  above  experiments  have  placed  the  coefficient  of  apparent  expan- 

K.    from   which 


sion  at  g^—  ;  we  have  therefore  the  equation 


we  get  t- 


{Y-p)t      ' 
a  formula  which  gives  the  temperature   /  when  the 


^^ 


6480/ 

weights  P  and  p  are  known. 

303.  Coefficient  of  tbe  expansion  of  g-lass. — As  the  absolute  expansion 
of  a  liquid  is  the  apparent  expansion  ^///j-  the  expansion  due  to  the  enve- 
lope, the  coefficient  of  the  cubical  expansion  of  glass  has  been  obtained  by 
taking  the  difference  between  the  coefficient  of  absolute  expansion  of 
mercury  in  glass  and  that  of  its  apparent  expansion.     That  is,  the  coeffi- 

\Vient  of  cubical  expansion  of  glass  is 

5^8  -6180  =18^00=0-002584. 

Regnault  has  found  that  the  coefficient  of  expansion  varies  with  different 
kinds  of  glass,  and  further  with  the  shape  of  the  vessels.  For  ordinary 
chemical  glass  tubes,  the  coefficient  is  0*0000254. 

304.  Coefficients  of  expansion  of  various  liquids. — The  apparent 
e^^pansion  of  liquids  may  be  determined  by  means  of  the  weight  thermo- 
meter, and  the  absolute  expansion  is  obtainedby  adding  to  this  coefficient 
the  expansion  of  the  glass. 

Totat  apparent  expansions  0/ liquids  between  0°  and  100°  C. 


Mercury    ....  0-01543       Oil  of  turpentine  . 

.  0-07 

Distilled  water  .        .        .  0-0466         Ether    . 

. 

.  0-07 

Water  saturated  with  salt  .  0*05             Fixed  oils     . 

.  o-o8 

Sulphuric  acid   .         .         ,  0-06             Nitric  acid    . 

. 

.011 

Hydrochloric  acid      .         .  o-o6            Alcohol 

. 

.  o-ii6 

The  coefficient  of  apparent  expansion  for  1°  C.  is 

obtained  by 

dividing 

these  numbers  by  100  ;  but  the  number  thus  obtained  does  not  represent 


-306]  Force  exerted  by  Liquids  in  expanding.  251 

the  mean  coefficient  of  expansion  of  liquids,  for  the  expansion  of  these 
bodies  increases  gradually  from  zero.  The  expansion  of  mercury  is  prac- 
tically constant  between  —  36°  and  100°  C,  while  water  contracts  from 
zero  to  4°,  and  then  expands. 

For  many  physical  experiments  a  knowledge  of  the  exact  expansion  of 
water  is  of  great  importance.  This  physical  constant  was  determined 
with  great  care  by  Dr.  Matthiessen,  who  found  that  between  4°  and  32^ 
it  may  be  expressed  by  the  formula 

V/=  I —0-00000253  (/  — 4) +  0*0000008389  (/-4)2  + 

0-00000007173  (/  — 4)3; 
and  between  30°  and  100°  by 

Nt  =  0-999695  +  0-0000054724/2  +  o-oooooooi  1 26/^ 

Many  liquids,  with  low  boiling  points,  especially  condensed  gases,  have 
very  high  coefficients  of  expansion.  Thilorier  found  that  liquid  carbonic 
acid  expands  four  times  as  much  as  air.  Drion  has  recently  confirmed 
this  observation,  and  has  obtained  analogous  results  with  chloride  of 
ethyle,  liquid  sulphurous  acid,  and  liquid  hyponitrous  acid. 

305.  Correction  of  tbe  barometric  beigrtat. — It  has  been  already  ex- 
plained under  the  Barometer  (159),  that,  in  order  to  make  the  indications 
of  this  instrument  comparable  in  different  places  and  at  different  times, 
they  must  be  reduced  to  a  uniform  temperature,  which  is  that  of  melting 
ice      The  correction  is  made  in  the  following  manner  : — 

Let  H  be  the  barometric  height  at  /°,  and  k  its  height  at  zero,  d  the 

density  of  mercury  at  zero,  and  d  its  density  at  /°.     The  heights  H  and 

k     df 
h  are  inversely  as  the  densities  d  and  d'\  that  is,   ^  =  -j-     If  we  call 

H     d 

I    the  volume  of  mercury  at  zero,  its  volume  at  f  will  be  i  +  D/,  D 

beiil  the    coefficient   of   absolute    expansion   of  mercury.     But   these 

volumes,  i  +  D/  and  i,  are  inversely  as  the  densities  d  and  d'  \  that  is, 

_  =  — ^— —     Consequently,  / ^  = — -,  whence  h  = —-  .       Replacing 

d     \^T>t  ^         ^'  H     i+D/  i  +  D/  ^         ^ 

D  by  its  value  rh^^^  we  have  h  = ~—    =  -i-^— . 

^  ''''  I  .     1 5508  +  / 

5508 

In  this  calculation,  the  coefficient  of  absolute  expansion  of  mercury  is 
taken,  and  not  that  of  apparent  expansion  ;  for  the  value  H  is  the  same 
as  if  the  glass  did  not  expand,  the  barometric  height  being  independent 
of  the  diameter  of  the  tube,  and  therefore  of  its  expansion. 

306.  Porce  exerted  by  liquids  in  expanding:. — The  force  which 
liquids  exert  in  expanding  is  very  great,  and  equal  to  that  which  would 
be  required  in  order  to  bring  the  expanded  liquid  back  to  its  original 
volume.  Now  we  know  what  an  enormous  force  is  required  to  com- 
press a  liquid  to  even  a  very  small  extent.  Thus  between  0°  and  10°, 
mercury  expands  by  0-0017905  of  its  volume  at  0°;  its  compressibility  is 
0-00000295  of  its  volume  for  one  atmosphere ;  hence  a  pressure  of  more 


252 


On  Heat. 


[306- 


than  600  atmospheres  would  be  requisite  to  prevent  mercury  expanding 
when  heated  from  0°  to  10°. 

307.  nxaximum  density  of  water. — Water  presents  the  remarkable 
phenomenon  that  when  its  temperature  sinks  it  contracts  up  to  4° ;  but 
from  that  point,  although  the  cooling  continues,  it  expands  up  to  the 
freezing  point,  so  that  4°  represent  the  point  of  greatest  contraction  of 
water. 

Many  methods  have  been  used  to  determine  the  maximum  density  of 
water.  Hope  made  the  following  experiment.  He  took  a  deep  vessel, 
perforated  by  two  lateral  apertures,  in  which  he  fixed  thermometers,  and 
having  filled  the  vessel  with  water  at  0°,  he  placed  it  in  a  room  at  a  tem- 
perature of  1 5°.  As  the  layers  of  liquid  at  the  sides  of  the  vessel  became 
heated  they  sank  to  the  bottom,  and  the  lower  thermometer  marked  4° 
while  that  of  the  upper  one  was  still  at  zero.  Hope  then  made  the  inverse 
experiment  :  having  filled  the  vessel  with  water  at  1 5°,  he  placed  it 
in  a  room  at  zero.  The  lower  thermometer  having  sunk  to  4°  re- 
mained stationary  for  some  time,  while  the  upper  one  cooled  down  until  it 
reached  zero.  Both  these  experiments  prave  that  water  is  heavier  at  4° 
than  at  0°,  for  in  both  cases  it  sinks  to  the  lower  part  of  the  vessel. 

This  last  experiment  maybe  adapted 
for  lecture  illustration  by  using  a 
cylinder  containing  water  at  15°  C, 
partially  surrounded  by  a  jacket  con- 
taining bruised  ice  (fig.  250). 

Hallstrom  made  a  determination  of 
the  maximum  density  of  water  in  the 
following  manner.  He  took  a  glass 
bulb,  loaded  with  sand,  and  weighed 
it  in  water  of  different  temperatures. 
Allowing  for  the  expansion  of  glass, 
he  found  that  4'i°  was  the  tempera- 
ture at  which  it  lost  most  weight  and 
consequently  this  was  the  temperature 
of  the  maximum  density  of  water. 

Despretz  arrived  at  the  temperature 
4°  by  another  method.  He  took  a 
water  thermometer,  that  is  to  say  a 
bulbed  tube  containing  water,  and 
placing  it  in  a  bath,  the  temperature  of 
which  was  indicated  by  an  ordinary 
mercury  thermometer,  found  that  the  water  contracted  to  the  greatest 
extent  at  4°,  and  that  this  is  therefore  the  point  of  greatest  density. 

This  phenomenon  is  of  great  importance  in  the  economy  of  nature.  In 
winter  the  temperature  of  lakes  and  rivers  falls  from  being  in  contact 
with  the  cold  air,  and  from  other  causes,  such  as  radiation.  The  colder 
water  sinks  to  the  bottom,  and  a  continual  series  of  currents  goes  on 
until  the  whole  has  a  temperature  of  4°.  The  cooling  on  the  surface 
still  ccntinues,  but  the  cooled  layers  being  lighter  remain  on  the  surface. 


Fig.  250. 


308] 


Expansion  of  Gases. 


253 


and  ultimately  freeze.  The  ice  formed  thus  protects  the  water  below, 
which  remains  at  a  temperature  of  4°,  even  in  the  most  severe  winters,  a 
temperatvire  at  which  fishes  and  other  inhabitants  of  the  waters  are  not 
destroyed. 

The  following  table  of  the  density  of  water  at  various  temperatures  is 
based  on  several  sets  of  observations  : — 


Density  of  water  between  0°  and  30°. 


Tempe- 
ratures 

Densities 

Tempe- 
ratures 

Densities" 

Tempe- 
ratures 

Densities 

0 

0-99988 

II 

0-99965 

22 

0-99785 

I 

0-99993 

12 

0-99955 

23 

0-99762 

2 

0-99997 

13 

0-99943 

24 

0-99738 

3 

0-99999 

14 

099930 

25 

0-99704 

4 

i-ooooo 

15 

0-99915 

26 

0-99089 

5 

099999 

16 

0-99900 

27 

0-99662 

6 

0-99997 

17 

0-99884 

28 

0-99635 

7 

0-99994 

18 

0-99800 

29 

0-99607 

8 

0-99988 

19 

0-99847 

30 

0-99579 

9 

1-99982 

20 

0-99807 

10 

0-99974 

21 

0-99806 

! 

CHAPTER   IV.      ■ 

EXPANSION  AND   DENSITY  OF  GASES. 

308.  Gay-Aussac's  method. — Gases  are  the  most  expansible  of  all 
bodies,  and  at  the  same  time  the  most  regular  in  their  expansion.  The  co- 
efficients of  expansion,  too,  of  the  several  gases  differ  only  by  very  small 
quantities.     The  cubical  expansion  of  gases  need  alone  be  considered. 

Gay-Lussac  first  determined  the  coefficient  of  the  expansion  of  gases 
by  means  of  the  apparatus  represented  in  fig.  251. 

In  a  rectangular  metal  bath,  about  16  inches  long,  was  fitted  an  air 
thermometer,  which  consisted  of  a  capillary  tube,  AB,  with  a  bulb.  A, 
at  one  end.  The  tube  was  divided  into  parts  of  equal  capacity,  and  the 
contents  of  the  bulb  ascertained  in  terms  of  these  parts.  This  was  effected 
by  weighing  the  bulb  and  tube  full  of  mercury  at  zero,  and  then  heating 
slightly  to  expel  a  small  quantity  of  mercury,  which  was  weighed.  The 
apparatus  being  again  cooled  down  to  zero,  the  vacant  space  in  the  tube 
corresponded  to  the  weight  of  mercury  which  had  overflowed;  the 
volume  of  mercury  remaining  in  the  apparatus,  and  consequently  the 
volume  of  the  bulb,  was  determined  by  calculations  analogous  to  those 
made  for  the  piezometer  (94). 

In  order  to  fill  the  thermometer  with  dry  air  it  was  first  filled  with 
mercury,   which  was   boiled  in  the  bulb  itself.     A  tube,   C,  filled  with 


254 


On  Heat, 


[308 


chloride  of  calcium,  was  then  fixed  on  to  its  end  by  means  of  a  cork.  A 
fine  platinum  wire  having  then  been  introduced  into  the  stem  A B,  through 
the  tube  C,  and  the  apparatus  being  slightly  inclined  and  agitated  from 
time  to  time,  air  entered,  having  been  previously  well  dried  by  passing 


Fig.  251. 

through  the  chloride  ot  calcium  tube.  The  whole  of  the  mercury  was 
displaced,  with  the  exception  of  a  small  thread,  which  remained  in  the 
tube  AB  as  an  index. 

The  air  thermometer  was  then  placed  in  the  box  filled  with  melting 
ice,  the  index  moved  towards  A,  and  the  point  was  noted  at  which  it 
became  stationary.  This  gave  the  volume  of  air  at  zero  ;  for  the  capacity 
of  the  bulb  was  known.  Water  or  oil  was  then  substituted  for  the  ice, 
and  the  bath  successively  heated  to  different  temperatures.  The  air  ex- 
panded and  moved  the  index  from  A  towards  B.  The  position  of  the 
index  in  each  case  was  noted,  and  the  corresponding  temperature  was 
indicated  by  means  of  the  thermometers  D  and  E. 

Assuming  that  the  atmospheric  pressure  did  not  vary  during  the 
experiment,  and  neglecting  the  expansion  of  the  glass  as  being  too  small 
in  comparison  with  that  of  the  air,  the  total  expansion  of  the  air  is 
obtained  by  subtracting  from  its  volume  at  a  given  temperature,  its  volume 
at  zero.  Dividing  this  by  a  given  temperature,  and  then  by  the  nurn- 
ber  of  units  contained  in  the  volume  at  zero,  the  quotient  is  the  coefficient 
of  expansion  for  a  single  unit  of  volume  and  a  single  degree ;  that  is,  the 
coefficient  of  expansion.  It  will  be  seen,  further  on,  how  corrections  for 
pressure  and  temperature  may  be  introduced. 

By  this  method  Gay-Lussac  found  that  the  coefficient  of  expansion  of 
air  was  00037 5  ;  and  he  enunciated  the  two  following  laws  in  reference 
to  the  expansion  of  gases  : — 

I.  All  gases  have  the  same  coefficient  of  expansion  as  air. 

II.  This  coefficient  is  the  same  whatever  be  the  pressure  supported  by 
the  gas. 

These  simple  laws  are  not,  however,  rigorously  exact  (310)  ;  they  only 
express  the  expansion  of  gases  in  an  approximate  manner. 


-310]  Expansion  of  Gases.  255 

309.  Problems  on  the  expansion  of  erases. — Many  of  the  problems 
relative  to  the  expansion  of  gases  are  similar  to  those  on  the  expansion  of 
liquids.  With  obvious  modifications,  they  are  solved  in  a  similar  manner. 
In  most  cases  the  pressure  of  the  atmosphere  must  betaken  into  account 
in  considering  the  expansion  of  gases.  The  following  is  an  example  of 
the  manner  in  which  this  correction  is  made  : — 

i.  The  volume  of  a  gas  at  /°,  and  under  the  pressure  H,  is  V  ;  what 
will  be  the  volume  V  of  the  same  gas  at  zero,  and  under  the  normal  pres- 
sure 760  millimetres  ? 

Here  there  are  two  corrections  to  be  made  ;  one  relative  to  the  tem- 
perature, and  the  other  to  the  pressure.  It  is  quite  immaterial  which  is 
taken  first.  If  a  be  the  coefficient  of  cubical  expansion  for  a  single 
degree,  by  reasoning  similar  to  that  in  the  case  of  hnear  expansion  (296), 
the  volume  of  the  gas  at  zero,  but  still  under  the  pressure  H,  will  be 

This  pressure  is  reduced  to  the  pressure  760,  in  accordance  with 

I  +  (it 

Boyle's  law  (166),  by  putting 

V  +  76o=    ^'    xH; 

I  +r  / 

whence  V  = 


750  (i  +tt/) 

ii.  A  volume  of  gas  weighs  P'  at  t° ;  what  will  be  its  weight  at  zero  ,^ 

Let  P  be  the  desired  weight,  a  the  coefficient  of  expansion  of  the  gas 

^'  its  density  at  /°,  and  d  its  density  at  zero.     As  the  weights  of  equal 

V    df 
volumes  are  proportional  to  the  densities,  we  have  -  = -.     If  i  be  the 

volume  of  a  gas  at  zero,  its  volume  at  t  will  be  i  +  ot\  but  as  the  densities 
are  inversely  as  the  volumes,  -  = 


d     I  +  0/ 


and  therefore 


P      i+a/' 

whence  P  =  P'(i+n/). 

P 

From  this  equation  we  get  P''  =  ,  which  gives   the  weight  at  /, 

1+0/ 

knowing  the  weight  at  zero,  and  which  further  shows  that  the  weight  P' 
is  inversely  as  the  binomial  of  expansion  i  +  at. 

310.  Regrnault's  metbod — M.  Regnault  used  successively  four  dif- 
ferent methods  for  determining  the  expansion  of  gases.  In  some  of  them 
the  pressure  was  constant  and  the  volume  variable,  as  in  Gay-Lussac's 
method  ;  in  others  the  volume  remained  the  same  while  the  pressure 
varied.  The  first  method  will  be  described.  It  is  the  same  as  that  used 
by  Rudberg  and  Dulong,  but  is  distinguished  by  the  care  with  which  all 
sources  of  error  are  avoided. 


256 


On  Heat, 


[310- 


The  apparatus  consisted  of  a  pretty  large  cylindrical  reservoir,  B  (fig. 
252),  terminating  in  a  bent  capillary  tube.     In  order  to  fill  the  reservoir 


Fig.  252. 


with  dry  air,  it  was  placed  in  a  hot  water  bath,  and  the  capillary  tube 
connected  by  a  caoutchouc  tube  with  a  series  of  drying  tubes.  These 
tubes  were  joined  to  a  small  air  pump,  P,  by 
which  a  vacuum  could  be  produced  in  the 
reservoir  while  at  a  temperature  of  100° 
The  reservoir  was  first  exhausted,  and  air 
afterwards  admitted  slowly  ;  this  operation 
was  repeated  a  great  many  times,  so  that  the 
air  in  the  reservoir  became  quite  dry,  for  the 
moisture  adhering  to  the  sides  passed  ofi"  in 
vapour  at  100°,  and  the  air  which  entered 
became  dry  in  its  passage  through  the  U 
tubes. 

The  reservoir  was  then  kept  for  half  an 
hour  at  the  temperature  of  boiling  water  ; 
the  air  pump  having  been  detached,  the 
drying  tubes  were  then  disconnected,  and 
the  end  of  the  tube  hermetically  sealed, 
the  height,  H,  of  the  barometer  being  noted. 
When  the  reservoir  B  was  cool,  it  was  placed 
in  the  apparatus  represented  in  fig.  253.  It 
was  there  quite  surrounded  with  ice,  and  the 
end  of  the  tube  dipped  in  the  mercury  bath, 
C.  After  the  air  in  the  reservoir  B  had  sunk  to  zero,  the  point  b  was 
broken  off  by  means  of  a  forceps  ;  the  air  in  the  interior  became  con- 
densed by  atmospheric  pressure,  the  mercury  rising  to  a  height  oQx.  In 
order  to  measure  the  height  of  this  column,  G<?,  which  will  be  called  /?, 


Fig.  253. 


-310]  Expansion  of  Gases.  257 

a  movable  rod,  go^  was  lowered  until  its  point,  ^,  was  flush  with  the 
surface  of  the  mercury  in  the  bath  ;  the  distance  between  the  point  o  and 
the  level  of  the  mercury  G  was  measured  by  means  of  the  cathetometer. 
The  point  b  was  finally  closed  with  wax  by  means  of  the  spoon  a,  and 
the  barometric  pressure  noted  at  this  moment.  If  this  pressure  be  H, 
the  pressure  in  the  reservoir  is  H'  —  k. 

The  reservoir  was  now  weighed  to  ascertain  P,  the  weight  of  the 
mercury  which  it  contained.  It  was  then  completely  filled  with  mercury 
at  zero,  in  order  to  have  the  weight  P'  of  the  mercury  in  the  reservoir  and 
in  the  tube. 

If  S  be  the  coefficient  of  the  cubical  expansion  of  glass,  and  D  the 
density  of  mercury  at  zero,  the  coefficient  a  of  the  cubical  expansion  of 
air  is  determined  in  the  following  manner.     The  volume  of  the  reservoir 

P^ 
and  of  the  tube  at  zero  is  — ,    from  the  formula  P  =  VD  (122) ;  conse- 
quently, this  volume  is 

^(i+^V) (I) 

at  the  temperature  /°,  assuming,  as  is  the  case,  that  the  reservoir  and 
tube  expand  as  if  they  were  solid  glass.  But  from  the  formula  P  =  VD, 
the  volume  of  air  in  the  reservoir  at  zero,  and  under  the  pressure  H'  — ^, 

P'  — P 

is  — — — .    At  the  same  pressure,  but  at  /°,  its  volume  would  be 

and,  by  Boyle's  law  (166),  at  the  pressure  H,  at  which  the  tube  was 
sealed,  this  volume  must  have  been 

(P-P)(l-fa/)(H--/0  .^. 

DH  ^"^ 

Now  the  volumes  represented  by  these  formulas,  (i)  and  (2),  are  each 
equal  to  the  volume  of  the  reservoir  and  the  tube  at  /°  ;  they  are  there- 
fore equal.     Removing  the  denominators,  we  have 

P'(i+tV)H  =  (F-P)  (i  +  oO  (H'->^) (3) 

from  which  the  value  of  a  is  deduced. 

The  means  of  a  great  number  of  experiments  between  zero  and  100° 
and  for  pressures  between  300  millimetres  and  500  milHmetres,  gave  the 
following  numbers  for  the  coefficients  of  expansion  for  a  single  degree : 

Air 0-003667  Carbonic  acid  ....  0-003710 

Hydrogen 6-003661  Nitrous  oxide   ....  0-003719 

Nitrogen 0-003661  Cyanogen 0*003877 

Carbonic  oxide     .     .     .  o-cxy^SGj  Sulphurous  acid    ...  0-003903 

These  numbers,  with  which  the  results  obtained  by  Magnus  closely 
agree,  show  that  the  coefficients  of  expansion  of  the  permanent  gases  differ 
very  little ;  but  that  they  are  somewhat  greater  in  the  case  of  the  conden- 


258  Ott  Heat.  [310- 

sible  gases,  such  as  carbonic  and  sulphurous  acids.  Regnault  has  further 
found  that,  at  the  same  temperature,  the  coefficient  of  expansion  of  any 
gas  increases  with  the  pressure  which  it  supports.  Thus,  while  the  co- 
efficient of  expansion  of  air  under  a  pressure  of  i  lo™™  is  0-003648,  under  a 
pressure  of  3655™™  or  nearly  five  atmospheres  it  is  0*003709. 

The  number  found  by  Regnault  for  the  coefficient  of  the  expansion  ot 
air,  0-003667,  is  equal  to  ^=^3  nearly;  and  if  we  take  the  coefficient 
of  expansion  at  0-0036666  ...  it  may  be  represented  by  the  fraction 
— lo,  which  is  very  convenient  for  purposes  of  calculation. 

311.  Air  thermometer. — The  aif-  thermometer  is  based  on  the  ex- 
pansion of  air.  When  it  is  used  to  measure  small  differences  of  tempe- 
rature, it  has  the  same  form  as  the  tube  used  by  Gay-Lussac  in  deter- 
mining the  expansion  of  air  (fig.  251),  that  is,  a  capillary  tube  with  a  bulb 
at  the  end.  The  reservoir  being  filled  with  dry  air,  an  index  of  coloured 
sillphuric  acid  is  passed  into  the  tube  ;  the  apparatus  is  then  graduated 
in  Centigrade  degrees  by  comparing  the  positions  of  the  index  with  the 
indications  of  a  mercurial  thermometer.  Of  course  the  end  of  the  tube 
must  remain  open  ;  otherwise,  the  air  above  the  index  condensing  or  ex- 
panding at  the  same  time  as  that  in  the  bulb,  the  index  would  remain 
stationary.  A  correction  must  be  made  at  each  observation  for  the  at- 
mospheric pressure. 

When  considerable  variations  of  temperature  are  to  be  measured,  the 
tube  has  a  form  like  that  used  in  Regnault's  experiments  (fig.  252  and 
253).  By  experiments  made  as  described  in  article  310,  P,  P',  H,  H', 
and  h,  may  be  found,  and  the  coefficients  a  and  I  being  known,  the  tem- 
perature t  to  which  the  tube  has  been  raised  is  readily  deduced  from  the 
equation  (3). 

Regnault's  researches  show  that  the  air  and  the  mercurial  thermometer 
agree  up  to  260°,  but  above  that  point  mercuiy  expands  relatively  more 
than  air. 

In  cases  where  very  high  temperatures  are  to  be  measured  the  reser- 
voir is  made  of  platinum.  The  use  of  an  air  thermometer  is  seen  in 
Dulong  and  Petit's  experiment  (300) ;  it  was  by  such  an  apparatus  that 
Pouillet  measured  the  temperature  corresponding  to  the  colours  which 
metals  take  when  heated  in  a  fire,  and  found  them  to  be  as  follows  : — 

Incipient  red  .  .  .  525°C.  Dark  orange  .  .  .  iioo°C. 
Dull  red  ....     700  White        ....     1300 

Cherry  red        .        ..         .     900  Dazzling  white  .         .         .     1500 

In  the  measurement  of  high  temperatures  Deville  and  Troost  have 
used  with  advantage,  the  vapour  of  iodine  instead  of  air,  and  as  platinum 
has  been  found  to  be  permeable  to  gases  at  high  temperature,  they  have 
employed  porcelain  instead  of  that  metal. 

312.  Density  of  grases.— The  relative  density  of  a  gas,  or  its  specific 
gravity,  is  the  ratio  of  the  weight  of  a  certain  volume  of  the  gas  to  that 
of  the  same  volume  of  air  ;  both  the  gas  and  the  air  being  at  zero  and  at 
a  pressure  of  760  millimetres. 

In  order,  therefore,  to  find  the  specific  gravity  of  a  gas,  it  is  necessary 


-312]  Density  of  Gases.  ^59 

to  determine  the  weight  of  a  certain  volume  of  this  gas  at  a  pressure  of 
760  millimetres,  and  a  temperature  of  zero,  and  then  the  weight  of  the 
same  volume  of  air  under  the  same  conditions.  For  this  purpose  a  large 
globe  of  about  two  gallons  capacity  is  used,  the  neck  of  which  is  pro- 
vided with  a  stopcock,  which  can  be  screwed  to  the  air  pump.  The 
globe  is  first  weighed  empty,  and  then  full  of  air,  and  afterwards  full  of 
the  gas  in  question.  The  weights  of  the  gas  and  of  the  air  are  obtained  by 
subtracting  the  weight  of  the  exhausted  globe  from  the  weight  of  the 
globes  filled,  respectively,  with  air  and  gas.  The  quotient,  obtained  by 
dividing  the  latter  by  the  former,  gives  the  specific  gravity  of  the  gas.  It 
is  difficult  to  make  these  determinations  at  the  same  temperature  and 
pressure,  and  therefore  all  the  weights  are  reduced  to  zero  and  the  normal 
pressure  of  760  millimetres. 

The  gases  are  dried  by  causing  them  to  pass  through  drying  tubes 
before  they  enter  the  globe,  and  air  must  also  be  passed  over  potash  to 
free  it  from  carbonic  acid.  And  as  even  the  best  air  pumps  never  pro- 
duce a  perfect  vacuum,  it  is  necessary  to  exhaust  the  globe  until  the 
manometer  in  each  case  marks  the  same  pressure. 

The  globe  having  been  exhausted,  dried  air  is  allowed  to  enter,  and 
the  process  is  repeated  several  times  until  the  globe  is  perfectly  dried. 
It  is  then  finally  exhausted  until  the  residual  tension,  in  millimetres,  is  e. 
The  weight  of  the  exhausted  globe  is  p.  Air,  which  has  been  dried  and 
purified  by  passing  through  potash  and  chloride  of  calcium  tubes,  is  then 
allowed  to  enter  slowly.  The  weight  of  the  globe  full  of  air  is  P.  If  H 
is  the  barometric  height  in  millimetres,  and  f  the  temperature  at  the 
time  of  weighing,  P  —p  is  the  weight  of  the  globe  full  of  air  at  the  tempe- 
rature /,  and  the  pressure  H  —  ^. 

To  reduce  this  weight  to  the  pressure  760  millimetres  and  the  tempera- 
ture zero,  let  a  be  the  coefficient  of  the  expansion  of  air,  and  <T  the  coef- 
ficient of  the  cubical  expansion  of  glass.     From  Boyle's  law  the  weight, 

which  is  P  —p  at  /°,  and  a  pressure  of  H  -^  would  be    ^    if-- —  under 

the  pressure  760  millimetres  and  at  the  same  temperature  f.  If  the  tem- 
perature is  0°,  the  capacity  of  the  globe  will  diminish  in  the  ratio  i  +  It 
to  r,  while  the  weight  of  the  gas  increases  in  the  ratio  i  :  i  +  o/,  as  follows 
from  the  problems  in  art.  309.  Consequently  the  weight  of  the  air  in  the 
globe  at  0°  and  at  the  pressure  760  millimetres  will  be 

(P-;»)       760(1+0/)  

Further,  let  a'  be  the  coefficient  of  expansion  of  the  gas  in  question  ;  let 
P'  be  the  weight  of  the  globe  full  of  gas  at  the  temperature  /'  and  the 
pressure  H',  and  let/'  be  the  weight  of  the  globe  when  it  is  exhausted  to 
the  pressure  e  ;  the  weight  of  the  gas  in  the  globe  at  the  pressure  760  and 
the  temperature  zero  will  be 

Dividing  the  latter  formula  by  the  former  we  obtain  the  density 


26o 


On  Heat 


[312- 


D 


V'-p')  (H-^)  (i+.-Y)  (i+fV) 


(P-/)    (H'-^)    (l-+aO    (l+<30 

If  the  temperature  and  the  pressure  do  not  vary  during  the  experi- 
ment, 

H  =  H'and  t  =  i'\  whence  D  =  (?lz41ii±^),  and  if  a  =  «',  V>-^'~^' 


(P-/)(i+«/) 


P-/ 


313.  Regrnault's  metbod  of  determining-  the  density  of  grases,— ^M. 
Regnault  has  so  modified  the  above  method  that  many  of  the  corrections 
may  be  dispensed  with.  The  globe  in  which  the  gas  is  weighed  is  sus- 
pended from  one  pan  of  a  balance,  and  is  counterpoised  by  means  of  a 
second  globe  of  the  same  dimensions,  and  hermetically  sealed,  suspended 
from  the  other.  These  two  globes  expanding  at  the  same  time  always 
displace  the  same  quantity  of  air,  and  consequently  variations  in  the 
temperature  and  pressure  of  the  atmosphere  do  not  influence  the 
weighing.  The  globe,  too,  is  filled  with  the  air  or  with  the  gas,  at  the 
temperature  of  zero.  This  is  effected  by  placing  it  in  a  vessel  full  of 
ice,  as  shown  in  fig.  254.     It  is  then  connected  with  a  three-way  cock, 


Fig-  254 

A,  by  which  it  may  be  connected  either  with  an  air-pump,  or  with  the 
tubes  M  and  N,  which  are  connected  with  the  reservoir  of  gas.  The 
tubes  M  and  N  contain  substances  by  which  their  action  on  the  gas  dry 
and  purify  it. 

The  stopcock  A  being  so  turned  that  the  globe  is  only  connected  with 
the  air  pump,  a  vacuum  is  produced;  by  means  of  the  same  cock,  the 
connection  with  the  machine  being  cut  off,  but  established  between  M 
and  N,  the  gas  soon  fills  the  globe.     But  as  the  exhaustion  could  not 


-314]  Density  of  Gases.  261 

have  been  complete,  and  some  air  must  have  been  left,  the  globe  is  again 
exhausted  and  the  air  allowed  to  enter,  and  the  process  repeated  until  it 
is  thought  all  air  is  removed.  The  globe  being  once  more  produced,  a 
differential  barometer  (fig.  113),  connected  with  the  apparatus  by  the 
tube  E,  indicates  the  pressure  of  the  residual  rarefied  gas  e.  Closing  the 
cock  B  and  detaching  A,  the  globe  is  removed  from  the  ice,  and  after 
being  cleaned  is  weighed. 

This  gives  the  weight  of  the  empty  globe  /  ;  it  is  again  replaced  in 
the  ice,  the  stopcock  A  adjusted,  and  the  gas  allowed  to  enter,  care  being 
taken  to  leave  the  stopcocks  open  long  enough  to  allow  the  gas  in  the 
globe  to  acquire  the  pressure  of  the  atmosphere,  which  is  marked  by  the 
barometer  H.  The  stopcock  B  is  then  closed,  A  removed,  and  the  globe 
weighed  with  the  same  precautions  as  before.  This  gives  the  weight  Pj 
of  the  gas. 

The  same  operations  are  then  repeated  on  this  globe  with  air,  and  two 
corresponding  weights  p  and  P  are  obtained.  The  only  correction 
necessary  is  to  reduce  the  weights  in  the  two  cases  to  the  standard 
pressure  by  the  method  described  in  the  preceding  paragraph.  The 
correction  for  temperature  is  not  needed,  as  the  gas  is  at  the  temperature 
of  melting  ice.  The  ratio  of  the  weight  of  the  gas  to  that  of  the  air  is 
thus  obtained  by  the  formula 

p-p 

314.  Bensity  of  grases  which  attack  metals. — For  gases  which 
attack  the  ordinary  metals,  such  as  chlorine,  a  metal  stopcock  cannot  be 
used,  and  vessels  with  ground  glass  stoppers  are  substituted.  The  gas  is 
introduced  by  a  bent  glass  tube,  the  vessel  being  held  either  upright  or 
inverted,  according  as  the  gas  is  heavier  or  lighter  than  air ;  when  the 
vessel  is  supposed  to  be  full,  the  tube  is  withdrawn,  the  stopper  inserted, 
and  the  weight  taken.  This  gives  the  weight  of  the  vessel  and  gas.  If 
the  capacity  of  the  vessel  be  measured  by  means  of  water,  the  weight  of 
the  air  which  it  contains  is  deduced,  for  the  density  of  air  at  0°  C.  and 
760  millimetres  pressure  is  y}^  that  of  distilled  water  under  the  same  cir- 
cumstances. The  weight  of  the  vessel  full  of  air,  less  the  weight  of  the 
contained  air,  gives  the  weight  of  the  vessel  itself  From  these  three  data 
— the  weight  of  the  vessel  full  of  the  gas,  the  weight  of  the  air  which  it 
contains,  and  the  weight  of  the  vessel  alone — the  specific  gravity  of  the 
gas  is  readily  deduced,  the  necessary  corrections  being  made  for  tempe- 
rature and  pressure. 

Dcfisity  of  gases  at  zero  aiid  at  a  pressure  of  'j^yo"  millimetres^  that  of  air 


being  taken  as  unity. 

Air      .         .         . 

I  -OOGO 

Nitrogen    . 

■     0-9714 

Hydrogen    . 

.     0-0693 

Binoxide  of  nitrogen 

.     1-0360 

Marsh  gas  . 

.     0-5590 

Oxygen     . 

.     1-1057 

Ammoniacal  gas 

.     0-5367 

Sulphuretted  hydrogen 

.     1-1912 

Carbonic  oxide   . 

.     0-9670 

Hydrochloric  acid      . 

.     1-2540 

262  On  HeaL  [314- 

Density  of  gases  at  zero — continued. 

Protoxide  of  nitrogen  .  1-5270  Sulphurous  acid  .  .  2-2474 
Carbonic  acid  .  .  .  J -5291  Chlorine  ....  3*4400 
Cyanogen  ....     i-86oo     Hydriodic  acid  .         .         .     4*4430 

Regnault  has  furnished  the  following  determinations  of  the  weight  of  a 
litre  of  the  most  important  gases  at  0°  C.-and  760  mm.:  — 

Air  .  .  .  1-293187  grms.  Nitrogen  .  .  1-256167  grms. 
Oxygen  .         .     1*429802  Carbonic  acid        .     1-9774 14 

Hydrogen     .         .     0*089578 


CHAPT^K^f  '  - 

CHANGES   OF   CONtkJTION.      VAPOURS. 

315.  Fusion.  Its  laws. — The  only  phenomena  of  heat  with  which  we 
have  hitherto  been  engaged  have  been  those  of  expansion.  In  the  case 
of  solids  it  is  easy  to  see  that  this  expansion  is  limited.  For  in  proportion 
as  a  body  absorbs  a  larger  quantity  of  heat,  the  repulsive  force  between 
the  molecules  is  increased,  and  ultimately  a  point  is  reached  at  which  the 
molecular  attraction  is  not  sufficient  to  retain  the  body  in  the  solid  state. 
A  new  phenomenon  is  then  produced  :  fusion  takes  place  ;  that  is,  the 
body  passes  from  the  solid  into  the  liquid  state. 

Some  substances,  however,  such  as  paper,  wood,  wool,  and  certain  salts, 
do  not  fuse  at  a  high  temperature,  but  are  decomposed.  Many  bodies 
have  long  been  considered  refractory  \  that  is,  incapable  of  fusion  ;  but, 
in  proportion  as  it  has  been  possible  to  produce  higher  temperatures,  their 
number  has  diminished.  Gaudin  has  succeeded  in  fusing  rock  crystal  by 
means  of  a  lamp  fed  by  a  jet  of  oxygen  ;  and  more  recently  Despretz,  by 
combining  the  effects  of  the  sun,  the  voltaic  battery,  and  the  oxy-hydro- 
gen  blow-pipe,  has  melted  alumina  and  magnesia,  and  softened  carbon, 
so  as  to  be  flexible,  which  is  a  condition  near  that  of  fusion. 

It  has  been  experimentally  found  that  the  fusion  of  bodies  is  governed 
by  the  two  following  laws  : — 

I.  Every  substance  begins  to  fuse  at  a  certain  temper  attire^  which  is  in- 
variable for  each  substance  if  the  pressure  be  constant. 

II.  Whatever  be  the  intensity  of  the  source  of  heat,  from  the  7noment 
fusion  cojnmences,  the  temperature  of  the  body  ceases  to  rise,  and  remains 

constant  until  the  fusion  is  complete. 

Fusing  points  of  certain  substances. 

Mercury        .         .         .         .  —  38-8°  Phosphorus      .  .  .  -44 

Bromine        .         .         .         .  —  12-5°  Spermaceti       .  .  .  -49 

Ice o  Potassium        .  .  .  •     ^S 

Butter    .         .         .        .         .  +  33  Margaric  acid  .  .  .     S7 


316] 


^ 


Changes  of  Condition.  * 

Fusing  point  of  certain  sul^stances — continued. 


V 


Stearine 

White  wax     . 

Wood's  fusible  metal 

Stearic  acid  . 

Sodium 

Rose's  fusible  metal 

Sulphur 

Tin       . 


60 

Bismuth 

65 

Cadmium     . 

68 

Lead   . 

70 

Zinc     . 

90 

Antimony     . 

94 

Silver  . 

114 

Gold     . 

228 

Iron      . 

263 


264 

321 

335 

422 

450 

1000 

1250 

1500 


Some  substances  pass  from  the  solid  to  the  liquid  state  without  showing 
any  definite  melting  point  ;  for  example,  glass  and  iron  become  gra- 
dually softer  and  softer  when  heated  and  pass  by  imperceptible  stages 
from  the  solid  to  the  liquid  condition.  This  intermediate  condition  is 
spoken  of  as  the  state  oivitreoits  fusion.  Such  substances  may  be  said 
to  melt  at  the  lowest  temperature  at  w4iich  perceptible  softening  occurs, 
and  to  be  fully  melted  when  the  further  elevation  of  temperature  does  not 
make  them  more  fluid  ;  but  no  precise  temperature  can  be  given  as  their 
melting  points. 

316.  Influence  of  pressure  on  the  melting:  point. — Thomson  and 
Clausius  have  deduced  from  the  principles  of  the  mechanical  theory  of  heat 
that,  with  an  increase  of  pressure,  the  melting  point  of  a  body  must  be  raised* 
All  bodies  which  expand  on  passing  from  the  solid  to  the  liquid  state 
have  to  perform  external  work — namely,  to  raise  the  power  of  the  atmo- 
sphere by  the  amount  of  this  expansion.  Under  ordinary  circumstances, 
the  amount  of  external  work  which  solids  and  liquids  thus  perform  is  so 
small  that  it  may  be  neglected.  But  if  the  external  pressure  be  increased, 
the  power  of  overcoming  it  can  only  be  obtained  by  an  increase  of 
vis  viva  of  the  molecules.  This  increase  can  do  more  work  ;  the  tempera- 
ture of  fusion  as  well  as  the  heat  of  fusion  are  both  increased.  Thus 
Bunsen  found  that  spermaceti,  which  melts  at  48°  under  a  pressure  of 
I  atmosphere,  melis  at  51°  under  a  pressure  of  156  atmospheres.  Hopkins 
found  that  spermaceti  melted  at  60°  under  a  pressure  of  519  atmospheres, 
and  at  80°  under  792  atmospheres  ;  the  melting  point  of  sulphur  under 
these  pressures  was  respectively  135^^  and  141°. 

But  in  the  case  of  those  bodies  which  contract  on  passing  from  the 
solid  to  the  liquid  state,  and  of  which  water  is  the  best  example,  the 
reverse  is  the  case.  Melting  ice  has  no  external  work  to  perform,  since 
it  has  no  external  pressure  to  raise  ;  on  the  contrary,  in  melting  it 
assimilates  external  work  which,  transformed  into  heat,  renders  a  smaller 
quantity  of  heat  necessary  ;  the  external  work  acts  in  the  same  direction 
as  the  internal  heat — namely,  in  breaking  up  the  crystalline  aggregates. 
Yet  these  differences  of  temperature  must  be  but  small,  for  the  molecular 
forces  in  solids  preponderate  far  oveir  the  external  pressure  ;  the  internal 
work  is  far  greater  than  the  external. 

Sir  W.  Thomson  found  that  pressures  of  S'l  and  i6-8  atmospheres 
low^ered  the  melting  point  of  ice  by  0-059^  and  0-126°"  respectively.    These 


264  ♦»  On  Heat.  [316- 

results  justify  the  theoretical  previsions  of  Prof.  T.  Thomson,  according 
to  which  an  increase  of  pressure  of  7t  atmospheres  lowers  the  melting 
point  of  ice  by  0-0074;^°  C. 

317.  Alloys.  Fluxes. — Alloys  are  generally  more  fusible  than  either 
of  the  metals  of  which  they  are  composed  ;  for  instance,  an  alloy  of  five 
parts  of  tin  and  one  of  lead  fuses  at  194°.  The  alloy  known  as  Rosens 
fusible  metal,  which  consists  of  4  parts  of  bismuth,  i  part  of  lead,  and  i 
of  tin,  melts  at  94°,  and  an  alloy  of  i  or  2  parts  of  cadmium  with  2  parts 
of  tin,  4  parts  of  lead,  and  7  or  8  parts  of  bismuth,  known  as  Wood's  fusible 
metal,  melts  between  66°  and  71°  C.  Fusible  alloys  are  of  extended 
use  in  soldering  and  in  taking  casts.  Steel  melts  at  a  lower  temperature 
than  iron,  though  it  contains  carbon,  which  is  almost  completely  in- 
fusible. 

Mixtures  of  the  fatty  acids  melt  at  lower  temperatures  than  the  pure 
acids.  A  mixture  of  the  chlorides  of  potassium  and  of  sodium  fuses 
at  a  lower  temperature  than  either  of  its  constituents  ;  the  same  is  the 
case  with  a  mixture  of  the  carbonates  of  potassium  and  sodium, 
especially  when  they  are  mixed  in  the  proportion  of  their  chemical 
equivalents. 

An  application  of  this  property  is  met  with  in  the  case  oi fluxes,  which 
are  much  used  in  metallurgical  operations.  They  consist  of  substances 
which,  when  added  to  an  ore,  partly  by  their  chemical  action,  help  the 
reduction  of  the  substance  to  the  metallic  state,  and,  partly  by  presenting 
a  readily  fusible  medium,  promote  the  formation  of  a  regulus. 

318.  Ziatent  heat. — Since,  during  the  passage  of  a  body  from  the  soHd 
to  the  liquid  state,  the  temperature  remains  constant  until  the  fusion  is 
complete,  whatever  be  the  intensity  of  the  source  of  heat,  it  must  be  con- 
cluded that,  in  changing  their  condition,  bodies  absorb  a  considerable 
amount  of  heat,  the  only  effect  of  which  is  to  maintain  them  in  the  liquid 
state.  This  heat,  which  is  not  indicated  by  the  thermometer,  is  called 
latent  heat  or  latent  heat  of  fusion,  an  expression  which,  though  not  in 
strict  accordance  with  modern  ideas,  is  convenient  from  the  fact  of  its 
universal  recognition  and  employment  (432). 

An  idea  of  what  is  meant  by  latent  heat  may  be  obtained  from  the  fol- 
lowing experiment.  If  a  pound  of  water  at  80°  is  mixed  with  a  pound  of 
water  at  zero,  the  temperature  of  the  mixture  is  40°.  But  if  a  pound  of 
pounded  ice  at  zero  is  mixed  with  a  pound  of  water  at  80°,  the  ice  melts, 
and  two  pounds  of  water  at  zero  are  obtained.  Consequently,  the  mere 
change  of  a  pound  of  ice  to  a  pound  of  water  at  the  same  temperature  re- 
quires as  much  heat  as  will  raise  a  pound  of  water  through  80°.  This 
quantity  of  heat  represents  the  latent  heat  of  the  fusion  of  ice,  or  the  latent 
heat  of  water. 

Every  liquid  has  its  own  latent  heat,  and  in  the  chapter  on  Calorimetry 
we  shall  show  how  this  is  determined. 

319.  Solution. — A  body  is  said  to  dissolve  when  it  becomes  liquid  in 
consequence  of  an  affinity  between  its  molecules,  and  those  of  a  liquid. 
Gum  arabic,  sugar,  and  most  salts  dissolve  in  water. 

During  solution,  as  well  as  during  fusion,  a  certain  quantity  of  heat 


-322]  Solidification.  265 

always  becomes  latent,  and  hence  it  is  that  the  solution  of  a  substance 
usually  produces  a  diminution  of  temperature.    In  certain  cases,  however,  — 

instead  of  the  temperature  being  lowered,  it  actually  rises,  as  when  caustic 
potass  is  dissolved  in  water.  This  depends  upon  the  fact  that  two  simul- 
taneous and  contrary  phenomena  are  produced.  The  first  is  the  passage 
from  the  solid  to  the  liquid  condition,  which  always  lowers  the  tempera- 
ture. The  second  is  the  chemical  combination  of  the  body  dissolved  with 
the  liquid,  and  which,  as  in  the  case  of  all  chemical  combinations,  pro- 
duces an  increase  of  temperature.  Consequently,  as  the  one  or  the  other 
of  these  effects  predominates,  or  as  they  are  equal,  the  temperature  either 
rises,  or  sinks,  or  remains  constant. 

320.  Solidification. — Solidification  or  congelation  is  the  passage  of  a 
body  from  the  liquid  to  the  solid  state.  This  phenomenon  is  regulated 
by  the  two  following  laws  : — 

I.  Every  body,  tinder  the  same  pressure ,  solidifies  at  a  fixed  temper a- 
ture,  which  is  the  same  as  that  of  fusion. 

II.  From  the  cojnmencement to  the  etidofthe  solidification,  the  tempera- 
ture of  a  liquid  7'emains  constant. 

Certain  bodies,  more  especially  some  of  the  fats,  present  an  exception 
to  the  first  law,  in  so  far  that  by  repeated  fusions  they  seem  to  undergo  a 
molecular  change  which  alters  their  melting  point. 

The  secoifd  law  is  a  consequence  of  the  fact  that  the  latent  heat  ab- 
sorbed during  fusion  becomes  free  at  the  moment  of  solidification. 

Many  liquids,  such  as  alcohol,  ether,  and  bisulphide  of  carbon,  do  not 
solidify  even  at  the  lowest  known  temperature.  But  M.  Despretz,  by  the 
cold  produced  by  a  mixture  of  liquid  protoxide  of  nitrogen,  solid  carbonic 
acid,  and  ether,  has  reduced  alcohol  to  such  a  consistence  that  the.vessel 
containing  it  could  be  inverted  without  losing  the  liquid. 

321.  Crystallisation. — Generally  speaking,  bodies  which  pass  slowly 
from  the  liquid  to  the  solid  state  assume  regular  geometrical  forms,  such 
as  the  cube,  prisms,  rhombohedra,  &c.  ;  these  are  called  crystals.  If 
the  crystals  are  formed  from  a  body  in  fusion,  such  as  sulphur  or  bismuth, 
the  crystallisation  is  said  to  take  place  by  the  dry  way.  But  if  the  crys- 
tallisation takes  place  owing  to  the  slow  evaporation  of  a  solution  of  a 
salt,  it  is  said  to  be  by  the  moist  way.  Snow,  ice,  and  many  salts  present 
examples  of  crystallisation. 

322.  Retardation  of  the  point  of  solidification. — The  freezing  point 
of  pure  water  can  be  diminished  by  several  degrees,  if  the  water  be  pre- 
viously freed  from  air  by  boiling  and  be  then  kept  in  a  perfectly  still  place. 
In  fact  it  may  be  cooled  to  —  15°  C,  and  even  lower,  without  freezing. 
But  when  it  is  slightly  agitated,  the  liquid  at  once  solidifies.  The  smaller 
the  quantity  of  Hquid  the  lower  the  temperature  to  which  it  can  be  cooled, 
and  the  greater  the  mechanical  disturbance  it  supports  without  freezing, 
Fournet  has  observed  the  frequent  occurrence  of  mists  formed  of  particles 
of  liquid  matter  suspended  in  an  atmosphere  whose  temperature  is  10°  or 
even  15°  below  zero. 

A  very  rapid  agitation  also  prevents  the  formation  of  ice.  The  same 
is  the  case  with  all  actions  which,  hindering  the  molecules  in  theirmove- 

A— ./^ 


266  On  Heat  [322- 

ments,  do  not  permit  them  to  arrange  themselves  in  the  conditions  neces- 
sary for  the  sohd  state.  M.  Despretz  was  able  to  lower  the  temperature 
of  water  contained  in  fine  capillary  tubes  to  —  20°  without  their  solidi- 
fying. This  experiment  shows  how  it  is  that  plants  in  many  cases  do  not 
become  frozen,  as  the  sap  is  contained  in  very  fine  capillary  vessels. 
Finally,  M.  Mousson  has  found  that  a  powerful  pressure  not  only  retards 
the  freezing  of  water,  but  prevents  its  complete  solidification.  In  this 
case  the  pressure  opposes  the  tendency  of  the  water  to  expand  on  freezing 
and  thus  virtually  lowers  the  point  of  solidification. 

If  water  contains  salts  or  other  foreign  bodies  its  freezing  point  is  low- 
ered. Sea  water  freezes  at  —2-5°  to  —3°  C. ;  the  ice  which  forms  is  quite 
pure,  and  a  saturated  solution  remains.  In  Finland,  advantage  is  taken 
of  this  property  to  concentrate  sea  water  for  the  purpose  of  extracting  salt 
from  it.  If  water  contains  alcohol,  precisely  analogous  phenomena  are 
observed  ;  the  ice  formed  is  pure,  and  practically  all  the  alcohol  is  con- 
tained in  the  residue. 

Dufour  has  observed  some  very  curious  cases  of  liquids  cooled  out  of 
contact  with  solid  bodies.  His  mode  of  experimenting  was  to  place  the 
liquid  in  another  of  the  same  specific  gravity  but  of  lower  melting  point, 
and  in  which  it  is  insoluble.  Spheres  of  water  for  instance,  suspended 
in  a  mixture  of  chloroform  and  oil,  usually  solidified  between— 4°  and 
—  12°,  while  some  smaller  globules  cooled  down  to  —  18°  or.  — 20°.  Con- 
tact with  a  fragment  of  ice  immediately  set  up  congelation.  Globules  of 
sulphur  (which  solidifies  at  1 1 5°)  remained  liquid  at  40° ;  and  globules  of 
phosphorus  (solidifying  point  42°)  at  20°. 

When  a  liquid  solidifies  after  being  cooled  below  its  normal  freezing 
point,  the  solidification  takes  place  very  rapidly,  and  is  accompanied  by  a 
disengagement  of  heat,  which  is  sufficient  to  raise  its  temperature  from 
the  point  at  which  solidification  begins  up  to  its  ordinary  freezing  point. 
This  is  well  seen  in  the  case  of  hyposulphite  of  sodium,  which  melts  in  its 
own  water  of  crystallisation  at  45°,  and  when  carefully  cooled  will  remain 
liquid  at  the  ordinary  temperature  of  the  atmosphere.  If  it  then  be  made 
to  solidify  by  agitation,  or  by  adding  a  small  fragment  of  the  solid  salt, 
the  rise  of  temperature  is  distinctly  felt  by  the  hand.  In  this  case  the 
heat  which  had  become  latent  in  the  process  of  liquefaction  again  becomes 
free,  and  a  portion  of  the  substance  remains  melted  ;  for  it  is  kept  liquid 
by  the  heat  of  sohdification  of  that  which  has  solidified. 

323.  Cbangre  of  volume  on  solidification  and  liquefaction. — The 
rate  of  expansion  of  bodies  generally  increases  as  they  approach  their 
melting  points,  and  is  in  most  cases  followed  by  a  further  expansion  at 
the  moment  of  liquefaction,  so  that  the  liquid  occupies  a  greater  volume 
than  the  solid  from  which  it  is  formed.  Phosphorus,  for  instance,  increases 
about  3-4  per  cent,  on  liquefaction  ;  that  is,  100  volumes  of  solid  phos- 
phorus at  44°  (the  melting  point)  become  103-4  at  the  same  temperature 
when  melted.  Sulphur  expands  about  5  per  cent,  on  liquefying,  and 
stearic  acid  about  1 1  per  cent. 

Water  presents  a  remarkable  exception  ;  it  expands  on  the  moment  of 
solidifying,  or  contracts  on  melting,  by  about  ten  per  cent.   One  volume  of 


-324]  Freezing  Mixtures.  267 

ice  at  0°  gives  0-9178  of  water  at  0°,  or  i  volume  of  water  at  0°  gives  :-io2 
of  ice  at  the  same  temperature.  In  consequence  of  this  expansion,  ice 
floats  on  the  surface  of  water.  According  to  Dufour  the  specific  gravity 
of  ice  is  0-9178  ;  Bunsen  found  for  ice  which  had  been  freed  from  water 
by  boiling  the  somewhat  smaller  number  0-91674. 

The  increase  of  volume  in  the  formation  of  ice  is  accompanied  by  an 
expansive  force  which  sometimes  produces  powerful  mechanical  effects, 
of  which  the  bursting  of  water-pipes  and  the  breaking  of  jugs  containing 
water  are  familiar  examples.  The  splitting  of  stones,  rocks,  and  the 
swelling  up  of  moist  ground  during  frost,  are  caused  by  the  fact  that  water 
penetrates  into  the  pores  and  there  becomes  frozen  ;  in  short,  the  great 
expansion  of  water  on  freezing  is  the  most  active  and  powerful  agent  of 
disintegration  on  the  earth's  surface. 

The  expansive  force  of  ice  was  strikingly  shown  by  some  experiments 
of  Major  Williams,  in  Canada.  Having  quite  filled  a  13-inch  iron  bomb- 
shell with  water,  he  firmly  closed  the  touch- hole  with  an  iron  plug 
weighing  three  pounds,  and  exposed  it  in  this  state  to  the  frost.  After  some 
time  the  iron  plug  was  forced  out  with  a  loud  explosion,  and  thrown  to  a 
distance  of  415  feet,  and  a  cylinder  of  ice  8  inches  long  issued  from  the 
opening.  In  another  case  the  shell  burst  before  the  plug  was  driven  out, 
and  in  this  case  a  sheet  of  ice  spread  out  all  round  the  crack.  It  is  pos- 
sible that  under  the  great  pressure  some  of  the  water  still  remained  liquid 
up  to  the  time  at  which  the  resistance  was  overcome  ;  that  it  then  issued 
from  the  shell  in  a  liquid  state,  but  at  a  temperature  below  0°,  and  there- 
fore instantly  began  to  solidify  when  the  pressure  was  removed,  and  thus 
retained  the  shape  of  the  orifice  whence  it  issued. 

Cast-iron,  bismuth,  and  antimony  expand  on  solidifying  like  water,  and 
can  thus  be  used  for  casting  ;  but  gold,  silver,  and  copper  contract,  and 
hence  coins  of  these  metals  cannot  be  cast,  but  must  be  stamped  with  a 
die. 

324.  Freezingr  mixtures. — The  absorption  of  heat  in  the  passage  of 
bodies  from  the  solid  to  the  liquid  state  has  been  used  to  produce  artificial 
cold.  This  is  effected  by  mixing  together  bodies  which  have  an  affinity 
for  each  other,  and  of  which  one  at  least  is  solid,  such  as  water  and  a 
salt,  ice  and  a  salt,  or  an  acid  and  a  salt.  Chemical  affinity  accelerates 
the  fusion  :  the  portion  which  melts  robs  the  rest  of  the  mixture  of  a  large 

i quantity  of  sensible  heat,  which  thus  becomes  latent.     In  many  cases  a 
very  considerable  diminution  of  temperature  is  produced. 
The  following  table  gives  the  names  of  the  substances  mixed,  their  pro- 
portions, and  the  corresponding  diminutions  of  temperature  : — 
i 


Substances  ^^'"'^  Reduction  of 

Substances  by  weight.  temperature. 

Sulphate  of  sodium      .         .         .     8  . 

TT   J      ui     •         J  _  h     .     .     .      -h  10"  to 

Hydrochloric  acid 

Pounded  ice  or  snow  . 

Common  salt 

Sulphate  of  sodium     . 

Dilute  nitric  acid 


j}     .     .     .      +10°  to  -18= 
H     .     .     .     +io°to  -19= 


26S  On  Heat.  [324- 


071  Heat. 

Substances. 

Sulphate  of  sodium     . 
Nitrate  of  ammonium . 
Dilute  nitric  acid 
Phosphate  of  sodium  . 
Dilute  nitric  acid 

Parts 
by  weight. 

.     6- 

.    5  ■     .    . 
.    4J 

•    9". 

.    4J      '    ' 

Reduction  of 
temperature. 

.        +10°  to    -2 
.        +  10°  to    -2 

26° 

29° 

If  the  substances  taken  be  themselves  first  previously  cooled  down,  a 
still  more  considerable  diminution  of  temperature  is  occasioned. 

Freezing  mixtures  are  frequently  used  in  chemistry,  in  physics,  and  in 
domestic  economy.  The  portable  ice-making  machines  which  have  come 
into  use  during  the  last  i&'N  years  consist  of  a  cylindrical  metallic  vessel 
divided  into  four  concentric  compartments.  In  the  central  one  is  placed 
the  water  to  be  frozen  ;  in  the  next  there  is  the  freezing  mixture,  which 
usually  consists  of  sulphate  of  sodium  and  hydrochloric  acid  ;  6  pounds  of 
the  former  and  5  of  the  latter  will  make  5  to  6  pounds  of  ice  in  an  hour. 
The  third  compartment  also  contains  water,  and  the  outside  one  contains 
some  badly-conducting  substance,  such  as  cotton  to  prevent  the  influence- 
of  the  external  temperature.  The  best  effect  is  obtained  when  pretty 
large  quantities  (2  or  3  pounds)  of  the  mixture  are  used,  and  when  they 
are  intimately  mixed.  It  is  also  advantageous  to  use  the  machines  for  a 
series  of  successive  operations. 


VAPOURS.      MEASUREMENT  OF  THEIR  TENSION. 

325.  Vapours. — We  have  already  seen  (141)  that  vapours  are  the 
aeriform  fluids  into  which  volatile  substances,  such  as  ether,  alcohol, 
water,  and  mercury,  are  changed  by  the  absorption  of  heat.  Volatile 
liquids  are  those  which  thus  possess  the  property  of  passing  into  the 
aeriform  state,  dcadi  fixed  liquids,  those  which  do  not  form  vapours  at  any 
temperature  without  undergoing  chemical  decomposition,  'such  as  the 
fatty  oils.  There  are  some  solids,  such  as  ice,  arsenic,  camphor,  and  in 
general  all  odoriferous  solid  substances,  which  can  directly  form  vapours 
without  first  becoming  liquid. 

Vapours  are  transparent  like  gases,  and  generally  colourless  :  there  are 
only  a  few  coloured  liquids,  which  also  give  coloured  vapours. 

326.  Vaporisation. — The  passage  of  a  liquid  into  the  gaseous  state  is 
designated  by  the  general  term  vaporisation  ;  the  term  evaporation  espe- 
cially refers  to  the  slow  production  of  vapour  at  the  free  surface  of  a 
liquid,  and  boiling  to  its  rapid  production  in  the  mass  of  the  liquid  itself. 
We  shall  presently  see  (339)  that  at  the  ordinary  atmospheric  pressure, 
ebulhtion,  like  fusion,  takes  place  at  a  definite  temperature.  This  is  not 
the  case  with  evaporation,  which  takes  place  even  with  the  same  liquid  at 
very  different  temperatures,  although  the  formation  of  a  vapour  seems  to 
cease  below  a  certain  point.  Mercury,  for  example,  gives  no  vapour 
below—  10°,  nor  sulphuric  acid  below  30°. 


-329] 


Vapours. 


269 


» 


327.  Elastic  force  of  vapours. — Like  gases,  vapours  have  a  certain 
elastic  force,  in  virtue  of  which  they  exert  pressures  on  the  sides  ot 
vessels  in  which  they  are  contained.     The  tension 

of  vapours  may  be  demonstrated  by  the  following 
experiment  :— A  quantity  of  mercury  is  placed  in  a 
bent  glass  tube  (fig.  254  rt),  the  shorter  leg  of  which 
is  closed ;  a  few  drops  of  ether  are  then  passed 
into  the  closed  leg,  and  the  tube  immersed  in  a 
water  bath  at  a  temperature  of  about  45°.  The 
mercury  then  sinks  slowly  in  the  short  branch,  and 
the  space  ab  is  filled  with  a  gas  which  has  alL  the 
appearance  of  air,  and  whose  elastic  force  counter- 
balances the  pressure  of  the  column  of  mercury  cd, 
and  the  atmospheric  pressure  on  d.  This  gas  is 
the  vapour  of  ether.  If  the  water  be  cooled,  or  if 
the  tube  be  removed  from  the  bath,  the  vapour 
which  fills  the  space  ab  disappears,  and  the  drop  of 
ether  is  reproduced.  If,  on  the  contrary,  the  bath 
be  heated  still  higher,  the  level  of  the  mercury 
descends  below  b,  indicating  an  increased  tension. 

328.  Formation  of  vapours  in  a  vacuum. — In 
the  previous  experiment  the  liquid  changed  very 
slowly  into  the  vaporous  condition  ;  the  same  is  the 
case  when  a  liquid  is  freely  exposed  to  the  air.  In 
both  cases  the  atmosphere  is  an  obstacle  to  the 
vaporisation.  In  a  vacuum  there  is  no  resistance, 
and  the  formation  of  vapours  is  instantaneous,  as  is  seen  in  the  following 
experiment : — Four  barometer  tubes,  filled  with  mercury,  are  immersed 
in  the  same  trough  (fig.  255).  One  of  them.  A,  serves  as  a  barometer, 
and  a  few  drops  of  water,  alcohol,  and  ether  are  respectively  introduced 
into  the  tubes,  B,  C,  D.  When  the  liquids  reach  the  vacuum,  a  depres- 
sion of  the  mercury  is  at  cmce  produced  And  as  this  depression 
cannot  be  produced  by  the  weight  of  the  liquid,  which  is  an  infinitely 
small  fraction  of  the  weight  of  the  displaced  mercury,  it  must  be  due  to 
the  formation  of  some  vapour  whose  elastic  force  has  depressed  the 
mercurial  column. 

The  experiment  also  shows  that  the  depression  is  not  the  same  in  all 
the  tubes  ;  it  is  greater  in  the  case  of  alcohol  than  of  water,  and  greater 
with  ether  than  with  alcohol.  We  con/equently  obtain  the  two  following 
laws  for  the  formation  of  vapours 

\.  In  a  vaaiutn  all  volatile  liquiiis  are  instantaneously  co?iverted  into 
vapour. 

11.  At  the  satne  temperature  ihe  vapours  of  different  liquids  have 
different  elastic  forces. 

For  example,  at  20°  the  tension  of  ether  vapour  is  25  times  as  great  as 
that  of  aqueous  vapour. 

329.  Saturated  vapours.  Maximum  of  tension. — When  a  very 
small  quantity  of  a  volatile  liquid,  such  as  ether,  is  introduced  into  a 


Fig.  254  a. 


70 


On  Heat, 


[329- 


barometer  tube,  it  is  at  once  completely  vaporised,  and  the  mercurial 
column  is  not  depressed  to  its  full  extent ;  for  if  some  more  ether  be  in- 
troduced the  depression  increases.  By  continuing  the  addition  of  ether, 
it  finally  ceases  to  vaporise,  and  remains  in  the  liquid  state.     There  is, 

therefore,  for  a  certain    temperature,   a 

L  limit  to  the  quantity  of  vapour  which  can 
A  B  E  c  10  be  formed  in  a  given  space.     This  space 
1  jl       ■  is    accordingly    said     to    be     sattu^ated. 
Jfj  Further,   when    the   vaporisation   of    the 
ll  H  j   i                    ether  ceases,  the  depression  of  the  mer 
■MMfc^                 curial  column  stops.     And  hence  there  is 

a  limit  to  the  tension  of  the  vapour,  a 
limit  which,  as  we  shall  presently  see 
(332),  varies  with  the  temperature,  but 
which  for  a  given  temperature  is  inde- 
pendent of  the  pi'cssure. 

To  show  that,  in  a  closed  space,  satur- 
ated with  vapour  and  containing  liquid 
in  excess,  the  temperature  remaining  con- 
stant, there  is  a  maximum  of  tension 
which  the  vapour  cannot  exceed,  a  baro- 
metric tube  is  used  which  dips  in  a  deep 
bath  (fig.  256).  This  tube  is  filled  with 
mercury,  and  then  so  much  ether  is  added 
as  to  be  in  excess  after  the  Torricellian 
vacuum  is  saturated.  The  height  of  the 
mercurial  column  is  next  noted  by  means 
of  the  scale  graduated  on  the  tube  itself. 
Now,  whether  the  tube  be  depressed, 
p.._^  ^  which  tends  to  compress  the  vapour,  or 

whether  it  be  raised,  which  tends  to  ex- 
pand it,  the  height  of  the  mercurial  column  is  constant.  The  tension  of 
the  vapour  remains  constant  in  the  two  cases,  for  the  depression  neither 
increases  nor  diminishes  it.  Hence  it  is  concluded  that  when  the  satu- 
rated vapour  is  compressed,  a  portion  returns  to  the  liquid  state  ;  that 
when,  on  the  other  hand,  the  pressure  is  diminished,  a  portion  of  the  ex- 
cess of  liquid  vaporises,  and  the  space  occupied  by  the  vapour  is  again 
saturated  ;  but  in  both  cases  the  tension  and  the  density  of  the  vapour 
remain  constant. 

330.  xron-saturated  vapours. — From  what  has  been  said,  vapours 
present  two  very  different  states,  according  as  they  are  saturated  or  not. 
In  the  first  case,  where  they  are  saturated  and  in  contact  with  the  liquid, 
they  differ  completely  from  gases,  since  for  a  given  temperature  they  can 
neither  be  compressed  nor  expanded  ;  their  elastic  force  and  their  den- 
sity remain  constant. 

In  the  second  case,  on  the  contrary,  where  they  are  not  saturated,  they 
exactly  resemble  gases.  For  if  the  experiments  (fig.  256)  be  repeated, 
only  a  small  quantity  of  ether  being  introduced,   so  that  the  vapour  is 


330] 


Non-saturated  Vapours, 


271 


not  saturated,  and  if  the  tube  be  then  sh'ghtly  raised,  the  level  of  the 
mercury  is  seen  to  rise,  which  shows  that  the  elastic  force  of  the  vapour 
has  diminished.  Similarly,  by  immersing  the  tube  still  more,  the  level  of 
the  mercury  sinks.     The  vapo.ir  consequently  behaves  just  as  a  gas  would 


Fig.  256. 


Fig.  257. 


do;  its  tension  diminishes  when  the  volume  increases,  and  vice  versa  ;  and 
as  in  both  cases  the  volume  of  the  vapour  is  inversely  as  the  pressure, 
it  is  concluded  that  non-saturated  vapours  obey  Boyte's  taw. 

When  a  non-saturated  vapour  is  heated,  its  volume  increases  like  that 
of  a  gas  ;  and  the  number  0-00366,  which  is  the  coefficient  of  the  expan- 
sion of  air,  may  be  taken  for  that  of  vapours. 

Hence  we  see  that  the  physical  properties  of  unsaturated  vapours  are 
comparable  with  those  of  permanent  gases,  and  that  the  formulae  for  the 
compressibility  and  expansibility  of  gases  (168  and  309)  also  apply  to 
unsaturated  vapours.  But  it  must  not  be  forgotten  that  there  is  always 
a  limit  of  pressure  or  of  cooling  at  which  unsaturated  vapours  pass  into  a 
state  of  saturation,  and  that  they  have  then  a  maximum  of  tension  and 


4-941 

millimetres. 

2-o8 

>j 

0-84 

» 

036 

J) 

"272  On  Heat.  [330- 

density  which  can  only  be  exceeded  when  the  temperature  rises  while 
they  are  in  contact  with  the  liquid. 

331.  Tension  of  aqueous  vapour  below  zero. — For  the  sake  of 
measuring  the  elastic  force  of  aqueous  vapour  below  zero,  Gay-Lussac 
used  two  barometer  tubes  filled  with  mercury,  and  placed  in  the  same 
bath  (fig.  257).  The  straight  tube  A  serves  as  a  barometer  ;  the  other 
B,  is  iDent,  so  that  part  of  the  Torricellian  vacuum  can  be  surrounded  by 
a  freezing  mixture  (324).  When  a  little  water  is  admitted  into  the  bent 
tube,  the  level  of  the  mercury  sinks  below  that  in  the  tube  A  to  an  extent 
which  varies  with  the  temperature  of  the  freezing  mixture. 

At      0°  the  depression  is 
„  — 10  „        „ 

-20° 

These  depressions,  which  must  be  due  to  the  tension  of  aqueous  vapour 
in  the  space  BC,  show  that  even  at  very  low  temperatures  there  is  always 
some  aqueous  vapour  in  the  atmosphere. 

Although  in  the  above  experiment  the  part  B  and  the  part  C  are  not 
both  immersed  in  the  freezing  mixture,  we  shall  presently  see  that  when 
two  communicating  vessels  are  at  different  temperatures,  the  tension  of 
the  vapour  is  the  same  in  both,  and  always  corresponds  to  that  of  the 
lowest  temperature. 

That  water  evaporates  even  below  zero  follows  from  the  fact,  that  wet 
linen  exposed  to  the  air  during  frost  first  becomes  stiff  and  then  dry, 
showing  that  the  particles  of  water  evaporate  even  after  the  latter  has 
been  converted  into  ice. 

332.  Tension  of  aqueous  vapour  bet\ireen  zero  and  one  hundred 
degrees — i.  Dalton^s  method.  Dalton  measured  the  elastic  force  of 
aqueous  vapour  between  0°  and  100°  by  means  of  the  apparatus  repre- 
sented in  fig.  258.  Two  barometer  tubes,  A  and  B,  are  filled  with  mer- 
cury, and  inverted  in  an  iron  bath  full  of  mercury,  and  placed  on  a  furnace. 
The  tube  A  contains  a  small  quantity  of  water.  The  tubes  are  supported 
in  a  cylindrical  vessel  full  of  water,  the  temperature  of  which  is  indicated 
by  the  thermometer.  The  bath  being  gradually  heated,  the  water  in  the 
cylinder  becomes  heated  too  ;  the  water  which  is  in  the  tube  A  vaporises, 
and  in  proportion  as  the  tension  of  its  vapour  increases,  the  mercury 
sinks.  The  depressions  of  the  mercury  corresponding  to  each  degree  of 
the  thermometer  are  indicated  on  the  scale  E,  and  in  this  manner  a  table 
of  the  elastic  forces  between  zero  and  100°  has  been  constructed. 

ii.  RegnauWs  ?nethod. — Dalton's  method  is  wanting  in  precision,  for 
the  liquid  in  the  cylinder  has  not  everywhere  the  same  temperature,  and 
consequently  the  exact  temperature  of  the  aqueous  vapour  is  not  indicated. 
Regnault's  apparatus  is  a  modification  of  that  of  Dalton.  The  cylindrical 
vessel  is  replaced  by  a  large  cylindrical  zinc  drum,  MN  (fig.  259),  in  the 
bottom  of  which  are  two  tubulures.  The  tubes  A  and  B  pass  through  these 
tubulures,  and  are  fixed  by  caoutchouc  collars.  The  tube  containing 
vapour,  B,  is  connected  with  a  flask,  a,  by  means  of  a  brass  three-way 


332] 


Tejision  of  Aqueous  Vapour, 


27?> 


tube,  O.  The  third  hmb  of  this  tube  is  connected  with  a  drying  tube,  D, 
containing  pumice  impregnated  with  sulphuric  acid,  which  is  connected 
with  the  air  pump. 

When  the  flask  a  contains  some  water,  a  small  portion  is  distilled  into 
B  by  gently  heating  the  flask.  Exhausting  then  by  means  of  the  air 
pump,  the  water  distils  continuously  from  the  flask  and  from  the  baro- 
metric tube  towards  D,    which  condenses  the  vapours.     After  having 


I 


Fig.  258. 


Fig.  259. 


vaporised  some  quantity  of  water,  and  when  it  is  thought  that  all  the  air  in 
the  tube  is  withdrawn,  the  capillary  tube  which  connects  B  with  the  three- 
way  tube  is  sealed.  The  tube  B  being  thus  closed,  it  is  experimented  with, 
as  in  Dalton's  method. 

The  drum  MN,  being  filled  with  water,  is  gently  heated  by  a  spirit  lamp, 
which  is  separated  from  the  tubes  by  a  wooden  screen.  By  means  of  a 
stirrer,  K,  all  parts  of  the  liquid  are  kept  at  the  same  temperature.  In 
the  side  of  the  drum  is  a  glass  window,  through  which  the  height  of  the 
mercury  in  the  tubes  can  be  read  off  by  means  of  a  cathetometer  ;  from 

N3 


r^\ 


274 


On  Heat 


[332 


the  difference  in  these  heights,  reduced  to  zero,  the  tension  of  vapour  is 
deduced.  By  means  of  this  apparatus,  the  elastic  force  of  vapour  between 
o°  and  50°  has  been  determined  with  accuracy. 

333.  Tension  of  aqueous  vapour  above  one  hundred  degrees. — Two 

methods  have  been  employed  for  determining  the  tension  of  aqueous 
vapour  at  temperatures  above  100°,  the  one  by  Dulong  and  Arago,  in  1830, 
and  the  other  by  Regnault,  in  1844. 

Fig.  260  represents  a  vertical  section  of  the  apparatus  used  by  Dulong 


rijT.  "iCo. 


jind  Arago.  It  consisted  of  a  copper  boiler,  k,  with  very  thick  sides,  and 
of  about  20  gallons  capacity.  Two  gun-barrels,  a,  of  which  only  one  is 
seen  in  the  drawing,  were  firmly  fixed  in  the  sides  of  the  boiler,  and 
plunged  in  the  water.  The  gun-barrels  were  closed  below,  and  contained 
mercury,  in  which  were  placed  thermometers,  /,  indicating  the  tempera- 
ture of  the  water,  and  of  the  vapour.  The  tension  of  the  vapour  was 
measured  by  means  of  a  manometer  with  compressed  air,  w,  previously 
graduated  (171)  and  fitted  into  an  iron  vessel,  d,  filled  with  mercury.  In 
order  to  see  the  height  of  the  mercury  in  the  vessel,  it  was  connected 
above  and  below  with  a  glass  tube,  «,  in  which  the  level  was  always  the 
same  as  in  the  bath.  A  copper  tube,  /,  connected  the  upper  part  of  the 
vessel,  d^  with  a  vertical  tube,  r,  fitted  in  the  boiler.  The  tube  i  and  the 
upper  part  of  the  bath  d  were  filled  with  water,  which  was  kept  cool  by 
means  of  a  current  of  cold  water  flowing  from  a  reservoir,  and  circulating 
through  the  tube  b. 

The  vapour  which  was  disengaged  from  the  tube  c  exercised  a  pres- 
sure on  the  water  of  the  tube  / ;  this  pressure  was  transmitted  to  the 
water  and  to  the  mercury  in  the  bath  d,  and  the  mercury  rose  in  the 


334] 


Tension  of  Aqueous  Vapour. 


75 


manometer.  By  noting  on  the  manometer  the  pressures  corresponding 
to  each  degree  of  the  thermometer,  Dulong  and  Arago  were  able  to 
make  a  direct  measurement  of  the  tension  up  to  24  atmospheres,  and 
the  tension  from  thence  to  50  atmospheres  was  determined  by  calcu- 
lation. 

334.  Tension  of  vapour  below^  and  above  one  hundred  deg-rees. — 
Regnault  has  devised  a  method  by  which  the  tension  of  vapour  may  be 
measured  at  temperatures  either  below  or  above  100°.  It  depends  on  the 
principle  that  when  a  liquid  boils,  the  tension  of  the  vapour  is  equal  to 
the  pressure  it  supports  (339).  If,  therefore,  the  temperature  and  the 
corresponding  pressure  are  known,  the  question  is  solved,  and  the  method 
n;ierely  consists  in  causing  water  to  boil  in  a  vessel  under  a  given  pressure, 
and  measuring  the  corresponding  temperature. 

The  apparatus  consists  of  a  copper  retort,   C  (fig.   261),  hermetically 


I 


Fig.  261. 

sealed,  and  about  two-thirds  full  of  water.  In  the  cover  there  are  four 
thermometers,  two  of  which  just  dip  into  the  water,  and  two  descend 
almost  to  the  bottom.  By  means  of  a  tube,  AB,  the  retort  C  is  connected 
with  a  glass  globe,  M,  of  about  6  gallons  capacity,  and  full  of  air.  The 
tube  AB  passes  through  a  metallic  cylinder,  D,  through  which  a  current 
of  cold  water  is  constantly  flowing  from  the  reservoir  E.  To  the  upper 
part  of  the  globe  a  tube  with  two  branches  is  attached,  one  of  which  is 
connected  with  a  manometer,  O;  the  other  tube,  HH',  which  is  of  lead, 


2/6 


On  Heat. 


[334- 


can  be  attached  either  to  an  exhausting  or  a  condensing  air  pump,  accord- 
ing as  the  air  in  the  globe  is  to  be  rarefied  or  condensed.  The  reservoir 
K,  in  which  is  the  globe,  contains  water  of  the  temperature  of  the  sur- 
rounding air. 

If  the  elastic  force  of  aqueous  vapour  below  ioo°  is  to  be  measured, 
the  end  H''  of  the  leaden  pipe  is  connected  with  the  plate  of  the  air  pump, 
and  the  air  in  the  globe  M,  and  consequently  that  in  the  retort  C,  is 
rarefied.  The  retort  being  gently  heated,  the  water  begins  to  boil  at  a 
temperature  below  ioo°,  in  consequence  of  the  diminished  pressure.  And 
since  the  vapour  is  condensed  in  the  tube  AB,  which  is  always  cool,  the 
pressure  originally  indicated  by  the  manometer  does  not  increase,  and 
therefore  the  tension  of  the  vapour  during  ebullition  remains  equal  to  the 
pressure  on  the  liquid. 

A  httle  air  is  then  allowed  to  enter  ;  this  alters  the  pressure,  and  the 
liquid  boils  at  a  new  temperature ;  both  these  are  read  off,  and  the  ex- 
periment repeated  as  often  as  desired  up  to  ioo°. 

In  order  to  measure  the  tension  above  ioo°,  the  tube  H'  is  connected 
with  a  condensing  pump,  by  means  of  which  the  air  in  the  globe  M  and 
that  in  the  vessel  C  are  exposed  to  successive  pressures,  higher  than  the 
atmosphere.  The  ebullition  is  retarded  (343),  and  it  is  only  necessary 
to  observe  the  difference  in  the  height  of  the  mercury  in  the  two  tubes  of 
the  manometer  O,  and  the  corresponding  temperature,  in  order  to  obtain 
the  tension  for  a  given  temperature. 

The  following  tables  by  M.  Regnault  give  the  tension  of  aqueous 
vapour  from  -  1°  to  101°. 

Tensions  of  aqueous  vapour  from  —10°  to  101°  C. 


k 

Tensions 

2. 

S 

i. 

6 

in 

tl 

Tensions  in 

E  3 

Tensions  in 

E  3 

Tensions  in 

milli- 

£  3 

millimetres 

millimetres 

millimetres 

1 

metres 

^^ 

29° 

fi!" 

-10° 

2-078 

12° 

10-457 

29-782 

85° 

433-41 

8 

2-456 

13 

1 1  -062 

30 

31-548 

90 

525-45 

6 

2-890 

14 

11-906 

31 

33-405 

91 

545-78 

4 

3-387 

15 

12-699 

32 

35-359 

92 

566-76 

2 

3-955 

16 

13-635 

33 

37-410 

93 

588-41 

0 

4-600 

17 

14-421 

34 

39-565 

94 

610-74 

+    I 

4-940 

18 

15-357 

35 

41-827 

95 

633-78 

2 

5-302 

19 

16-346 

40 

54-906 

96 

657-54 

3 

5-687 

20 

17-391 

45 

71-391 

97 

682-03 

4 

6-097 

21 

18-495 

50 

91-982 

98 

707-26 

5 

6-534 

22 

19-659 

55 

117-478 

98-5 

720-15 

6 

6-998 

23 

20-888 

60 

148-791 

99-0 

733-21 

7 

7-492 

24 

22-184 

65 

186-945 

99-5 

746-50 

8 

8-OI7 

25 

23-550 

70 

233-093 

1 00-0 

760-00 

9 

8-574 

26 

24-998 

75 

288-517 

100-5 

773-71 

10 

9-165 

27 

26-505 

80 

354-643 

101 -0 

787-63 

TI 

9-792 

28 

28-101 

-336] 


Tension  of  the  Vapours  of  Mixed  Liquids. 


277 


In  the  second  table  the  numbers  were  obtained  by  direct  observation 
up  to  24  atmospheres  ;  the  others  were  calculated  by  the  aid  of  a  formula 
of  interpolation. 

Tensions  in  atmospheres  from  100°  to  230'9°. 


% 

Z 

^  ■"    1 

^ 

s 

3 

II 

E  0 

1 

^"1 
S  0 

2 

S  0 

s 

3  6 

s 

3  g 

£ 

3  s 

s 

3    S 

^ 

^^ 

^ 

^^l 

E^ 

J^i 

E^ 

;2;t5 

ioo-o° 

I 

170-8° 

^      1 

198-8° 

'5   ' 

217-9° 

22 

1 1 2-2 

I* 

175-8 

9    ! 

201-9 

16  1 

220-3 

23 

.  I20-6 

2 

180-3 

10      ' 

204-9 

17 

222-5 

24 

133-9 

3 

184-5 

II 

207-7 

18 

2247 

25 

144-0 

4 

188-4 

12 

210-4 

19 

226-8 

26 

152-2 

5 

192-1 

13 

213-0 

20 

228-9 

27 

159-2 

6 

195-5 

14 

215-5 

21 

230-9 

28 

165-3 

7 

These  tables  show  that  the  elastic  force  increases  much  more  rapidly 
than  the  temperature.  The  law  which  regulates  this  increase  is  not 
accurately  known. 

335.  Tension  of  tbe  vapours  of  different  liquids. — Regnault  has 
determined  the  elastic  force  at  various  temperatures,  of  a  certain  number 
of  liquids  which  are  given  in  the  following  table  : — 


Liquids 

Tempera- 
tures 

Tensions  in 
millimetres 

Liquids 

Tempera- 
tures 

Tensions  in 
millimetres 

Mercury     .    • 
Alcohol      .    ■ 

Bisulphide 
of  carbon 

50° 

100 

0 

50 

100 

-20 

0 

60 

ICO 

o-ii 
0-74 

13 

220 

1695 

43 

132 

1164 

3329 

Ether    .     .   ■ 

Sulphurous    . 
acid 

Ammonia 

-20° 

0 

60 

100 

-20 

0 

60 

-30 

0 

30 

68 

182 

1728 

4950 

479 
1165 
8124 

876 

3163 
8832 

336.  Tension  of  tbe  vapours  of  mixed  liquids. — Regnault's  experi- 
ments on  the  tension  of  the  vapour  of  mixed  liquids  prove  that  (i.)  when 
two  liquids  exert  no  solvent  action  on  each  other — such  as  water  and 
bisulphide  of  carbon,  or  water  and  benzole — the  tension  of  the  vapour 
which  rises  from  them  is  nearly  equal  to  the  sum  of  the  tensions  of  the 
two  separate  liquids  at  the  same  temperature  ;  (ii.)  with  water  and  ether, 
which  partially  dissolve  each  other,  the  tension  of  the  mixture  is  much 


278 


On  Heat. 


[336- 


less  than  the  sum  of  the  tensions  of  the  separate  liquids,  being  scarcely 
equal  to  that  of  the  ether  alone;  (iii.)  when  two  liquids  dissolve  in  all 
proportions,  as  ether  and  bisulphide  of  carbon,  or  water  and  alcohol,  the 
tension  of  the  vapour  of  the  mixed  liquid  is  intermediate  between  the 
tensions  of  the  separate  liquids. 

Wiillner  has  shown  that  the  tension  of  aqueous  vapour  emitted  from  a 
sahne  solution,  as  compared  with  that  of  pure  water,  is  diminished  by  an 
amount  proportional  to  the  quantity  of  anhydrous  salt  dissolved,  when 
the  salt  crystallises  without  water  or  yields  efflorescent  crystals  ;  when  the 
salt  is  deliquescent,  or  has  a  powerful  attraction  for  water,  the  reduction 
of  tension  is  proportional  to  the  quantity  of  crystallised  salt. 

337.  Tension  in  two  communicating- vessels  at  different  tempera- 
tures.— When  two  vessels  containing  the  same  liquid,  but  at  different 
temperatures,  are  connected  with  each  other,  the  elastic  force  is  not  that 


corresponding  to  the  mean  of  the  two  temperitiires,  a^  woiild  naturally 
be  supposed.  Thus,  if  there  are  two  globes,  fig.  262,  one.  A,  containing 
water  kept  at  zero  by  means  of  melting  ice,  the  other,  B,  containing 
water  at  100°,  the  tension,  as  long  as  the  globes  are  not  connected,  is  4  to 
6  millimetres  in  the  first,  and  760  millimetres  in  the  second.  But  when 
they  are  connected  by  opening  the  stopcock  C,  the  vapour  in  the  globe 
B,  from  its  greater  tension,  passes  into  the  other  globe,  and  is  there  con- 
densed, so  that  the  vapour  in  B  can  never  reach  a  higher  temperature 
than  that  in  the  globe  A.  The  liquid  simply  distils  from  B  towards  A 
without  any  increase  of  tension. 

From  this  experiment  the  general  principle  may  be  deduced  that  when 
two  vessels  containing  the  same  liquid,  but  at  different  temperatures,  are 
coJtnected,  the  tension  is  identical  in  both  vessels,  and  is  the  same  as  that 
corresponding  to  the  lower  tempe?'atui'e  An  application  of  this  principle 
has  been  made  by  Watt  in  the  condenser  of  the  steam-engine. 


-339] 


Lazvs  of  Ebullition. 


279 


r'-^\ 


I 


338.  Svaporation.  Causes  which  accelerate  it. — Evaporation^  as 
has  been  already  stated  (326),  is  the  slow  production  of  vapour  at  the 
surface  of  a  liquid.  It  is  in  consequence  of  this  evaporation  that  wet 
clothes  dry  when  exposed  to  the  air, 
and  that  open  vessels  containing  water 
become  emptied.  The  vapours  which, 
rising  in  the  atmosphere,  condense, 
and  becoming  clouds  fall  as  rain,  are 
due  to  the  evaporation  from  the  seas, 
lakes,  rivers,  and  the  soil. 

Four  causes  influence  the  rapidity 
of  the  evaporation  of  a  liquid  :  i.  the 
temperature  ;  ii.  the  quantity  of  the 
same  vapour  in  the  surrounding  atmo- 
sphere ;  iii.  the  renewal  of  this  atmo- 
sphere ;  iv.  the  extent  of  the  surface 
of  evaporation. 

Increase  of  temperature  accelerates 
the  evaporation  by  increasing  the 
elastic  force  of  the  vapours. 

In  order  to  understand  the  influence 
of  the  second  cause,  it  is  to  be  ob- 
served that  no  evaporation  could  take 
place  in  a  space  already  saturated  with 
vapour  of  the  same  liquid,  and  that  it 
would  reach  its  maximum  in  air  completely  freed  from  this  vapour.  It 
therefore  follows  that  between  these  two  extremes  the  rapidity  of  evapo- 
ration varies  according  as  the  surrounding  atmosphere  is  already  more  or 
less  charged  with  the  same  vapour. 

The  effect  of  the  renewal  of  this  atmosphere  is  similarly  explained  ;  for 
if  the  air  or  gas,  which  surrounds  the  liquid,  is  not  renewed,  it  soon 
becomes  saturated,  and  evaporation  ceases. 

The  influence  of  the  fourth  cause  is  self-evident. 

339.  I>aws  of  ebullition. — Ebullition,  or  boiling  is  the  rapid  produc- 
tion of  elastic  bubbles  of  vapour  in  the  mass  of  a  liquid  itself. 

When  a  liquid,  water  for  example,  is  heated  at  the  lower  part  of  a 
vessel,  the  first  bubbles  are  due  to  the  disengagement  of  air  which  had 
previously  been  absorbed.  Small  bubbles  of  vapour  then  begin  to 
rise  from  the  heated  parts  of  the  sides,  but  as  they  pass  through  the 
upper  layers,  the  temperature  of  which  is  lower,  they  condense  before 
reaching  the  surface.  The  formation  and  successive  condensation  of 
these  first  bubbles,  occasion  the  singing  noticed  in  liquids  before  they 
begin  to  boil.  Lastly,  large  bubbles  rise  and  burst  on  the  surface,  and 
this  constitutes  the  phenomenon  of  ebullition  (tig.  263). 

The  laws  of  ebullition  have  been  determined  experimentally,  and  are 
as  follows  : —  • 

I.  The  tempetnture  of  ebullition,  or  the  boiling  point,  increases  with  the 
pressure. 


Fig.  263. 


28o 


On  Heat. 


[339 


II.  For  a  given  pressure  ebullition  begins  at  a  certain  temperature^ 
which  varies  in  different  liquids,  but  which,  for  equal  pressures,  is  always 
the  same  hi  the  same  liquid. 

III.  Whatever  be  the  intensity  of  the  source  of  heat,  as  soon  as  ebulli- 
tion begins,  the  temperature  of  the  liquid  remains  stationary. 


YCtik- 


Sulphurous  acid    . 

.    -IO° 

Turpentine    . 

Chloride  of  ethyle 

+  II 

Butyric  acid  . 

Ether    .... 

yi 

Phosphorus   . 

Bisulphide  of  carbon    . 

48 

Strong  sulphuric  acid 

Bromine 

63 

Mercury 

Alcohol 

.     78 

Sulphur 

Distilled  water      . 

100 

Cadmium 

Acetig  acid   .        .        .        . 

117 

Zinc       .         .      ^  , 

^.\ 

^-^  '-^. 

xt  tUc- 

Boiling  points  under  the  pressure  760  millimetres.  ^ 

160° 
157 

290 

325 
320 

447 

860 

1040 

There  are  many  causes  which  influence  the  boiling  point  of  a  liquid, 
such  as  the  substances  dissolved,  the  nature  of  the  vessel,  and  the  pres- 
sure. We  shall  illustrate  the  effects  of  these  different  causes,  more  par- 
ticularly on  water. 

Kopp  has  pointed  out  that  in  analogous  chemical  compounds  the  same 
difference  in  chemical  composition  frequently  involves  the  same  difference 
of  boiling  points  ;  and  he  has  endeavoured  to  show  that  in  a  very  ex- 
tensive series  of  compounds  the  difference  of  CH^  is  attended  by  a  differ- 
ence of  19°  C.  in  the  boiling  point. 

340.  Theoretical  explanation  of  evaporation  and  ebullition. — 
From  what  has  been  said  about  the  nature  of  the  motion  of  the  mole- 
cules in  liquids  (273),  it  may  readily  be  conceived  that  in  the  great  variety 
of  these  motions,  the  case  occurs  in  which  by  a  fortuitous  concurrence  of  the 
progressive  vibratory  and  rotatory  motions  a  molecule  is  projected  from  the 
surface  of  the  liquid  with  such  force  that  it  overleaps  the  sphere  of  the 
action  of  its  circumjacent  molecules  before,  by  their  attraction,  it  has 
lost  its  initial  velocity  ;  and  that  it  then  flies  into  the  space  above  the 
liquid. 

Let  us  first  suppose  this  space  limited  and  originally  vacuous,  it 
gradually  fills  with  the  propelled  molecules  which  act  like  a  gas  and  in 
their  motion  are  driven  against  the  sides  of  the  envelope.  One  of  these 
sides,  however,  is  the  surface  of  the  liquid  itself,  and  a  molecule  when  it 
strikes  against  this  surface  will  not  in  general  be  repelled  but  be  retained 
by  the  attraction  which  the  adjacent  ones  exert.  Equilibrium  will  be 
established  when  as  many  molecules  are  dispersed  in  the  surrounding 
space  as,  on  the  average,  impinge  against  the  surface  and  are  retained 
by  it  'in  the  unit  of  time.  This  state  of  equihbrium  is  not,  however,  one  of 
rest,  in  which  evaporation  has  ceased,  but  a  condition,  in  which  evaporation 
and  condensation,  which  are  equally  strong,  continually  compensate  each 
other. 

The  density  of  a  vapour  depends  on  the  number  of  molecules  which 


-341]        Explanation  of  Evaporation  and  Ebullition.  281 

are  repelled  in  a  given  time,  and  this  manifestly  depends  on  the  motion  of 
the  molecules  in  the  liquid. 

What  has  been  said  respecting  the  surface  of  the  liquid  clearly  applies 
to  the  other  sides  of  the  vessel  within  which  the  vapour  is  formed  ; 
some  vapour  is  condensed,  this  is  subject  to  evaporation,  and  a  con- 
dition ultimately  occurs  in  which  evaporation  and  precipitation  are 
equal.  The  quantity  of  vapour  necessary  for  this  depends  on  the 
density  of  vapour  in  the  closed  space,  on  the  temperature  of  the  vapour 
and  the  side  and  on  the  force  with  which  this  attracts  the  molecules.  The 
maximum  will  be  reached  when  the  sides  are  covered  with  a  layer  of 
liquid,  which  then  acts  like  the  free  surface  of  a  liquid. 

In  the  interior  of  a  liquid  it  may  happen  that  the  molecules  repel  each 
other  with  such  force  as  to  momentarily  destroy  the  coherence  of  the 
mass.  The  small  vacuous  space  which  is  thereby  formed,  is  entirely  sur- 
rounded by  a  medium  which  does  not  allow  of  the  passage  of  the  repelled 
molecules.  Hence  it  cannot  increase  and  maintain  itself  as  a  bubble  of 
vapour,  unless  so  many  molecules  are  projected  from  the  inner  sides  that 
the  internal  pressure  which  thereby  results,  can  balance  the  external 
pressure  which  tends  to  condense  the  bubble.  The  expansive  force  of  the 
enclosed  vapour  must  therefore  be  so  much  the  greater,  the  greater  the 
external  pressure  on  the  liquid,  and  thus  we  see  the  dependence  of  pres- 
sure on  the  temperature  of  boiling. 

341.  Influence  of  substances  in  solution  on  the  boillngr  point. — 
The  ebullition  of  a  liquid  is  the  more  retarded  the  greater  the  quantity 
of  any  substance  it  may  contain  in  solution,  provided  that  the  substance 
be  not  volatile,  or,  at  all  events,  be  less  volatile  than  the  liquid  itself. 
Water  which  boils  at  100°  when  pure,  boils  at  the  following  temperatures 
when  saturated  with  different  salts  : — 

Water  saturated  with  common  salt     .         .         boils  at  109° 
„  „  nitrate  of  potassium  „         116 

„  „  carbonate  of  potassium       „         135 

„  „  chloride  of  calcium  „         179 

Acids  in  solution  present  analogous  results  ;  but  substances  merely 
mechanically  suspended,  such  as  earthy  matters,  bran,  wooden  shavings, 
etc.,  do  not  affect  the  boiling  point. 

Dissolved  air  exerts  a  very  marked  influence  on  the  boiling  point  of 
water.  Deluc  first  observed  that  water  freed  from  air  by  ebullition, 
and  placed  in  a  flask  with  a  long  neck,  could  be  raised  to  112°  without 
boiling.  M.  Donny  found  that  water  deprived  of  air  and  sealed  up  in  a 
long  glass  tube  may  be  heated  at  one  end  as  high  as  138°  without  boil- 
ing, and  is  then  suddenly  and  violently  thrown  to  the  other  by  a  burst  of 
vapour. 

When  a  liquid  is  suspended  in  another  of  the  same  specific  gravity, 
but  higher  boiling  point,  with  which  it  does  not  mix,  it  may  be  raised  far 
beyond  its  boiling  point  without  the  formation  of  a  trace  of  vapour. 
Dufour  has  made  a  number  of  valuable  experiments  on  this  subject ;  he 


282  Oh  Heat.  [341- 

used  in  the  case  of  water  a  mixture  of  oil  of  cloves  and  linseed  oil ;  and 
placed  in  it  globules  of  water,  and  then  gradually  heated  the  oil ;  in  this 
way  ebulhtion  rarely  set  in  below  iio°  or  115°,  very  commonly  globules 
of  10  millimetres  diameter  reached  a  temperature  of  120°  or  130°,  while 
very  small  globules  of  i  to  3  millimetres  reached  the  temperature  of  175*^, 
a  temperature  at  which  the  tension  of  vapour  on  a  free  surface  is  8  or  9 
atmospheres. 

At  these  high  temperatures  the  contact  of  a  solid  body,  or  the  produc- 
tion of  gas  bubbles  in  the  liquid,  occasioned  a  sudden  vaporisation  of  the 
globule,  accompcinied  by  a  sound  like  the  hissing  of  a  hot  iron  in  water. 

Saturated  aqueous  solutions  of  sulphate  of  copper,  chloride  of  sodium, 
etc.,  remained  liquid  at  a  temperature  far  beyond  their  boiling  point,  when 
immersed  in  melted  stearic  acid.  In  like  manner,  globules  of  chloroform 
(which  boils  at  61°)  suspended  in  a  solution  of  chloride  of  zinc  could  be 
heated  to  97°  or  98°  without  boiling. 

It  is  a  disputed  question  as  to  what  is  the  temperature  of  the  vapour 
from  boiling  saturated  saline  solutions.  It  has  been  stated  by  Rudberg 
to  be  that  of  pure  water  boiling  under  the  same  pressure  ;  the  most  recent 
experiments  of  Magnus  seem  to  show,  however,  that  this  is  not  the  case, 
but  that  the  vapour  of  boiling  solutions  is  hotter  than  that  of  pure 
water  ;  and  that  the  temperature  rises  as  the  solutions  become  more 
concentrated,  and  therefore  boil  at  higher  temperatures.  Nevertheless, 
the  vapour  was  always  found  somewhat  cooler  than  the  mass  of  the 
boihng  solution,  and  the  difference  was  greater  at  high  than  at  low 
temperatures. 

The  boiling  point  of  a  liquid  is  usually  lowered  when  it  is  mixed  with  a 
more  volatile  liquid  than  itself,  but  raised  when  it  contains  one  which  is 
less  volatile.  Thus  a  mixture  of  two  parts  alcohol  and  one  of  water 
boils  at  83°,  a  mixture  of  two  parts  of  bisulphide  of  carbon  and  one  part 
of  ether  bcils  at  38°.  In  some  cases  the  boiling  point  of  a  mixture  is 
lower  than  that  of  either  of  its  constituents.  A  mixture  of  water  and 
bisulphide  boils  at  43°,  the  boiling  point  of  the  latter  being  46°.  On  this 
depends  the  following  curious  experiment.  If  water  and  bisulphide  of 
carbon,  both  at  the  temperature  45°,  are  mixed  together,  the  mixture  at 
once  begins  to  boil  briskly. 

342.  Influence  of  the  nature  of  tlie  vessel  on  tbe  boiling:  point. — 
Gay-Lussac  observed  that  water  in  a  glass  vessel  required  a  higher 
temperature  for  ebullition  than  in  a  metal  one.  Taking  the  temperature 
of  boiling  water  in  a  copper  vessel  at  100°,  its  boiling  point  in  a  glass 
vessel  was  found  to  be  101°  ;  and  if  the  glass  vessel  had  been  previously 
cleaned  by  means  of  sulphuric  acid  and  of  potass,  the  temperature  would 
rise  to  105°,  or  even  to  106°,  before  ebullition  commenced.  A  piece  of 
metal  placed  in  the  bottom  of  the  vessel  was  always  sufficient  to  lower 
the  temperature  to  100°,  and  at  the  same  time  to  prevent  the  violent  con- 
cussions which  accompany  the  ebullition  of  saline  or  acid  solutions  in 
glass  vessels.  Whatever  be  the  boiling  point  of  water,  the  temperature  of 
its  vapour  is  uninfluenced  by  the  substance  of  the  vessels. 


-343]  Iiiflueiice  of  Pressure  on  the  Boiling  Point.         283 

343.  Influence  of  pressure  on  the  1>oillnir  point.— We  see  from  the 
table  of  tensions  (334)  that  at  100°,  the  temperature  at  which  water  boils 
under  a  pressure  of  760  millimetres, 
aqueous  vapour  has  a  tension  ex- 
actly equal  to  this  pressure.  This 
principle  is  general,  and  may  be 
thus  enunciated  :  A  liquid  boils 
when  the  teiision  of  its  vapour  is 
equal  to  the  pressure  it  supports. 
Consequently,  as  the  pressure  in- 
creases or  diminishes,  the  tension 
of  the  vapour,  and  therefore  the 
temperature  necessary  for  ebulli- 
tion, must  increase  or  diminish. 

In  order  to  show  that  the  boil- 
ing point  is  lower  under  diminished 
pressure,  a  small  dish  containing 
water  at  30°  is  placed  under  the 
receiver  of  an  air  pump,  which  is 
then  exhausted.  The  liquid  soon 
begins  to  boil,  the  vapour  formed 
being  pumped  out  as  rapidly  as  it 
is  generated. 

A  paradoxical  but  very  simple 
experiment  also  well  illustrates  the 
dependence  of  the  boiling  point  on  the  pressure.  In  a  glass  flask,  water 
is  boiled  for  some  time,  and  when  all  air  has  been  expelled  by  the  steam, 
the  flask  is  closed  by  .a  cork  and  inverted  as  shown  in  fig.  264.  If  the 
bottom  is  then  cooled  by  a  stream  of  cold  water  from  a  sponge,  the 
water  begins  to  boil  again.  This  arises  from  the  condensation  of  the 
steam  above  the  surface  of  the  water,  by  which  a  partial  vacuum  is  pro- 
duced. 

It  is  in  consequence  of  this  diminution  of  pressure  that  liquids  boil  on 
high  mountains  at  lower  temperatures.  On  Mont  Blanc,  for  example, 
water  boils  at  84°,  and  at  Quito  at  90?. 

On  the  more  rapid  evaporation  of  water  under  feeble  pressures  is 
based  the  use  of  the  air  pump  in  concentrating  those  solutions  which 
either  cannot  bear  a  high  degree  of  heat,  or  which  can  be  more  cheaply 
evaporated  in  an  exhausted  space.  Mr.  Howard  made  a  most  important 
and  useful  application  of  this  principle  in  the  manufacture  of  sugar.  The 
syrup,  in  his  method,  is  enclosed  in  an  air-tight  vessel,  which  is  exhausted 
by  a  steam-engme.  The  evaporation  consequently  goes  on  at  a  lower 
temperature,  which  secures  the  syrup  from  injury.  The  same  plan  is 
adopted  in  evaporating  the  juice  of  certain  plants  used  in  preparing 
medicinal  extracts. 

On  the  other  hand,  ebullition  is  retarded  by  increasing  the  pressure  ; 
under  the  pressure  of  two  atmospheres,  for  example,  water  only  boils  at 
i2o°-6. 


Fig.   264. 


284 


On  Heat. 


[344- 


344.  Franklin's  experiment. — The  influence  of  pressure  on  ebullition 
may  further  be  illustrated  by  means  of  an  experiment  of  Franklin's.  The 
apparatus  consists  of  a  bulb.  «,  and  a  tube,  b,  joined  by  a  tube  of  smaller 
^^N— — *''''^^^^^'*^*\^^  dimensions  (fig.  265).    The  tube 

^'"^  T*^  J)  js  drawn  out,  and  the  appara- 

tus filled  with  water,  which  is 
then  in  great  part  boiled  aw^y 
by  means  of  a  spirit  lamp. 
When  it  has  been  boiled  suffi- 
ciently long  to  expel  all  the  air, 
the  tube  b  is  sealed.  There  is 
then  a  vacuum  in  the  apparatus, 
or  rather  there  is  a  pressure  due 
to  the  tension  of  aqueous  vapour, 
which  at  ordinary  temperatures  is  very  small.  Consequently,  if  the 
bulb  a  be  placed  in  the  hand,  the  heat  is  sufficient  to  produce  a  tension 


Fi^.  265. 


345.  Measurement  of  heigrbts  by  tbe  boiling:  point. — From  the  con- 
nection between  the  boiling  point  of  water  and  the  pressure,  the  heights 
of  mountains  may  be  measured  by  the  thermometer  instead  of  by  the 
barometer.  Suppose,  for  example,  it  is  found  that  water  boils  on  the 
summit  of  a  mountain  at  90°,  and  at  its  base  at  98° ;  at  these  tempera- 
tures the  elastic  force  or  tension  of  the  vapour  is  equal  to  that  of  the 
pressure  on  the  liquid,  that  is,  to  the  pressure  of  the  atmosphere  at  the 
two  places  respectively.  Now  the  tensions  of  aqueous  vapour  for  various 
temperatures  have  been  determined,  and  accordingly  the  tensions  corre- 
sponding to  the  above  temperatures  are  sought  in  the  tables.  These 
numbers  represent  the  atmospheric  pressures  at  the  two  places  :  in  other 
words,  they  give  the  barometric  heights,  and  from  these  the  height  of  the 
mountain  may  be  calculated  by  the  method  already  given  (165).  An 
ascent  of  about  1080  feet  produces  a  diminution  of  1°  C.  in  the  boiling 
point. 

The  instruments  used  for  this  purpose  are  called  thermo-barometers 
or  hypsometers^  and  were  first  applied  by  Wollaston.  They  consist 
essentially  of  a  small  metallic  vessel  for  boiling  water,  fitted  with  very 
delicate  thermometers,  which  are  only  graduated  from  80°  to  i(X>°  ;  so  that 
each  degree  occupying  a  considerable  space  on  the  scale,  the  loths,  and 
even  the  looths,  of  a  degree  may  be  estimated,  and  thus  it  is  possible  to 
determine  the  height  of  a  place  by  means  of  the  boiling  point  to  within 
about  10  feet. 

346.  Formation  of  vapour  in  a  closed  tube. — We  have  hitherto 
considered  vapours  as  being  produced  in  an  indefinite  space,  or  where 
they  could  expand  freely,  and  it  is  only  under  this  condition  that 
ebullition  can  take  place.  In  a  closed  vessel  the  vapours  produced 
finding  no  issue,  their  tension  and  their  density  increase  with  the 
temperature,  but  the  rapid  disengagement  of  vapour  which  constitutes 
ebullition  is  impossible.  Hence,  while  the  temperature  of  a  liquid  in  an 
open  vessel  can  never  exceed  that  of  ebullition,  in  a  closed  vessel  it  may 


t 


-347]  Formation  of  Vapour  ift  a  closed  Space.  285 

be  much  higher.  The  liquid  state,  has,  nevertheless,  a  limit  ;  for,  accord- 
ing to  experiments  by  Cagniard-Latour,  if  either  water,  alcohol,  or  ether 
be  placed  in  strong  glass  tubes,  which  are  hermetically  sealed  after  the 
air  has  been  expelled  by  boiling,  when  these  tubes  are  exposed  to  a 
sufficient  degree  of  heat,  a  moment  is  reached  at  which  the  liquid  suddenly 
disappears,  and  is  converted  into  vapour  at  200°,  occupying  a  space  less 
than  double  its  volume  in  the  liquid  state,  and  that  the  tension  was  then 
38  atmospheres. 

Alcohol  which  half  fills  a  tube  is  converted  into  vapour  at  207°  C. 
If  a  glass  tube  about  half  filled  with  water,  in  which  some  carbonate  of 
soda  has  been  dissolved,  to  diminish  the  action  of  the  water  in  the  glass, 
be  heated,  it  is  completely  vaporised  at  about  the  temperature  of  melting 
zinc. 

When  chloride  of  ethyle  was  heated  in  a  very  thick  sealed  tube,  the 
upper  surface  ceased  to  be  distinct  at  1 70°,  and  was  replaced  by  an  ill- 
defined  nebulous  zone.  As  the  temperature  rose  this  zone  increased  in 
width  in  both  directions,  becoming  at  the  same  time  more  transparent ; 
after  a  time  the  liquid  was  completely  vaporised,  and  the  tube  became 
transparent  and  seemingly  empty.  On  cooling,  the  phenomena  were 
reproduced  in  the  opposite  order.  Similar  appearances  were  observed  on 
heating  ether  in  a  sealed  tube  at  190°. 

Andrews  has  observed  that  when  liquid  carbonic  acid  was  heated  in 
a  closed  tube  to  31°  C.  the  surface  of  demarcation  between  the  liquid  and 
the  gas  became  fainter,  lost  its  curvature,  and  gradually  disappeared. 
The  space  was  then  occupied  by  a  homogeneous  fluid,  which,  when  the 
pressure  was  suddenly  diminished,  or  the  temperature  slightly  lowered, 
exhibited  a  peculiar  appearance  of  moving  or  flickering  striae  throughout 
its  whole  mass.  Above  30°  no  apparent  liquefaction  of  carbonic  anhy^ 
dride,  or  separation  into  two  distinct  forms  of  matter,  could  be  effected, 
not  even  when  the  pressure  of  400  atmospheres  was  applied.  It  would  thus 
seem  that  there  exists  for  every  liquid  a  temperature,  the  critical  tempera- 
ture. While  below  this  critical  point  a  sudden  transition  from  gas  to 
liquid  is  accompanied  by  a  sudden  diminution  of  volume,  and  liquid  and 
gas  are  separated  by  a  sharp  line  of  demarcation  ;  above  this  critical 
point  the  change  is  connected  with  a  gradual  diminution  of  volume,  and 
is  quite  imperceptible.  The  condensation  can,  indeed,  only  be  recognised 
by  a  sudden  ebullition  when  the  pressure  is  lessened.  Hence,  ordinary 
condensation  is  only  possible  below  the  critical  point,  and  it  is  not  sur- 
prising, therefore,  that  mere  pressure,  however  greatj^ should  fail  to  liquefy 
many  of  the  bodies  which  usually  exist  as  gases. 

347.  Papin's  digrester. — Papin,  a  French  physician  appears  to  have 
been  the  first  to  study  the  effects  of  the  productions  of  vapour  in  closed 
vessels.  The  apparatus  which  bears  his  name  consists  of  a  cylindrical 
iron  vessel  (fig.  266),  provided  with  a  cover,  which  is  firmly  fastened  down 
by  the  screw  B.  In  order  to  close  the  vessel  hermetically,  sheet  lead  is 
placed  between  the  edges  of  the  cover  and  the  vessel.  At  the  bottom  of  a 
cyhndrical  cavity,  which  traverses  the  cyhnder  S,  and  the  tubulure  ^,  the 
cover  is  perforated  by  a  small  orifice  in  which  there  is  a  rod,  n.   This  rod 


^86  On  Heat,  [347- 

presses  against  a  lever,  A,  movable  at  a,  and  the  pressure  may  be  regu- 
lated by  means  of  a  weight  movable  on  this  lever.    The  lever  is  so  weighted, 

that  when  the  tension  in  the  interior  is 
equal  to  6  atmospheres,  for  example, 
the  valve  rises  and  the  vapour  escapes. 
The  destruction  of  the  apparatus  is 
thus  avoided,  and  the  mechanism  has 
hence  received  the  name  of  safety 
valve.  The  digester  is  filled  about 
two-thirds  with  water,  and  is  heated 
on  a  furnace.  The  water  may  thus 
be  raised  to  a  temperature  far  above 
ioo°,  and  the  tension  of  the  vapour 
increased  to  several  atmospheres,  ac- 
cording to  the  weight  on  the  lever. 

We  have  seen  that  water  boils  at 
much  lower  temperatures  on  high 
mountains  (343)  ;  the  temperature  of 
water  boiling  in  open  vessels  in  such 
localities  is  not  sufficient  to  soften 
animal  fibre  completely  and  extract 
the  nutriment,  and  hence  Papin's  di- 
gester is  used  in  the  preparation  of 
food. 

Papin's  digester  is  used  in  extract- 
ing gelatine.  When  bones  are  digested  in  this  apparatus  they  are  soft- 
ened so  that  the  gelatine  which  they  contain  is  dissolved. 

348.  l^atent  heat  of  vapour. — As  the  temperature  of  a  liquid  remains 
constant  during  ebullition,  whatever  be  the  source  of  heat  (339),  it  follows 
that  a  considerable  quantity  of  heat  becomes  absorbed  in  ebullition,  the 
only  effect  of  which  is  to  transform  the  body  from  the  liquid  to  the  gaseous 
condition.  And  conversely  when  a  saturated  vapour  passes  into  the  state 
of  liquid,  it  gives  out  an  amount  of  heat. 

These  phenomena  were  first  observed  by  Black,  and  he  described  them 
by  saying  that  during  vaporisation  a  quantity  of  sensible  heat  became 
latent,  and  that  the  latent  heat  again  became  free  during  condensation. 
The  quantity  of  heat  which  a  liquid  must  absorb  in  passing  from  the 
liquid  to  the  gaseous  state  and  which  it  gives  out  in  passing  from  the 
state  of  vapour  to  that  of  liquid,  is  spoken  of  as  the  latent  heat  of  evapo- 
ration. 

The  analogy  of  these  phenomena  to  those  of  fusion  will  be  at  once 
seen  ;  the  modes  of  determining  them  will  be  described  in  the  chapter  on 
Calorimetry  ;  but  the  following  results,  which  have  been  obtained  for  the 
latent  heats  of  evaporation  of  a  few  liquids,  may  be  here  given  : — 

Water    .... 

Alcohol 

Acetic  acid    . 

Ether    .... 


Fig.    266. 


536 

Bisulphide  of  carbon 

.     87 

208 

Turpentine 

•     74 

102 

Bromine  .... 

.     46 

90 

Iodine      .         <,       .        . 

.     24 

-349]  Cold  due  to  Evaporation.  287 

The  meaning  of  these  numbers  is,  in  the  case  of  water,  for  instance 
that  it  requires  as  much  heat  to  convert  a  pound  of  water  from  the  state 
of  Mquid  at  the  boiling  point  to  that  of  vapour  at  the  same  temperature, 
as  would  raise  a  pound  of  water  through  540  degrees,  or  540  pounds  of 
water  through  one  degree  ;  or  that  the  conversion  of  one  pound  of  vapour 
of  alcohol  at  78°  into  liquid  alcohol  of  the  same  temperature  would  heat 
208  pounds  of  water  through  one  degree. 

Watt,  who  investigated  the  subject,  found  that  the  whole  quantity  of 
heat  necessary  to  raise  a  given  weight  of  water  from  zero  at  any  tempera- 
ture, and  theft  to  evaporate  it  entirely,  is  a  constant  quantity.  His  experi- 
ments showed  that  this  quantity  is  640.  Hence  the  lower  the  tempera- 
ture the  greater  the  latent  heat,  and,  on  the  other  hand,  the  higher  the 
temperature  the  less  the  latent  heat.  The  latent  heat  of  the  vapour  of 
water  evaporated  at  100°  would  be  540,  while  at  50°  it  would  be  590.  At 
higher  temperatures  the  latent  heat  of  aqueous  vapour  would  go  on  dimin- 
ishing. Water  evaporated  under  a  pressure  of  15  atmospheres  at  a  tem- 
perature of  200°,  would  have  a  latent  heat  of  440,  and  if  it  could  be 
evaporated  at  640°  it  would  have  no  latent  heat  at  all. 

Experiments  by  Southern  and  Creighton  in  1803  led  to  a  different  con- 
clusion :  namely,  that  the  latent  heat  of  evaporation  isaconstatit  quantity 
for  all  temperatures,  afid  that  the  total  quantity  of  heat  fiecessary  to 
evaporate  water  is  the  sensible  heat  plus  this  co7istant,  which  they  found 
in  round  numbers  to  be  540 ;  consequently,  to  evaporate  water  at  100^,640 
thermal  units  (418)  would  be  needed,  while  it  would  require  200  +  540  = 
740  thermal  units  to  evaporate  it  at  200°. 

Regnault,  who  examined  this  question  with  great  care,  arrived  at  results 
which  differed  from  both  these  laws.  He  found  that  the  total  quantity  of 
heat  necessary  for  the  evaporation  of  water  increases  with  the  tempej-atnre, 
and  is  not  constant,  as  Watt  had  supposed.  It  is  represented  by  the 
formula. 

Q  =  606-5  +0-305  T, 

in  which  Q  is  the  total  quantity  of  heat,  and  T  the  temperature  of  the 
water  during  evaporation,  while  the  numbers  are  constant  quantities.  The 
total  quantity  of  heat  necessary  to  evaporate  water  at  100°  is  606-5  + 
(0-305  X  100)  =637  ;  at  120°  it  is  643  ;  at  150°  it  is  651  ;  and  at  180°  it  is 
661. 

Thus  the  heat  required  to  raise  a  pound  of  water  from  zero  and  convert 
it  into  steam  at  100°  represents  a  mechanical  work  of  885430  units,  which 
would  be  sufficient  to  raise  a  ton  weight  through  a  height  of  nearly  400 
feet. 

349.  Cold  due  to  evaporation.  XtKercury  frozen. — Whatever  be  the 
temperature  at  which  a  vapour  is  produced,  an  absorption  of  heat  always 
takes  place.  If,  therefore,  a  liquid  evaporates,  and  does  not  receive  from 
without  a  quantity  of  heat  equal  to  that  which  is  expended  in  producing 
the  vapour,  its  temperature  sinks,  and  the  cooling  is  greater  in  proportion 
as  the  evaporation  is  more  rapid. 

Leslie  succeeded  in  freezing  water  by  means  of  rapid  evaporation. 


2SS 


On  Heat. 


[349- 


Under  the  receiver  ot  the  air  pump  is  placed  a  vessel  containing  strong 
sulphuric  acid,  and  above  it  a  thin  metallic  capsule  (fig.  267)  containing  a 
small  quantity  of  water.  By  exhausting  the  receiver  the  water  begins  to 
boil  (343),  and  since  the  vapours  are  absorbed  by  the  sulphuric  acid  as 


Fig.  268. 

fast  as  they  are  formed,  a  rapid  evaporation  is  produced,  which  quickly 
effects  the  freezing  of  the  water. 

This  experiment  is  best  performed  by  using,  instead  of  the  thin  metallic 
vessel,  a  watch-glass,  coated  with  lampblack  and  resting  on  a  cork.  The 
advantage  of  this  is  twofold  :  firstly,  the  lampblack  is  a  very  bad 
conductor,  and,  secondly,  it  is  not  moistened  by  the  liquid,  which  remains 
in  the  form  of  a  globule  not  in  contact  with  the  glass.  A  small  porous 
dish  may  advantageously  be  used. 

The  same  result  is  obtained  by  means  of  Wollaston's  cyrophorus  (fig. 
268),  which  consists  of  a  bent  glass  tube  provided  with  a  bulb  at  each  end. 

The  apparatus  is  prepared  by  introducing  a  small  quantity  of  water, 
which  is  then  boiled  so  as  to  expel  all  air.  It  is  then  hermetically  sealed, 
so  that  on  cooling  it  contains  only  water  and  the  vapour  of  water. 

The  water  being  introduced  into  the  bulb  A,  the  other  is  immersed  in 
a  freezing  mixture.  The  vapours  in  the  tube  are  thus  condensed  ;  the 
water  in  A  rapidly  yields  more.  But  this  rapid  production  of  vapour  re- 
quires a  large  amount  of  heat,  which  is  abstracted  from  the  water  in  A, 
and  its  temperature  is  so  much  reduced  that  it  freezes. 

Carre  has  constructed  an  apparatus  which  is  based  upon  Leslie's  ex- 
periment, and  by  which  considerable  quantities  of  water  may  be  frozen 
in  a  very  short  time.  It  consists  of  a  horizontal  brass  cylinder,  about 
fifteen  inches  in  length  and  four  in  diameter,  lined  on  the  inside  with  an 
alloy  of  antimony  and  lead,  so  as  to  resist  the  action  of  strong  sulphuric 
acid,  with  which  it  is  about  half  filled.  In  the  top  of  the  cylinder,  and 
at  one  end,  is  fitted  a  brass  tube,  bent  twice  at  right  angles,  and  con- 
structed in  such  a  manner  that  a  flask  containing  water  can  be  easily 
fitted  on  air-tight.  At  the  other  end  of  the  cylinder,  also  at  the  top,  there 
is  a  somewhat  wide  upright  tube  B.  This  is  connected  with  a  simple  air 
pump,  specially  devised  for  the  purpose,  and  there  is  an  arrangement  so 


I 


-349]  Cold  due  to  Evaporation.  289 

that  the  motion  which  works  the  pump  works  also  a  stirrer,  which  keeps 
the  acid  in  continual  agitation.  A  fresh  surface  is  thus  continually  ab- 
sorbing aqueous  vapour  ;  and  as  the  space  to  be  exhausted  is  small,  and 
the  pump  very  effective,  soon  after  its  working  commences  the  water  first 
boils  and  then  freezes.  These  apparatus  have  been  introduced  for  indus- 
trial purposes  ;  and  where  there  is  a  continual  demand  and  use  for  dilute 
sulphuric  acid,  there  seems  no  reason  why  this  should  not  be  an  econo- 
mical mode  of  making  ice. 

By  using  liquids  more  volatile  than  water,  more  particularly  liquid  sul- 
phurous acid,  which  boils  at  —  10°,  a  degree  of  cold  is  obtained  sufficiently 
intense  to  freeze  mercury.  The  experiment  may  be  made  by  covering 
the  bulb  of  a  thermometer  with  cotton  wool,  and  after  having  moistened 
it  with  liquid  sulphurous  acid,  placing  it  under  the  receiver  of  the  air 
pump.     When  a  vacuum  is  produced  the  mercury  is  quickly  frozen. 

Thilorier,  by  directing  a  jet  of  liquid  carbonic  acid  on  the  bulb  of  an 
alcohol  thermometer,  obtained  a  cold  of  —  100°  without  freezing  the  alco- 
hol. We  have  already  seen,  however  (320),  that  with  a  mixture  of  solid 
carbonic  acid,  liquid  protoxide  of  nitrogen  and  ether,  M.  Despretz 
obtained  a  sufficient  degree  of  cold  to  reduce  alcohol  to  the  viscous 
state. 

By  means  of  the  evaporation  of  bisulphide  of  carbon,  the  formation  of 
ice  may  be  illustrated  without  the  aid  of  an  air  pump.  A  little  water  is 
dropped  on  a  board,  and  a  capsule  of  thin  copper  foil,  containing  bi- 
sulphide of  carbon,  is  placed  on  the  water.  The  evaporation  of  the 
bisulphide  is  accelerated  by  means  of  a  pair  of  bellows,  and  after  a 
few  minutes  the  water  freezes  round  the  capsule,  so  that  the  latter  adheres 
to  the  wood. 

In  like  manner,  if  some  water  be  placed  in  a  test  tube  which  is  then 
dipped  in  a  glass  containing  some  ether,  and  a  current  of  air  be  blown 
through  the  ether  by  means  of  a  glass  tube  fitted  to  the  nozzle  of  a  pair 
of  bellows,  the  rapid  evaporation  of  the  ether  very  soon  freezes  the  water 
in  the  tube. 

Richardson's  apparatus  for  producing  local  anaesthesia  also  depends  on 
the  cold  produced  by  the  evaporation  of  ether. 

The  cold  produced  by  evaporation  is  used  in  hot  climates  to  cool  water 
by  means  of  alcarrazas.  These  are  porous  earthen  vessels,  through  which 
water  percolates,  so  that  on  the  outside  there  is  a  continual  evaporation 
which  is  accelerated  when  the  vessels  are  placed  in  a  current  of  air.  For 
the  same  reason  wine  is  cooled  by  wrapping  the  bottles  in  wet  cloths  and 
placing  them  in  a  draught. 

In  Harrison's  method  of  making  ice  artificially,  a  steam  engine  is  used 
to  work  an  air  pump,  which  produces  a  rapid  evaporation  of  some  ether, 
in  which  is  immersed  the  vessel  containing  the  water  to  be  frozen.  The 
apparatus  is  so  constructed  that  the  vaporised  ether  can  be  condensed 
and  used  again. 

The  cooling  effect  produced  by  a  wind  or  draught  does  not  necessarily, 
arise  from  the  wind  being  cooler,  for  it  may,  as  shown  by  the  thermo- 
meter, be   actually   warmer ;  but   arises  from  the  rapid  evaporation  it 

o 


290 


On  Heat. 


[349 


causes  from  the  surface  of  the  skin.  We  have  the  feeling  of  oppression, 
even  at  moderate  temperatures,  when  we  are  in  an  atmosphere  saturated 
by  moisture,  in  which  no  evaporation  takes  place. 

,  350.  Carre's  apparatus  for  freezing-  water. — We  have  already  seen 
that  when  any  liquid  is  converted  into  vapour  it  absorbs  a  considerable 
quantity  of  sensible  heat ;  this  furnishes  a  source  of  cold  which  is  the 
more  abundant  the  more  volatile  the  liquid  and  the  greater  its  heat  of 
vaporisation. 

This  property  of  liquids  has  been  utilised  by  M.  Carre,  in  freezing 
water  by  the  distillation  of  ammonia.  The  apparatus  consists  of  a  cyhn- 
drical  boiler  C  (figs.  269,  270)  and  of  a  slightly  conical  vessel  A,  which  is 


Fig.  269. 


Fig.  270. 


^^  freezer.  These  two  vessels  are  connected  by  a  tube  ;;z,  and  a  brace  «, 
binds  them  firmly.  They  are  made  of  strong  galvanised  iron  plate,  and 
can  resist  a  pressure  of  seven  atmospheres. 

The  boiler  C,  which  holds  about  two  gallons,  is  three  parts  filled  with  a 
strong  solution  of  ammonia.  In  a  tubulure  in  the  upper  part  of  the  boiler 
some  oil  is  placed,  and  in  this  a  thermometer  t  indicating  temperatures 
from  icx)°  to  150°.  The  freezer  A  consists  of  two  concentric  envelopes, 
in  such  a  manner  that  its  centre  being  hollow,  a  metal  vessel  G,  con- 
taining the  water  to  be  frozen,  can  be  placed  in  this  space.  Hence  only 
the  annular  space  between  the  sides  of  the  freezer  is  in  communication 
with  the  boiler  by  means  of  the  tube  m.  In  the  upper  part  of  the  freezer 
there  is  a  small  tubulure,  which  can  be  closed  by  a  metal  stopper,  and  by 
which  the  solution  of  ammonia  is  introduced. 

The  formation  of  ice  comprehends  two  distinct  operations.  In  the 
first,  the  boiler  is  placed  in  a  furnace  F,  and  the  freezer  in  a  bath  of  cold 


-352]  Carre's  Apparatus  for  Freezing  Water.  291 

water  of  about  1 2°  The  boiler  being  heated  to  1 30°  the  ammoniacal 
gas  dissolved  in  the  water  of  the  boiler  is  disengaged,  and,  in  virtue  of 
its  own  pressure,  is  liquefied  in  the  freezer,  along  with  about  a  tenth  of 
its  weight  of  water.  This  distillation  of  C  towards  A  lasts  about  an  hour 
and  a  quarter,  and  when  it  is  finished  the  second  operation  commences  ; 
this  consists  in  placing  the  boiler  in  the  cold-water  bath  (fig.  270),  and  the 
freezer  outside,  care  being  taken  to  surround  it  with  very  dry  flannel. 
The  vessel  G,  about  three-quarters  full  of  water,  is  placed  in  the  freezer. 
As  the  boiler  cools,  the  ammoniacal  gas  with  which  it  is  filled  is  again 
dissolved ;  the  pressure  thus  being  diminished  the  ammonia  which  has 
been  liquefied  in  it  is  converted  into  the  gaseous  form,  and  now  distils 
from  A  towards  C,  to  redissolve  in  the  water  which  has  remained  in  the 
boiler.  During  this  distillation  the  ammonia  which  is  rarefied  absorbs  a 
great  quantity  of  heat,  which  is  withdrawn  from  the  vessel  G  and  the 
water  it  contains.  Hence  it  is  that  this  water  freezes.  In  order  to  have 
better  contact  between  the  sides  of  the  vessel  G  and  the  freezer,  alcohol 
is  poured  between  them.  In  about  an  hour  and  a  quarter  a  perfectly 
compact  cylindrical  block  of  ice  can  be  taken  from  the  vessel  G. 

This  apparatus  gives  about  four  pounds  of  ice  in  an  hour,  at  a  price  of 
about  a  farthing  per  pound  ;  large  continuously  working  apparatus  have, 
however,  been  constructed,  which  produce  as  much  as  800  pounds  of  ice 
in  an  hour. 

LIQUEFACTION   OF  VAPOURS  AND   GASES. 

351.  liiquefaction  of  vapours. — The  liquefaction  or  condensation  of 
vapours  is  their  passage  from  the  aeriform  to  the  liquid  state.  Conden- 
sation may  be  due  to  three  causes — cooling,  compression,  or  chemical 
affinity.  For  the  first  two  causes  the  vapours  must  be  saturated  (330), 
while  the  latter  produces  the  liquefaction  of  the  most  rarefied  vapours. 
Thus,  a  large  number  of  salts  absorb  and  condense  the  aqueous  vapour  in 
the  atmosphere,  however  small  its  quantity. 

When  vapours  are  condensed,  their  latent  heat  becomes  free,  that  is,  it 
affects  the  thermometer.  This  is  readily  seen  when  a  current  of  steam 
at  100°  is  passed  into  a  vessel  of  water  at  the  ordinary  temperature.  The 
liquid  becomes  rapidly  heated,  and  soon  reaches  100°.  The  quantity  of 
heat  given  up  in  liquefaction  is  equal  to  the  quantity  absorbed  in  pro- 
ducing the  vapour. 

352.  Blstillatlon.  Stills. — Distillation  is  an  operation  by  which  a 
volatile  liquid  may  be  separated  from  substances  which  it  holds  in  solu- 
tion, or  by  which  two  liquids  of  different  volatilities  may  be  separated. 
The  operation  depends  on  the  transformation  of  liquids  into  vapours  by 
the  action  of  heat,  and  on  the  condensation  of  these  vapours  by  cooling. 

The  apparatus  used  in  distillation  is  called  2l  still.  Its  form  may  vary 
greatly,  but  consists  essentially  of  three  parts  :  ist,  the  body^  A  (fig.  271), 
a  copper  vessel  containing  the  liquid,  the  lower  part  of  which  fits  in  the 
furnace  :  2nd,  the  head,  B,  which  fits  on  the  body,  and  from  which  a 
lateral  tube,  C,  leads  to,  3rd,  worm,  S,  a  long  spiral  tin  or  copper  tube. 


292 


On  Heat. 


[352- 


placed  in  a  cistern  kept  constantly  full  of  cold  water.  The  object  of  the 
worm  is  to  condense  the  vapour,  by  exposing  a  greater  extent  of  cold 
surface. 


To  free  ordinary  well  water  from  the  many  impurities  which  it  contains, 
it  is  placed  in  a  still  and  heated.     The  vapours  disengaged  are  condensed 


Fig.  272. 

in  the  worm,  and  the  distilled  water  arising  from  the  conden.sation  is  col- 
lected in  the  receiver,  D.     The  vapours  in  condensing  rapidly  heat  the 


-354]      Determination  of  the  Alcoholic  Value  of  Wines,     293 

water  in  the  cistern,  which  must,  therefore,  be  constantly  renewed.  For 
this  purpose  a  continual  supply  of  cold  water  passes  into  the  bottom  of 
the  cistern,  while  the  lighter  heated  water  rises  to  the  surface  and  escapes 
by  a  tube  in  the  top  of  the  cistern. 

353.  Ibiebigr's  condenser. — In  distilling  smaller  quantities  of  liquids, 
or  in  taking  the  boiling  point  of  a  liquid,  so  as  not  to  lose  any  of  it,  the 
apparatus  known  as  Liebig's  condenser  is  extremely  useful.  It  consists  of 
a  glass  tube,  //,  fig.  272,  about  thirty  inches  long,  fitted  in  a  copper  or  tin 
tube  by  means  of  perforated  corks.  A  constant  supply  of  cold  water  from 
the  vessel  a  passes  into  the  space  between  the  two  tubes,  being  conveyed 
to  the  lower  part  of  the  condenser  by  a  funnel  and  tubej^  and  flowing  out 
from  the  upper  part  of  the  tube  g.  The  liquid  to  be  distilled  is  contained 
in  a  retort,  the  neck  of  which  is  placed  in  the  tube ;  the  condensed  hquid 
drops  quite  cold  into  a  vessel  placed  to  receive  it  at  the  other  extremity 
of  the  condensing  tube. 

354.  Apparatus  for  determinlngr  tbe  alcobolic  value  of  wines. — 
One  of  the  forms  of  this  apparatus  consists  of  a  glass  flask  resting  on  a 
tripod,  and  heated  by  a  spirit  lamp  (fig.  273).     By  means  of  a  caout- 


Fig.  273. 

chouc  tube  this  is  connected  with  a  serpentine  placed  in  a  copper  vessel 
filled  with  cold  water,  and  below  which  is  a  test-glass  for  collecting  the 
distillate.  On  this  are  three  divisions,  one  a,  which  measures  the  quan- 
tity of  wine  taken  ;  the  two  others  indicating  one-half  and  one-third  of 
this  volume. 

The  test-glass  is  filled  with  the  wine  up  to  a,  this  is  then  poured  into 
the  flask,  which,  having  been  connected  with  the  serpentine,  the  distilla- 
tion is  commenced.  The  liquid  which  distils  over  is  a  mixture  of  alcohol 
and  water  ;  for  ordinary  wines,  such  as  clarets  and  hocks,  about  one-third 
is  distilled  over,  and  for  wines  richer  in  spirit,  such  as  sherries  and  ports, 


294 


071  Heat. 


[354- 


one-half  must  be  distilled ;  experiment  has  shown  that  under  these  cir- 
cumstances all  the  alcohol  passes  over  in  the  distillate.  The  measure  is 
then  filled  up  with  distilled  water  to  a  ;  this  gives  the  mixture  of  alcohol 
and  water  of  the  same  volume  as  the  wine  taken,  free  from  all  solid  mat- 
ters, such  as  sugar,  colouring  matter,  and  acid,  but  containing  all  the 
alcohol.  The  specific  gravity  of  this  distillate  is  then  taken  by  means  of 
an  alcoholometer  (125),  and  the  number  thus  obtained  corresponds  to  a 
certain  strength  of  alcohol  as  indicated  by  the  tables. 

355.  Safety  tube. — In  preparing  gases  and  collecting  them  overmer-" 
cury  or  water,  it  occasionally  happens  that  these  liquids  rush  back  into 
the  generating  vessel,  and  destroy  the  operation.  This  arises  from  an 
excess  of  atmospheric  pressure  over  the  tension  in  the  vessel.  If  a  gas, 
sulphurous  acid,  for  example,  be  generated  in  the  flask  m  (fig.  274),  and 
be  passed  into  water  in  the  vessel  A,  as  long 
as  the  gas  is  given  off  freely,  its  tension  ex- 
ceeds the  atmospheric  pressure  and  the 
weight  of  the  column  of  water,  071,  so  that  the 
water  in  the  vessel  cannot  rise  in  the  tube, 
and  absorption  is  impossible.  But  if  the  ten- 
sion decreases  either  through  the  flask  be- 
coming cooled,  or  the  gas  being  disengaged 
too  slowly,  the  external  pressure  prevails, 
and  when  it  exceeds  the  internal  tension  by 
more  than  the  weight  of  the  column  of  water 
CO.  the  water  rises  into  the  flask  and  the 
This  accident  is  prevented  by  means  of  safety 


Fig,  274. 


operation   is   spoiled. 
htbes. 

These  are  tubes  which  prevent  absorption  by  allowing  air  to  enter  in 
proportion  as  the  internal  tension  decreases.     The  simplest  is  a  tube  Qo, 


Fig.  275. 


Fig.  276. 


fig.  275,  passing  through  the  cork  which  closes  the  flask  M,  in  which  the 
gas  is  generated,  and  dipping  in  the  liquid.  When  the  tension  of  the  gas 
diminishes  in  M,  the  atmospheric  pressure  on  the  water  in  the  bath  E 


-356]  Liquefaction  of  Gases.  295 

causes  it  to  rise  to  a  certain  height  in  the  tube  DA ;  but  this  pressure, 
acting  also  on  the  hquid  in  the  tube  Co,  depresses  it  to  the  same  extent, 
assuming  that  this  liquid  has  the  same  density  a5  the  water  in  E.  Now 
as  the  distance  or  is  less  than  the  height  DH,  air  enters  by  the  aperture  o, 
before  the  water  in  the  bath  can  rise  to  A,  and  no  absorption  takes  place. 

Fig.  276  represents  another  kind  of  safety  tube.  It  has  a  bulb  a,  con- 
taining a  certain  quantity  of  liquid,  as  does  also  id.  When  the  tension 
of  the  gas  in  the  retort  M  exceeds  the  atmospheric  pressure,  the  level  in 
the  leg  id  rises  higher  than  in  the  bulb,  a  ;  if  the  gas  has  the  tension  of 
one  atmosphere,  the  level  is  the  same  in  the  tube  as  in  the  bulb.  Lastly, 
if  the  tension  of  the  gas  is  less  than  the  atmospheric  pressure,  the  level 
sinks  in  the  leg  di  ;  and,  as  care  is  taken  that  the  height  ia  is  less  than 
bh,  as  soon  as  the  air  which  enters  through  c  reaches  the  curved  part  /,  it 
raises  the  column  ia,  and  passes  into  the  retort  before  the  water  in  the 
cylinder  can  reach  b ;  the  tension  in  the  interior  is  then  equal  to  the  ex- 
terior pressure,  and  no  absorption  takes  place. 

356.  Iiiquefaction  of  g:ases. — We  have  already  seen  that^a  saturated 
vapour,  the  temperature  of  which  is  constant,  is  liquefied  by  increasing 
the  pressure,  and  that,  the  pressure  remaining  constant,  it  is  brought  into 
the  liquid  state  by  diminishing  the  temperature. 

Unsaturated  vapours  behave  in  all  respects  like  gases.  And  it  is  natu- 
ral to  suppose  that  what  are  ordinarily  called  permanejit  gases  are  really 
unsaturated  vapours.  For  the  gaseous  form  is  accidental,  and  is  not 
inherent  in  the  nature  of  the  substance.  At  ordinary  temperatures  sul- 
phurous acid  is  a  gas,  while  in  countries  near  the  poles  it  is  a  liquid  ;  in 
temperate  climates  ether  is  a  Hquid,  at  a  tropical  heat  it  is  a  gas.  And  just 
as  unsaturated  vapours  may  be  brought  to  the  state  of  saturation  and  then 
liquefied  by  suitably  diminishing  the  temperature  or  increasing  the 
pressure,  so  by  the  same  means  gases  may  be  liquefied.  But  as  they  are 
mostly  very  far  removed  from  this  state  of  saturation,  great  cold  and 
pressure  are  required.  Some  of  them  may  indeed  be  liquefied  either  by 
cold  or  by  pressure  ;  for  the  majority,  however,  both  agencies  must  be 
simultaneously  employed.  Few  gases  can 
resist  these  combined  actions,  and  probably 
those  which  have  not  yet  been  liquefied, 
hydrogen,  oxygen,  nitrogen,  binoxide  of  nitro- 
gen, and  carbonic  oxide,  would  become  so 
if  submitted  to  a  sufficient  degree  of  cold 
and  pressure. 

Faraday  was  the  first  to  liquefy  some  of 
the  gases.  His  method  consists  in  enclosing 
in  a  bent  glass  tube  (fig.  277)  substances  by 
whose  chemical  action  the  gas  to  be  liquefied 
is  produced  and  then  sealing  the  shorter  leg.  '^'  ^'^^' 

In  proportion  as  the  gas  is  disengaged  its  pressure  increases,  and  it  ulti- 
mately liquefies  and  collects  in  the  shorter  leg,  more  especially  if  its  con- 
densation is  assisted  by  placing  the  shorter  leg  in  a  freezing  mixture.  A 
small  manometer  may  be  placed  in  the  apparatus  to  indicate  the  pressure. 


296  On  Heat.  [356- 

Cyanogen  gas  is  readily  liquefied  by  heating  cyanide  of  mercury  in  a 
bent  tube  of  this  description  ;  and  carlDonic  acid  by  heating  bicarbonate 
of  sodium  ;  other  gases  have  been  condensed  by  taking  advantage  of  special 
reactions,  the  consideration  of  which  belongs  rather  to  chemistry  than  to 
physics.  For  example,  chloride  of  silver  absorbs  about  200  times  its 
volume  of  ammoniacal  gas  ;  when  the  compound  thus  formed  is  placed  in 
a  freezing  tube  and  gently  heated,  while  the  shorter  leg  is  immersed  in  a 
freezing  mixture,  a  quantity  of  liquid  ammoniacal  gas  speedily  collects  in 
the  shorter  leg. 

357.  Apparatus  to  liquefy  and  soUaify  grases. — Thilorier  first  con- 
structed an  apparatus  by  which  considerable  quantities  of  carbonic  acid 
could  be  liquefied.  Its  principle  is  the  same  as  that  used  by  Faraday  in 
working  with  glass  tubes  ;  the  gas  is  generated  in  an  iron  cylinder,  and 
passes  through  a  metallic  tube  into  another  similar  cylinder  where  it  con- 
denses. The  use  of  this  apparatus  is  not  free  from  danger  ;  many  acci- 
dents have  already  happened  with  it,  and  it  has  been  superseded  by  an 
apparatus  constructed  by  Natterer,  of  Vienna,  which  is  both  convenient 
and  safe. 

A  perspective  view  of  the  apparatus,  as  modified  by  M.  Bianchi,  is  repre- 
sented in  fig.  279,  and  a  section  on  a  larger  scale  in  fig.  278.  It  consists  of 
a  wrought-iron  reservoir  A,  of  something  less  than  a  quart  capacity,  which 
can  resist  a  pressure  of  more  than  600  atmospheres.  A  small  force  pump 
is  screwed  on  the  lower  part  of  this  reservoir.  The  piston  rod  t  is  moved 
by  the  crank  rod  E,  which  is  worked  by  the  handle  M.  As  the  com- 
pression of  the  gas  and  the  friction  of  the  piston  produce  a  considerable 
disengagement  of  heat,  the  reservoir  A  is  surrounded  by  a  copper  vessel, 
in  which  ice  or  a  freezing  mixture  is  placed.  The  water  arising  from  the 
melting  of  the  ice  passes  by  a  tube,  w,  into  a  cylindrical  copper  case  C, 
which  surrounds  the  force  pump,  from  whence  it  escapes  through  the 
tube  n^  and  the  stopcock  0.  The  whole  arrangement  rests  on  an  iron 
frame,  PQ. 

The  gas  to  be  Hquefied  is  previously  collected  in  air-tight  bags,  R,  from 
whence  it  passes  into  a  bottle,  V,  containing  some  suitable  drying  sub- 
stance ;  it  then  passes  into  the  condensing  pump  through  the  vulcanised 
india-rubber  tube  H.  After  the  apparatus  has  been  worked  for  some  time 
the  reservoir  A  can  be  unscrewed  from  the  pump  without  any  escape  of 
the  liquid,  for  it  is  closed  below  by  a  valve  S  (fig.  278).  In  order  to  collect 
some  of  the  liquid  gas  the  reservoir  is  inverted  and  on  turning  the  stop- 
cock r,  the  liquid  escapes  by  a  small  tubulure  x. 

When  carbonic  acid  has  been  liquefied,  and  is  allowed  to  escape  into 
the  air,  a  portion  only  of  the  liquid  volatilises,  in  consequence  of  the  heat 
absorbed  by  this  evaporation  ;  the  rest  is  so  much  cooled  as  to  solidify  in 
white  flakes  like  snow  or  anhydrous  phosphoric  acid. 

Solid  carbonic  acid  evaporates  very  slowly.  By  means  of  an  alcohol 
thermometer  its  temperature  has  been  found  to  be  about  —90°.  A  small 
quantity  placed  on  the  hand  does  not  produce  the  sensation  of  such  great 
cold  as  might  be  expected.  This  arises  from  the  imperfect  contact.  But 
if  the  solid  be  mixed  with  ether  the  cold  produced  is  so  intense  that  when 


357] 


Liquefaction  of  Gases. 


297 


a  little  is  placed  on  the  skin  all  the  effects  of  a  severe  burn  are  produced. 

A  mixture  of  these  two  substances  solidifies  four  times  its  weight  of  mer-         

cury  in  a  few  minutes.  When  a  tube  containing  liquid  carbonic  acid  is 
placed  in  this  mixture,  the  liquid  becomes  solid,  and  looks  like  a  trans- 
parent piece  of  ice. 

The  most  remarkable  liquefaction  obtained  by  this  apparatus  is  that  ot 
protoxide  of  nitrogen.     The  gas  once  liquefied  only  evaporates  slowly,  and 


Fig.  279. 


produces  a  temperature  of  88°  below  zero.  Mercury  placed  in  it  in  small 
quantities  instantly  solidifies.  The  same  is  the  case  with  water ;  it  must 
be  added  drop  by  drop,  otherwise  its  latent  heat  being  much  greater  than 
that  of  mercury,  the  heat  given  up  by  the  water  in  solidifying  would  be 
sufficient  to  cause  an  explosion  of  the  protoxide  of  nitrogen. 

Protoxide  of  nitrogen  is  readily  decomposed  by  heat,  and  has  the  pro- 

03 


298  On  Heat.  [357- 

perty  of  supporting  the  combustion  of  bodies  with  almost  as  much  bril- 
liancy as  oxygen;  and  even  at  low  temperatures  it  preserves  this  pro- 
perty. When  a  piece  of  incandescent  charcoal  is  thrown  on  liquid  pro- 
toxide of  nitrogen  it  continues  to  burn  with  a  brilliant  light. 

The  cold  produced  by  the  evaporation  of  ether  has  been  used  by  MM. 
Loir  and  Drion  in  the  liquefaction  of  gases.  By  passing  a  current  of  air 
from  a  blowpipe  bellows  through  several  tubes  into  a  few  ounces  of  ether, 
a  temperature  of  —  34°  C,  can  be  reached  in  five  or  six  minutes,  and  may 
be  kept  up  for  fifteen  or  twenty  minutes.  By  evaporating  liquid  sulphu- 
rous acid  in  the  same  manner  a  great  degree  of  cold,  —  50°  C,  is  obtained. 
At  this  temperature  ammoniacal  gas  may  be  liquefied.  By  rapidly 
evaporating  liquid  ammonia  under  the  air  pump,  in  the  presence  of 
sulphuric  acid,  a  temperature  of  —87°  is  attained,  which  is  found  suffi- 
cient to  liquefy  carbonic  acid  under  the  ordinary  pressure  of  the  atmo- 
sphere. 

By  means  of  a  bath  of  ether  and  of  solid  carbonic  acid,  and  by  using  very 
high  pressures,  Andrews  succeeded  in  reducing  air  to  -^^  of  its  bulk 
oxygen  to  ^f^,  hydrogen  to  -^-^^  carbonic  oxide  to  gf  g,  and  nitric  oxide  to 
ilo  of  its  original  volume,  but  without  producing  liquefaction.  Hydrogen 
and  carbonic  oxide  departed  less  from  Boyle's  law  than  oxygen  and 
nitric  oxide.  ^  ,  . 

\JL       a>/^^^  ■        MIXTURES   OF  GASES   AND   VAPOURS. 

358.  Iiaws  of  the  mixture  of  g:ases  and  vapours. — Every  mixture  of 
a  gas  and  a  vapour  obeys  the  following  two  laws  :  — 

I.  The  tension  J  and,  consegue7ttly,  the  quantity  of  vapour  which  satu- 
rates a  given  space,  are  the  same  for  the  same  temperature,  whether  this 
space  contains  a  gas  or  is  a  vacuum. 

II.  The  tension  of  the  mixture  of  a  gas  and  a  vapour  is  equal  to  the 
sum  of  the  tensions  which  each  would  possess  if  it  occupied  the  same  space 
alone. 

These  are  known  as  Dalton^s  laws,  from  their  discoverer,  and  are  de- 
monstrated by  the  following  apparatus,  which  was  invented  by  Gay- 
Lussac  : — It  consists  of  a  glass  tube  A  (fig.  280),  to  which  two  stopcocks, 
b  and  d,  are  cemented.  The  lower  stopcock  is  provided  with  a  tubulure, 
which  connects  the  tube  A  with  a  tube  B  of  smaller  diameter.  A  scale 
between  the  two  tubes  serves  to  measure  the  heights  of  the  mercurial 
columns  in  these  tubes. 

The  tube  A  is  filled  with  mercury,  and  the  stopcocks  b  and  d  are 
closed.  A  glass  globe,  M ,  filled  with  dry  air  or  any  other  gas  is  screwed 
on  by  means  of  a  stopcock  in  the  place  of  the  funnel  C.  All  three  stop- 
cocks are  then  opened,  and  a  little  mercury  is  allowed  to  escape,  which 
is  replaced  by  the  dry  air  of  the  globe.  The  stopcocks  are  then  closed, 
and  as  the  air  in  the  tube  expands  on  leaving  the  globe  the  pressure  on  it 
is  less  than  that  of  the  atmosphere.  Mercury  is  accordingly  poured  into 
the  tube  B  until  it  is  at  the  same  level  in  both  tubes.  The  globe  is  then 
removed,  and  replaced  by  a  funnel  C,  provided  with  a  stopcock  ^  of  a 


359] 


Mixtures  of  Gases  and  Vapours. 


299 


peculiar  construction.  It  is  not  perforated,  but  has  a  small  cavity,  as  re- 
presented in  ;/,  on  the  left  of  the  figure.  Some  of  the  liquid  to  be  vaporised 
is  poured  into  C,  and  the  height  of  the  mercury,  k,  having  been  noted 
the  stopcock  b  is  opened,  and  a  turned,  so  that  its  cavity  becomes  filled 
with  liquid ;  being  again  turned,  the  liquid  enters  the  space  A  and 
vaporises.  The  Hquid  is  allowed  to  fall  drop 
by  drop  until  the  air  in  the  tube  is  saturated, 
which  is  the  case  when  the  level  k  of  the 
mercury  ceases  to  sink  (329). 

As  the  tension  of  the  vapour  produced  in 
the  space  A  is  added  to  that  of  the  air 
already  present,  the  total  volume  of  gas  is 
increased.  It  may  easily  be  restored  to  its 
original  volume  by  pouring  mercury  into  B. 
When  the  mercury  in  the  large  tube  has  been 
raised  to  the  level  k,  there  is  a  difference, 
B<?,  in  the  level  of  the  mercury  in  the  two 
tubes,  which  obviously  represents  the  tension 
of  the  vapour ;  for  as  the  air  has  resumed  its 
original  volume,  its  tension  has  not  changed. 
Now  if  a  few  drops  of  the  same  liquid  be 
passed  into  the  vacuum  of  a  barometric  tube 
a  depression  exactly  equal  to  B<7  is  produced, 
which  proves  that,  for  the  same  temperature, 
the  tension  of  a  saturated  vapour  is  the  same 
in  a  gas  as  in  a  vacuum  ;  from  which  it  is 
concluded  that  at  the  same  temperature  the 
quantity  of  vapour  is  also  the  same. 

The  second  law  is  likewise  proved  by  this 
experiment,  for  when  the  mercury  has  re- 
gained its  level,  the  mixture  supports  the 
atmospheric  pressure  on  the  top  of  the  column 
B,  in  addition  to  the  weight  of  the  column  of  '^^^^^a=^^^^^^^ 


Fig.  280. 


mercury  B^.     But  of  these  two  pressures,  one 

represents  the  tension  of  the  dry  air,  and  the 

other  the  tension  of  the  vapour.   The  second  law  is,  moreover,  a  necessary 

consequence  of  the  first. 

Experiments  can  only  be  made  with  this  apparatus  at  ordinary  tem- 
peratures :  but  M.  Regnault,  by  means  of  an  apparatus  which  can  be 
used  at  different  temperatures,  has  investigated  the  tensions  of  the 
vapours  of  water,  ether,  bisulphide  of  carbon,  and  benzole,  both  in  vacuo 
and  in  air.  He  has  found  that  the  tension  in  air  is  less  than  it  is  in 
vacuo,  but  the  differences  are  so  small  as  not  to  invahdate  Dalton's  law. 
M.  Regnault  is  even  inclined  to  consider  this  law  as  theoretically  true, 
attributing  the  differences  which  he  observed  to  the  hygroscopic  pro- 
perties of  the  sides  of  the  tube. 

359.  Problems  on  mixtures  of  grases  and  vapours. — I.  A  volume  of 
dry  air  V,  at  the  pressure  H,  being  given,  what  will  be  its  volume  V, 


300  On  Heat.  [359- 

when  it  is  saturated  with  vapour,  the  temperature  and  the  pressure  re- 
maining the  same  ? 

If  F  be  the  elastic  force  of  the  vapour  which  saturates  the  air,  the 
latter,  in  the  mixture,  only  supports  a  pressure  equal  to  H  —  F  (358).  But 
by  Boyle's  law  the  volumes  V  and  V  are  inversely  as  their  pressures, 
consequently 

I I.  Let  V  be  a  given  volume  of  saturated  air  at  the  pressure  H,  and  the 
temperature  /,  what  will  be  its  volume  V,  also  saturated,  at  the  pressure 
H',  and  the  temperature  /'? 

If/be  the  maximum  tension  of  aqueous  vapour  at  /°  and/'  its  maxi- 
mum tension  at  t'°,  the  air  alone  in  each  of  the  mixtures  V  and  V  will  be 
respectively  under  the  pressures  H— /and  W —f  \  consequently,  assum- 
ing first  that  the  temperature  is  constant,  we  obtain 

Y,'=  H  -/ 

V       H'-/'  .         * 

But  as  the  volumes  V  and  V  of  air,  at  the  temperatures  /'  and  /,  are  in 
the  ratio  of  i  -1-  df  to  i  -f-  a/,  a  being  the  coefficient  of  the  expansion  of  air, 
the  equation  becomes 

V^_  H-/-^i  +  o/^ 
V      W-f^'i^.t' 

III.  What  is  the  weight  P  of  a  volume  of  air  V,  saturated  with  aqueous 
vapour  at  the  temperature  /  and  pressure  H  ? 

If  we  call  F  the  maximum  tension  of  the  vapour  at  f,  the  tension  of 
the  air  alone  will  be  H  —  F,  and  the  problem  reduces  itself  to  finding  : 
I  St,  the  weight  of  V  cubic  inches  of  dry  air  at  /,  and  under  the  pressure 
H  —  F  ;  and  2nd,  the  weight  of  V  cubic  inches  of  saturated  vapour  at  f 
under  the  pressure  F. 

To  solve  the  first  part  of  the  problem,  we  know  that  a  cubic  inch  of  dry 
air  at  0°  and  the  pressure  760  millimetres  weighs  0*3 1  grains,  and  that 

at  /°,  and  the  pressure  H  -  F,  it  weighs  -^ — \--JZ^  (309A  consequently 

V  cubic  inches  of  dry  air  weigh 

o-3i(H-F)V 

(l+c./)   760 ^    ^ 

To  obtain  the  weight  of  the  vapour,  the  weight  of  the  same  volume  of 
dry  air  at  the  same  temperature  and  pressure  must  be  sought,  and  this 
is  to  be  multiplied  by  the  relative  density  of  the  vapour.     Now  as  V 

cubic  inches  of  dry  air  at  t°.  and  the   pressure  F,   weis^h  — ^ — ^ 

V  cubic  inches  of  aqueous  vapour,  whose  density  is  |  of  that  of  air  (362), 
weigh 

0*31  X  VF      5  /  \ 

-^ X  -'- (2  ) 

(i+o/}76o     8  ^^ 


-360]  Spheroidal  Condition.  30 1 

and  as  the  weight  P  is  equal  to  the  sum  of  the  weights  (i)  and  (2)  we 
have 

o'3ixV(H-F)      ro'3ixVF     ^  sH  _  0-31  xVF    .h-JF) 
(i+a/)76o         L(i+a^)76o      8 J      (1+0^)760^        '    '^* 


SPHEROIDAL  CONDITION. 

360.  iLeidenfrost's  pbenoxnenon.  Bouti^ny's  experiments. — When 
hquids  are  thrown  upon  incandescent  metaUic  surfaces  they  present  re- 
markable phenomena,  which  were  first  observed  by  Leidenfrost  a  century 
ago,  and  have  been  named  after  their  discoverer.  They  have  since  then 
been  studied  by  other  physicists,  and  more  especially  by  M.  Boutigny,  to 
whom  our  present  knowledge  of  the  subject  is  mainly  due. 

When  a  tolerably  thick  silver  or  platintim  dish  is  heated  to  redness, 
and  a  little  water,  previously  warmed,  dropped  into  the  dish,  by  means  of 
a  pipette,  the  liquid  does  not  spread  itself  out  on  the  dish,  and  does  not 
moisten  it,  as  it  would  at  the  ordinary  temperature,  but  assumes  the  form 
of  a  flattened  globule,  which  fact  M.  Boutigny  expresses  by  saying  that 
it  has  passed  into  the  spheroidal  state.  It  rotates  rapidly  round  on  the 
bottom  of  the  dish,  takmg  sometimes  the  form  of  a  star,  and  not  only  does 
it  hot  boil,  but  its  evaporation  is  only  about  one  fiftieth  as  rapid  as  if  it 
boiled.  As  the  dish  cools,  a  point  is  reached  at  which  it  is  not  hot 
enough  to  keep  the  water  in  the  spheroidal  state  ;  it  is  accordingly 
moistened  by  the  liquid,  and  a  violent  ebullition  suddenly  ensues. 

All  volatile  liquids  can  assume  the  spheroidal  condition  ;  the  lowest 
temperature  at  which  it  can  be  produced  varies  with  each  liquid,  and  is 
more  elevated  the  higher  the  boiling  point  of  the  liquid.  For  water,  the 
dish  must  have  at  least  a  temperature  of  200°  ;  for  alcohol,  134°  ;  and  for 
ether,  61°. 

The  temperature  of  a  liquid  in  the  spheroidal  state  is  always  below  its 
boiling  point.  This  temperature  has  been  measured  by  M.  Boutigny  by 
means  of  a  very  delicate  thermometer  ;  but  his  method  is  not  free  from 
objections,  and  it  is  probable  that  the  temperatures  he  obtained  were  too 
high.  He  found  that  of  water  to  be  95°  ;  alcohol,  75°  ;  ether,  34°  ;  and 
liquid  sulphurous  acid,— 11°.  But  the  temperature  of  the  vapour  which 
is  disengaged  appears  to  be  as  high  as  that  of  the  vessel  itself. 

This  property  of  liquids  in  the  spheroidal  state  remaining  below  their 
boiling  point  has  been  applied  by  M.  Boutigny  in  a  remarkable  experi- 
ment, that  of  freezing  water  in  a  red-hot  crucible.  He  heated  a  platinum 
dish  to  bright  redness,  and  placed  a  small  quantity  of  liquid  sulphurous 
acid  in  it.  It  immediately  assumed  the  spheroidal  condition,  and  its 
evaporation  was  remarkably  slow.  Its  temperature,  as  has  been  stated, 
was  about  -11°,  and  when  a  small  quantity  of  water  was  added  it 
immediately  solidified,  and  a  small  piece  of  ice  could  be  thrown  out  of 
the  red-hot  crucible.  In  a  similar  manner  Faraday,  by  means  of  a  mix- 
ture of  solid  carbonic  acid  and  ether,  succeeded  in  freezing  mercury  in  a 
red-hot  crucible. 

In  the  spheroidal  state  the  liquid  is  not  in  contact  with  the  vessel. 


302  On  Heat.  [360- 

M.  Boutigny  proved  this  by  heating  a  silver  plate  placed  in  a  horizontal 
position,  and  dropping  on  it  a  little  dark  coloured  water.  The  Hquid 
assumed  the  spheroidal  condition,  and  the  flame  of  a  candle  placed  at 
some  distance  could  be  distinctly  seen  between  the  drop  and  the  plate. 
If  a  plate  perforated  by  several  fine  holes  be  heated,  a  liquid  will  assume 
the  spheroidal  state  when  projected  upon  it.  This  is  also  the  case  with 
a  flat  helix  of  platinum  wire  pressed  into  a  slightly  concave  shape.  An 
experiment  of  another  class,  due  to  Mr.  A.  H.  Church,  also  illustrates  the 
same  fact.  A  polished  silver  dish  is  made  red-hot,  and  a  few  drops  of  a 
solution  of  sulphide  of  sodium  are  projected  on  it.  The  liquid  passes 
into  the  spheroidal  condition,  and  the  silver  undergoes  no  alteration. 
But  if  the  dish  is  allowed  to  cool,  the  liquid  instantly  moistens  it,  pro- 
ducing "a  dark  spot,  due  to  the  formation  of  sulphide  of  silver.  In  like 
manner  nitric  acid  assumes  the  spheroidal  state  when  projected  on  a 
heated  silver  plate,  and  does  not  attack  the  metal  so  long  as  the  plate 
remains  hot. 

An  analogous  phenomenon  is  observed  when  potassium  is  placed  on 
water.  Hydrogen  is  liberated,  and  burns  with  a  yellow  flame  ;  hydrate 
of  potassium,  which  is  formed  at  the  same  time,  floats  on  the  surface 
without  touching  it,  owing  to  its  high  temperature.  In  a  short  time  it 
cools  down,  and  the  globule  coming  in  contact  with  water  bursts  with  an 
explosion. 

Similarly  liquids  may  be  made  to  roll  upon  liquids,  and  sohd  bodies 
which  vaporise  without  becoming  liquid  also  assume  a  condition  analo- 
gous to  the  spheroidal  state  of  liquids  when  they  are  placed  on  a  surface 
whose  temperature  is  sufficiently  high  to  vaporise  them  rapidly.  This 
is  seen  when  a  piece  of  carbonate  of  ammonium  is  placed  in  a  red-hot 
platinum  crucible. 

The  phenomena  of  the  spheroidal  state  seem  to  prove  that  the  liquid 
globule  rests  upon  a  sort  of  cushion  of  its  own  vapour,  produced  by  the 
heat  radiated  from  the  hot  surface  against  its  under-side.  As  fast  as 
this  vapour  escapes  from  under  the  globule,  its  place  is  supplied  by  a 
fresh  quantity  formed  in  the  same  way,  so  that  the  globule  is  constantly 
buoyed  up  by  it,  and  does  not  come  in  actual  contact  with  the  heated 
surface.  When,  however,  the  temperature  of  the  latter  falls,  the  forma- 
tion of  vapour  at  the  under-surface  becomes  less  and  less  rapid,  until  at 
length  it  is  not  sufficient  to  prevent  the  globule  touching  the  hot  metal  or 
liquid  on  which  it  rests.  As  soon  as  contact  occurs  heat  is  rapidly 
imparted  to  the  globule,  it  enters  into  ebullition,  and  quickly  boils  away. 
These  experiments  on  the  spheroidal  state  explain  the  fact  that  the 
hand  may  be  dipped  into  melted  lead,  or  even  melted  iron,  without  in- 
jury. It  is  necessary  that  the  liquid  metal  be  heated  greatly  above  its 
solidifying  point.  Usually  the  natural  moisture  of  the  hand  is  sufficient, 
but  it  is  better  to  wipe  it  with  a  damp  cloth.  In  consequence  of  the 
great  heat  the  hand  becomes  covered  with  a  layer  of  spheroidal  fluid, 
which  prevents  the  contact  of  the  metal  with  the  hand.  Radiant  heat 
alone  operates,  and  this  is  principally  expended  in  forming  aqueous 
vapour  on  the  surface  of  the  hand.  If  the  hand  is  immersed  in  boiling 
water,  the  water  adheres  to  the  flesh,  and  consequently  a  scald  is  produced. 


361] 


Density  of  Vapours. 


303 


The  tales  of  ordeals  by  fire  during  the  middle  ages,  of  men  who  could 
run  barefooted  over  red-hot  iron  without  being  injured,  are  possibly 
true  in  some  cases,  and  would  find  a  ready  explanation  in  the  preceding 
phenomena. 


O 


DENSITY  OF  VAPOURS. 

361.  Gay-]Lussac's  xnethod. — The  density  of  a  vapour  is  the  relation 
between  the  weight  of  a  given  volume  of  this  vapour  and  of  that  of  the 
same  volume  of  air  at  the  same  temperature  and  pressure. 

Two  methods  principally  are  used  in  determining  the  density  of 
vapours  :  Gay-Lussac's,  which  serves  for  liquids  that  boil  at  about  100°, 
and  Dumas',  which  can  be  used  up  to  350° 

Fig.  281  represents  the  apparatus  used  by  Gay-Lussac.  It  consists 
of  an  iron  vessel  containing  mercury,  in  which 
there  is  a  glass  cylinder,  M.  This  is  filled 
with  water  or  oil,  and  the  temperature  is  in- 
dicated by  the  thermometer,  T.  In  the  in- 
terior of  the  cylinder  is  a  graduated  glass 
jar,  C,  which,  at  first,  is  filled  with  mercury. 

The  liquid  whose  vapour  density  is  to  be 
determined  is  placed  in  a  small  glass  bulb.  A, 
represented  on  the  left  of  the  figure.  The 
bulb  is  then  sealed  and  weighed  ;  the  weight 
of  the  liquid  taken  is  obviously  the  weight 
of  the  bulb  when  filled,  minus  its  weight 
while  empty.  The  bulb  is  then  introduced 
into  the  jar  C,  and  the  liquid  in  M  gradually 
heated  somewhat  higher  than  the  boiling 
point  of  the  liquid  in  the  bulb.  In  conse- 
quence of  the  expansion  of  this  liquid  the 
bulb  breaks,  and  the  liquid  becoming  con- 
verted into  vapour  the  mercury  is  depressed, 
as  represented  in  the  figure.  The  bulb  must 
be  so  small  that  all  the  liquid  in  it  is  vapo- 
rised. The  volume  of  the  vapour  is  given 
by  the  graduation  on  the  jar.  Its  tempera- 
ture is  indicated  by  the  thermometer  T,  and  the  pressure  is  indicated  by 
the  difference  between  the  height  of  the  barometer  at  the  time  of  the  ob- 
servation, and  the  height  of  the  column  of  mercury  in  the  gas  jar.  It  is 
only  necessary  then  to  calculate  the  weight  of  a  volume  of  air  equal  to 
that  of  the  vapour  under  the  same  conditions  of  temperature  and  pressure. 
The  quotient,  obtained  by  dividing  the  weight  of  the  vapour  by  that  of 
the  air,  gives  the  required  density  of  the  vapour. 

Let  /  be  the  weight  of  the  vapour  in  grains,  2/  its  volume  in  cubic 
inches,  and  /  its  temperature  ;  if  H  be  the  height  of  the  barometer,  and 
h  that  of  the  mercury  in  the  gas  jar,  the  pressure  on  the  vapour  will  be 

It  is  required  to  find  the  weight  p'  of  a  volume  of  air  v,  at  the  tern- 


Fig.  28] 


304 


On  Heat. 


[361- 


perature  /,  and  under  a  pressure  H  — //.  At  zero,  under  the  pressure  760 
millimetres,  a  cubic  inch  of  air  weighs  0-31  grain;  consequently,  under 
the  same  conditions,  v  cubic  inches  will  weigh  0*31  v  grains.  And  there- 
fore the  weight  of  v  cubic  inches  of  air,  at  f  and  the  pressure  760  miUi- 
metres,  is 

~^—  gram  [309,  prob.  n.]. 
As  the  weight  of  a  volume  of  air  is  proportional  to  the  pressure,  the 


above  weight  may  be  reduced  to  the  pressure  H 

H-k     ,  .  ,      . 

which  gives 


•  k  by  multiplying  by 


760 


0-31  V  (H— /«) 


(l+at)  760 

for  the  weight  /'  of  the  volume  of  air  v,  at  the  pressure  H-k  at  /°. 
Consequently,  for  the  desired  density  we  have 

D  =  /  ^ ^(i+oQ  760  ^ 
p'     0-31  V  (H—k)' 

362.  Dumas'  metbod. — The  method  just  described  cannot  be  applied 
to  liquids  whose  boiling  point  exceeds  150°  or  160°.  In  order  to  raise 
the  oil  in  the  cyHnder  to  this  temperature  it  would  be  necessary  to  heat 
the  mercury  to  such  a  degree  that  the  mercurial  vapours  would  be  dan- 
gerous to  the  operator.  And,  moreover,  the  tension  of  the  mercurial 
vapours  in  the  graduated  jar  would  increase  the  tension  of  the  vapour  of 
the  liquid,  and  so  far  vitiate  the  result. 

The  following  method,  devised  by  M.  Dumas,  can  be  used  up  to  the 
temperature  at  which  glass  begins  to  soften  ;  that  is,  about  400°.  A  glass 
globe  is  used  with  the  neck  drawn  out  to  a  fine  point  (fig.  282).  The 
globe,  having  been  dried  externally  and  inter- 
nally, is  weighed,  the  temperature  /  and  baro- 
metric height  /i  being  noted.  This  weight  W 
is  the  weight  of  the  glass  G  in  addition  to  p, 
the  weight  of  the  air  it  contains.  The  globe 
is  then  gently  warmed  and  its  point  immersed 
in  the  liquid  whose  vapour  density  is  to  be 
determined  :  on  cooling,  the  air  contracts,  and 
a  quantity  of  liquid  enters  the  globe.  The 
globe  is  then  immersed  in  a  bath,  either  of 
oil  or  fusible  metal,  according  to  the  tempera- 
ture to  which  it  is  to  be  raised.  In  order 
to  keep  the  globe  in  a  vertical  position  a 
metal  support  on  which  a  movable  rod  slides, 
is  fixed  on  the  side  of  the  vessel.  This  rod 
has  two  rings,  between  which  the  globe  is 
placed,  as  shown  in  the ,  figure.  There  is  an- 
other rod,  to  which  a  weight  thermometer,  D, 
Fig.  282.  is  attached. 

The  globe  and  thermometer  having  been  immersed  in  the  bath,  the 


-363]  Density  of  Vapours.  305 

latter  is  heated  until  slightly  above  the  boiling  point  of  the  liquid  in  the 
globe.  The  vapour  which  passes  out  by  the  point  expels  all  the  air  in 
the  interior.  When  the  jet  of  vapour  ceases,  which  is  the  case  when  all 
the  liquid  has  been  converted  into  vapour,  the  point  of  the  globe  is  her- 
metically sealed,  the  temperature  of  the  bath,  /',  and  the  barometric 
height  h\  being  noted.  When  the  globe  is  cooled,  it  is  carefully  cleaned 
and  again  weighed.  This  weight,  W',  is  that  of  the  glass,  G,  plus  p' ,  the 
weight  of  the  vapour  which  fills  the  globe  at  the  temperature  t'  and  pres- 
sure h\  or  W'  =  G  +/^  To  obtain  the  weight  of  the  glass  alone,  the 
weight  p  of  air  must  be  known,  which  is  determined  in  the  following 
manner  :  The  point  of  the  globe  is  placed  under  mercury  and  the  ex- 
tremity broken  off  with  a  small  pair  of  pinchers  :  the  vapour  being 
condensed,  a  vacuum  is  produced,  and  mercury  rushes  up,  completely 
filling  the  globe,  if,  in  the  experiment,  all  the  air  has  been  completely 
.expelled.  The  mercury  is  then  poured  into  a  carefully  graduated  mea- 
sure, which  gives  the  volume  of  the  globe.  From  this  result,  the  volume 
of  the  globe  at  the  temperature  t'  may  be  easily  calculated  and  conse- 
quently the  volume  of  the  vapour.  From  this  determination  of  the  volume 
of  the  globe  the  weight  p  of  the  air  at  the  temperature  /  and  pressure  h  is 
readily  calculated,  and  this  result  subtracted  from  W  gives  G,  the  weight 
of  the  glass.  Now  the  weight  of  the  vapour  p'  is  W'  ~  G.  We  now  know 
the  weight  p'  of  a  given  volume  of  vapour  at  the  temperature  f  and  pres- 
sure h\  and  it  is  only  necessary  to  calculate  the  weight  p"  of  the  same 
volume  of  air  under  the  same  conditions,  which  is  easily  accomplished. 

The  quotient  ^  is  the  required  density  of  the  vapour. 
Densities  of  Vapours. 


Air           .... 

i-oooo 

Vapour  of  phosphorus    . 

4-3256 

Vapour  of  water 

0-6235 

„            turpentine      . 

5-0130 

„          alcohol  . 

1-6138 

„            sulphur 

6-6542 

„          ether 

2-5860 

„            mercur)' 

6-9760 

„  bisulphide  of  carbon 

2-6447 

„            iodine 

8-7160 

The  density  of  aqueous  vapour,  when  a  space  is  saturated  with  it,  is  at 
all  temperatures  |,  or,  more  accurately,  0*6225,  of  the  density  of  air  at 
the  same  temperature  and  pressure. 

363.  Deville  and  Troost's  znetliod. — Deville  and  Troost  have  modi- 
fied Dumas'  method  so  that  it  can  be  used  for  determining  the  vapour 
density  of  liquids  with  very  high  boiling  points.  The  globe  is  heated  in 
an  iron  cylinder  in  the  vapour  of  mercury  or  of  sulphur,  the  temperatures 
of  which  are  constant  respectively  at  350°  and  460°.  In  other  respects 
the  determination  is  the  same  as  in  Dumas'  method. 

For  determinations  at  higher  temperatures,  Deville  and  Troost  have 
employed  the  vapour  of  zinc,  the  temperature  of  which  is  1040°.  As 
glass  vessels  are  softened  by  this  heat,  they  use  porcelain  globes  with 
finely  drawn  out  necks,  which  are  sealed  by  means  of  the  oxyhydrogen 
flame. 


3o6  On  Heat.  [364  - 

364.  Relation  between  the  volume  of  a  liquid  and  that  of  its 
vapour. — The  density  of  vapour  being  known,  we  can  readily,  calculate 
the  ratio  between  the  volume  of  a  vapour  in  the  saturated  state  at  a  given 
temperature,  and  that  of  its  liquid  at  zero.  We  may  take,  as  an  example 
the  relation  between  water  at  zero  and  steam  at  100°. 

The  ratio  between  the  weights  of  equal  volumes  of  air  at  zero,  and  the 
normal  barometric  pressure,  and  of  water  under  the  same  circumstance  is 
as  I  :  773.  But  from  what  has  been  already  said  (309),  the  density  of  air 
at  zero  is  to  its  density  at  100°  as  i  -r  «/  :  i.  Hence  the  ratio  between 
the    weights    of   equal    volumes   of  air   at    100°  and    water    at    0°    is 

\^ •  nZi  or  073178 :  773. 

1+0-003665x100    "^'  '^  '       '^^ 

Now  from  the  above  table  the  density  of  steam  at  100°  C,  and  the 
normal  pressure,  compared  with  that  of  air  under  the  same  circumstances, 
is  as  0*6225  •  I-  Hence  the  ratio  between  the  weights  of  equal  volumes 
of  steam  at  100°,  and  water  at  0°,  is 

073178  X  0-6225  •  773j  or  o"4555  '•  773  or  i  :  1698. 

Therefore,  as  the  volumes  of  bodies  are  inversely  as  their  densities,  one 
volume  of  water  at  zero  expands  into  1698  volumes  of  steam  at  100°  C. 
The  practical  rule  that  a  cubic  inch  of  water  yields  a  cubic  foot  of 
steam,  though  not  quite  accurate,  expresses  the  relation  in  a  convenient 
form. 


CHAPTER  VI. 

HYGROMETRY. 


365.  Object  of  hygrometry. — The  object  of /y/^r^M^/ry  is  to  deter- 
mine the  quantity  of  aqueous  vapour  contained  in  a  given  volume  of  air. 
This  quantity  is  very  variable ;  but  the  atmosphere  is  never  completely 
saturated  with  vapour,  at  any  rate,  in  our  climates.  Nor  is  it  ever 
completely  dry ;  for  if  hygro7netric  substances,  that  is  to  say,  sub- 
stances with  a  great  affinity  for  water,  such  as  chloride  of  calcium,  sul- 
phuric acid,  etc.,  be  at  any  time  exposed  to  the  air,  they  absorb  aqueous 
vapour. 

366.  Bygrrometric  state.— As  in  general  the  air  is  never  saturated, 
the  ratio  of  the  quantity  of  aqueous  vapour  actually  present  in  the 
atmosphere,  to  that  which  it  would  contain  if  it  were  saturated,  the  tem- 
perature remaining  the  same,  is  called  the  hygrometric  state,  or  degree  of 
saturation. 

The  degree  of  moisture  does  not  depend  on  the  absolute  quantity  of 
aqueous  vapour  present  in  the  air,  but  on  the  greater  or  less  distance  of 
the  air  from  its  point  of  saturation.  When  the  air  is  cold  it  may  be 
moist  with  very  little  vapour,  and,  on  the  contrary,  when  it  is  warm,  very 
dry,  even  with  a  large  quantity  of  vapour.  In  summer  the  air  usually 
contains  more  aqueous  vapour  than  in  winter,  notwithstanding  which  it 
is  less  moist,  because,  the  temperature  being  higher,  the  vapour  is  farther 


-368]  Hygrometry.  307 

from  its  point  of  saturation.  When  a  room  is  warmed,  the  quantity  of 
moisture  is  not  diminished,  but  the  humidity  of  the  air  is  lessened,  because 
its  point  of  saturation  is  raised.  The  air  may  thus  become  so  dry  as  to 
be  injurious  to  the  health,  and  it  is  hence  usual  to  place  vessels  of  water 
on  the  stoves  used  for  heating. 

As  Boyle's  law  applies  to  nonsaturated  vapours  as  well  as  to  gases 
C329),  it  follows  that,  with  the  same  temperature  and  volume,  the  weight 
of  vapour  in  a  nonsaturated  space  increases  with  the  pressure  and  there- 
fore with  the  tension  of  the  vapour  itself.  Instead,  therefore,  of  the  ratio 
of  the  quantities  of  vapour,  that  of  the  corresponding  tensions  may  be  sub- 
stituted, and  it  may  be  said  that  the  hygrometric  state  is  the  ratio  of  the 
tension  of  the  aqueoits  vapour  which  the  air  actually  contains^  to  the  tension 
of  the  vapour  which  it  would  contain  at  the  same  temperature  if  it  were 
saturated. 

If/ is  the  actual  tension  of  aqueous  vapour  in  the  air,  and  F  that  of 
saturated  vapour  at  the  same  temperature,  and  E  the  hygrometric  state; 

we  have  E  =^  ;  whence/"  =  F  x  E. 
F 

As  a  consequence  of  this  second  definition,  it  is  important  to  notice 
that  the  temperature  having  varied,  the  air  may  contain  the  same 
quantity  of  vapour  and  yet  not  have  the  same  hygrometric  state.  For, 
when  the  temperature  rises,  the  tension  of  the  vapour  which  the  air 
would  contain  if  saturated  increases  more  rapidly  than  the  tension  of 
the  vapour  actually  present  in  the  atmosphere,  and  hence  the  ratio 
between  the  two  forces,  that  is  to  say,  the  hygrometric  state,  becomes 
smaller. 

It  will  presently  be  explained  (374)  how  the  weight  of  the  vapour  con- 
tained in  a  given  volume  of  air  may  be  deduced  from  the  hygrometric  state. 

367.  Different  kinds  of  bygrrometers. — Hygrometers  are  instruments 
for  measuring  the  hygrometric  state  of  the  air.  There  are  numerous 
varieties  of  them — chemical  hygrometers,  condensing  hygrometers,  and 
psychrometers. 

368.  Chemical  liy^ometer. — The  method  of  the  chemical  hygro- 
meter consists  in  passing  a  known  volume  of  air  over  a  substance  which 
readily  absorbs  moisture— chloride  of  calcium,  for  instance.  The  sub- 
stance having  been  weighed  before  the  passage  of  air,  and  then  after- 
wards, the  increase  in  weight  represents  the  amount  of  aqueous  vapour 
present  in  the  air.  By  means  of  the  apparatus  represented  in  fig.  283,  it 
is  possible  to  examine  any  given  volume.  Two  brass  reservoirs  A  and  B, 
of  the  same  size  and  construction,  act  alternately  as  aspirators,  by  being 
lixed  to  the  same  axis,  about  which  they  can  turn.  They  are  connected 
by  a  central  tubulure,  and  by  means  of  two  tubulures  in  the  axis  the  lower 
reservoir  is  always  in  connection  with  the  atmosphere,  while  the  upper 
one,  by  means  of  a  caoutchouc  tube,  is  connected  with  two  tubes  M  and 
N,  filled  either  with  chloride  of  calcium,  or  with  pumice  stone  im- 
pregnated with  sulphuric  acid.  The  first  absorbs  the  vapour  in  the  air 
drawn  through,  while  the  other,  M,  stops  any  vapour  which  might  diffuse 
from  the  reservoirs  to  the  tube  N. 


308 


Oil  Heat 


[368- 


The  lower  reservoir  being  full  of  water,  and  the  upper  one  of  air,  the 
apparatus  is  inverted  so  that  the  liquid  flows  slowly  from  A  to  B.  A 
vacuum  being  formed  in  A,  air  enters  by  the  tubes  NM,  in  the  first  of 
which  all  the  vapour  is  absorbed.  When  all  the  water  has  run  into  B  it 
is  turned ;  the  same  flow  recommences,  and  the  same  volume  of  air  is 


Fig.  283. 


drawn  through  the  tube  N.  Thus,  if  each  reservoir  holds  a  gallon,  for 
example,  and  the  apparatus  has  been  turned  five  times,  6  gallons  of  air 
have  traversed  the  tube  N,  and  have  been  dried.  If  then,  before  the 
experiment,  the  tube  with  its  contents  has  been  weighed,  the  increase  in 
weight  gives  the  weight  of  aqueous  vapour  present  in  6  gallons  of  air  at 
the  time  of  the  experiment. 

369.  Condensing- bygrrometers. — When  a  body  gradually  cools  in  a 
moist  atmosphere,  as,  for  instance,  when  a  lump  of  ice  is  placed  in  water 
contained  in  a  polished  metal  vessel,  the  layer  of  air  in  immediate  contact 
with  it  cools  also,  and  a  point  is  ultimately  reached  at  which  the  vapour 
present  is  just  sufficient  to  saturate  the  air  :  the  least  diminution  of  tem- 
perature then  causes  a  precipitation  of  moisture  on  the  vessel  in  the  form 
of  dew.  When  the  temperature  rises  again,  the  dew  disappears.  The 
mean  of  these  two  temperatures  is  taken  as  the  dew  point,  and  the  object 
of  condensing  hygrometers  is  to  observe  this  point.  Daniell's  and 
Regnault's  hygrometers  belong  to  this  class. 

370.  Daniell's  byg-rometer. — This  consists  of  two  glass  bulbs  at  the 
extremities  of  a  glass  tube  bent  twice  (fig.  284).  The  bulb  A  is  two-thirds 
full  of  ether,  and  a  very  delicate  thermometer  plunges  in  it ;  the  rest  of 
the  space  contains  nothing  but  the  vapour  of  ether,  the  ether  having  been 


-371] 


Regnaulfs  Hygroineter. 


309 


Fis.  284. 


boiled  before  the  bulb  B  was  sealed.  The  bulb  B  is  covered  with  muslin 
and  ether  is  dropped  upon  it.  The  ether 
in  evaporating  cools  the  bulb,  and  the 
vapour  contained  in  it  is  condensed.  The 
internal  tension  being  thus  diminished, 
the  ether  in  A  forms  vapours  which  con- 
dense in  the  other  bulb  B.  In  propor- 
tion as  the  liquid  distils  from  the  lower 
to  the  upper  bulb,  the  ether  becomes 
cooler,  and  ultimately  the  temperature 
of  the  air  in  immediate  contact  with  A 
sinks  to  that  point  at  which  its  vapour 
is  more  than  sufficient  to  saturate  it,  and 
it  is,  accordingly,  deposited  on  the  out- 
side as  a  ring  of  dew  corresponding  to 
the  surface  of  the  ether.  The  tempera- 
ture of  this  point  is  noted  by  means  of 
the  thermometer  in  the  inside.  .  The 
addition  of  ethen  to  the  bulb  B  is  then 
discontinued,  the  temperature  of  A  rises, 
and  the  temperature  at  which  the  dew 
disappears  is  noted.  In  order  to  render 
the  deposition  of  dew  more  perceptible, 
the  bulb  A  is  made  of  black  glass. 

These  two  points  having  been  determined,  theirmean  is  taken  as  that  of 
the  dew  point.  The  temperature  of  the  air  at  the  time  of  the  experiment  is 
indicated  by  the  thermometer  on  the  stem.  The  tension/  corresponding 
to  the  temperature  of  the  dew  point,  is  then  found  in  the  table  of  tensions 
(335).  This  tension  is  exactly  that  of  the  vapour  present  in  the  air  at 
the  time  of  the  experiment.  The  tension  F  of  vapour  saturated  at  the 
temperature  of  the  atmosphere  is  found  by  means  of  the  same  table  ;  the 
quotient  obtained  by  dividing/ by  F,  represents  the  hygrometric  state  of 
the  air  (366).  For  instance,  the  temperature  of  the  air  being  15°,  sup- 
pose the  dew  point  is  5°.  From  the  table  the  corresponding  tensions  are 
/=6'534  millimetres,  and  F  =  12-699  millimetres,  which  gives  0-5 14  for  the 
ratio  of/ to  F,  or  the  hygrometric  state. 

There  are  many  sources  of  error  in  DanielFs  hygrometer.  The 
principal  are  :  ist,  that  as  the  evaporation  in  the  bulb  A  only  cools 
the  liquid  on  the  surface,  the  thermometer  dipping  on  it  does  not 
exactly  give  the  dew  point ;  2nd,  that  the  observer  standing  near  the 
instrument  modifies  the  hygrometric  state  of  the  surrounding  air,  as 
well  as  its  temperature  ;  the  cold  ether  vapour  too  flowing  from  'the 
upper  bulb  may  cause  inaccuracy. 

371.  Regrnault's  hygrrometer.— Regnault's  hygrometer  is  free  from 
the  sources  of  error  incidental  to  the  use  of  Daniell's.  It  consists  of  two 
very  thin  poHshed  silver  thimbles  175  inch  in  height,  and  075  inch  in 
diameter  (fig.  285).  In  these  are  fixed  two  glass  tubes,  D  and  E,  in  each 
of  which  is  a  thermometer.     A  bent  tube.  A,  open  at  both  ends,  passes 


310 


On  Heat. 


[371- 


through  the  cork  of  the  tube  D,  and  reaches  nearly  to  the  bottom  of 
the  thimble.  There  is  a  tubulure  on  the  side  of  D,  fitting  in  a  brass 
tube  which  forms  a  support  for  the  apparatus.  The  end  of  this  tube 
is  connected  with  an  aspirator  G.  The  tube  E  is  not  connected  with 
the  aspirator ;  its  thermometer  simply  indicates  the  temperature  of  the 
atmosphere. 

The  tube  D  is  then  half  filled  with  ether,  and  the  stopcock  of  the 
aspirator  opened.  The  water  contained  in  it  runs  out,  and  just  as  much 
air  enters  through  the  tube  A,  bubbhng  through  the  ether,  and  causing 


Fig.  285. 

it  to  evaporate.  This  evaporation  produces  a  diminution  of  temperature, 
so  that  dew  is  deposited  on  the  silver  just  as  on  the  bulb  in  Daniell's 
hygrometer  :  the  thermometer  T  is  then  instantly  to  be  read,  and  the 
stream  from  the  aspirator  stopped.  The  dew  will  soon  disappear  again, 
and  the  thermometer  T  is  again  to  be  read ;  the  mean  of  the  two 
readings  is  taken  :  the  thermometer  /gives  the  corresponding  temperature 
of  the  air,  and  hence  there  are  all  the  elements  necessary  for  calculating 
the  hygrometric  state. 

As  in  this  instrument,  all  the  ether  is  at  the  same  temperature  in 
consequence  of  the  agitation,  and  the  temperatures  are  read  off  at  a 
distance  by  means  of  a  telescope,  the  sources  of  error  in  Daniell's  hygro- 
meter are  avoided. 

A  much  simpler  form  of  the  apparatus  may  be  constructed  out  of  a 
common  test  tube  containing  a  depth  of  i|  inch  of  ether.     The  tube  is 


372] 


Psychronieter. 


311 


provided  with  a  loosely  fitting  cork  in  which  is  a  delicate  thermometer 
and  a  narrow  bent  tube  dipping  in  the  ether.  On  blowing  through  the 
ether,  by  a  caoutchouc  tube  of  considerable  length,  a  diminution  of 
temperature  is  caused,  and  dew  is  ultimately  deposited  on  the  glass  ;  after 
a  little  practice  the  whole  process  can  be  conducted  almost  as  well  as 
in  Regnault's  complete  instrument.  The  temperature  of 
the  air  is  indicated  by  a  free  thermometer. 

372.  Psycbrometer.  "Wet  bulb  byg^rometer. — A 
moist  body  evaporates  in  the  air  more  rapidly  in  propor- 
tion as  the  air  is  drier,  and  in  consequence  of  this  evapo- 
ration the  temperature  of  the  body  sinks.  T\\&psychrometer^ 
or  wet  biilb  hygrometer,  is  based  on  this  principle,  the 
application  of  which,  to  this  purpose,  was  first  suggested 
by  Leslie.  The  form  usually  adopted  in  this  country  is 
due  to  Mason.  It  consists  of  two  delicate  thermometers 
placed  on  a  wooden  stand  (fig.  286).  One  of  the  bulbs  is 
covered  with  muslin,  and  is  kept  continually  moist  by 
being  connected  with  a  reservoir  of  water  by  means  of  a 
string.  Unless  the  air  is  saturated  with  moisture  the  wet 
bulb  thermometer  always  indicates  a  lower  temperature 
than  the  other,  and  the  difference  between  the  indications 
of  the  two  thermometers  is  greater  in  proportion  as  the  air 
can  take  up  more  moisture.  The  tension  e  of  the  aqueous 
vapour  in  the  atmosphere  may  be  calculated  from  the 
indications  of  the  thermometer  by  means  of  the  following 
empirical  formula  : — 

e  =  e^  —  o-oooyy  {t  —  t^h, 
in  which  e'  is  the  maximum  tension  corresponding  to  the 
temperature  of  the  wet  bulb  thermometer,  h  is  the  barometric  height, 
and  /  and  f  the  respective  temperatures  of  the  dry  and  wet  bulb  thermo- 
meters.    If,  for  example,  ^  =  750  milhmetres, /=  15°  C,  /  =  io°  C;  ac- 
cording to  the  table  of  tensions  (334),  ^'  =  9*165,  and  we  have 
^  =  9-165— 0-00077  X  5  X  750  =  6-278. 

This  tension  corresponds  to  a  dew  point  of  about  4-5°  C.  If  the  air  had 
been  saturated,  the  tension  would  have  been  12-699,  ^^^  the  air  is  there- 
fore about  half  saturated  with  moisture. 

This  formula  expresses  the  result  with  tolerable  accuracy,  but  the 
above  constant  0-00077  requires  to  be  controlled  for  different  positions 
of  the  instrument  ;  in  small  closed  rooms  it  is  0-00128,  in  large  rooms  it  is 
0-00 1 00,  and  in  the  open  air  without  wind  it  is  0-00090  :  the  number 
0-00077  is  its  value  in  a  large  room  with  open  windows.  Regnault  found 
that  the  difference  in  temperature  of  the  two  bulbs  depends  on  the 
rapidity  of  the  current  of  air  ;  he  also  found  that  at  a  low  temperature 
and  in  very  moist  air,  the  results  obtained  with  the  psychrometer  differed 
from  those  yielded  by  his  hygrometer.  It  is  probable  that  the  indica- 
tions of  the  psychrometer  are  only  true  for  mean  and  high  temperatures, 
and  when  the  atmosphere  is  not  too  moist. 


Fig.  286. 


312 


On  Heat. 


[372 


According  to  Glaisher  the  temperature  of  the  dew  point  may  be  ob- 
tained by  multiplying  the  difference  between  the  temperatures  of  the  wet 
and  dry  bulb  by  a  constant  depending  on  the  temperature  of  the  air  at 
the  time  of  observation,  and  subtracting  the  product  thus  obtained  from 
this  last-named  temperature.     The  following  are  the  numbers  : — 


Dry  Bulb 
Temperature  F.° 

Factor 

Dry  Bulb 
Temperature  F.° 

Factor 

Below  24° 

f5 

34to35 

2-8 

24t025 

6-9 

35—40 

2-5 

25—26 

6-5 

40-45 

2-2 

26—27 

6-1 

45—50 

2-1 

27—28 

5-6 

50—55 

2-0 

28—29 

5-1 

55—60 

1-9 

29—30 

46 

60—65 

1-8 

30—31 

4-1 

65—70 

1-8 

31—32 

37 

70—75 

17 

32—33 

3-3 

75-80 

17 

33—34 

3-0 

80-85 

1-6 

These  are  often  known  as  Glaisher's  factors. 

A  formula  frequently  used  in  this  country  is  that  given  by  Dr.  Apjohn. 
It  is 


^    88^-5= 


orF=/-4 


96     30 


in  which  d  is  the  difference  of  the  wet  and  dry  bulb  thermometers  in 
Fahre7iheit  degrees  ;  h  the  barometric  height  in  inches ;  y  the  tension  of 
vapour  for  the  temperature  of  the  wet  bulb,  and  F  the  elastic  force  of 
vapour  at  the  dew  point,  from  which  the  dew  point  may  if  necessary  be 
found  from  the  tables.  The  constant  coefficient  88,  for  the  specific  heats 
of  air  and  aqueous  vapour,  is  to  be  used  when  the  reading  of  the  wet  bulb 
is  above  32°  F.,  and  96  when  it  is  below. 

373.  Hyg^roxneters  of  absorption. — These  hygrometers  are  based  on 
the  property  which  organic  substances  have,  of  elongating  when  moist, 
and  of  again  contracting  as  they  become  dry.  The  most  common  form 
is  the  hair  or  Saussure^s  hygrometer. 

It  consists  of  a  brass  frame  (fig.  287),  on  which  is  fixed  a  hair,  c,  fas- 
tened at  its  upper  extremity  in  a  clamp,  a,  provided  with  a  screw,  d. 
This  clamp  is  moved  by  a  screw  b.  The  lower  part  of  the  hair  passes 
round  a  pulley,  o,  and  supports  a  small  weight,  p.  On  the  pulley  there  is 
a  needle,  which  moves  along  a  graduated  scale.  When  the  hair  becomes 
shorter,  the  needle  rises,  when  it  becomes  longer  the  weight  p  makes  it 
sink. 

The  scale  is  graduated  by  calling  that  point  zero  at  which  the  needle 
would  stand  if  the  air  were  completely  dry,  and  100  the  point  at  which 
it  stands  in  air  completely  saturated  with  moisture.  The  distance  be- 
tween these  points  is  divided  into  100  equal  degrees. 


375] 


Hygrometry. 


313 


Regnault  has  devoted  much  study  in  order  to  render  the  air  hygro- 
meter scientifically  useful,  but  without  much  success.  And  the  utmost  that 
can  be  claimed  for  it  is  that  it  can  be  used  as  a  hygroscope ;  that  is,  an 
instrument  which  shows  approximately  whether  the  air  is  more  or  less 
moist,  without  giving  any  indication  as  to  the  quantity  of  moisture  present. 

To  this  class  of  hygroscopes  belong  the  chimney  ornaments,  one  of  the 
most  common  forms  of  which  is  that  of  a  small  male  and 
female  figure,  so  arranged  in  reference  to  a  little  house, 
with  two  doors,  that  when  it  is  moist  the  man  goes  out, 
and  the  woman  goes  in,  and  vice  versa  when  it  is  fine. 
They  depend  on  the  property  which  twisted  strings  or 
pieces  of  catgut  possess,  of  untwisting  when  moist,  and  of 
twisting  when  dry. 

As  these  hygroscopes  only  change  slowly,  their  indi- 
cations are  always  behindhand  with  the  state  of  the 
weather ;  nor  are  they,  moreover,  very  exact.    « 

374.  3IXoisture  of  the  atmospbere. — The  absolute 
moisture  varies  with  the  temperature  both  in  the  course 
of  the  year  and  of  the  day.  In  summer  there  is  a  maxi- 
mum at  eight  in  the  morning  and  evening,  and  a  mini- 
mum at  3  P.M.,  and  at  3  A.M.,  because  the  ascending 
current  of  air  carries  the  moisture  upwards.  The  abso- 
lute moisture  is  greatest  in  the  tropics,  where  it  amounts 
to  25  ™™,  while  in  our  latitudes  it  does  not  exceed  10"™. 
The  relative  moisture  on  the  other  hand  is  at  its  mirii- 
mum  in  the  hottest,  and  at  its  maximum  in  the  coolest 
part  of  the  day.     It  varies  also  in  different  regions. 


Fig.  287. 

Thus  in  some  parts 
of  East  Africa  the  springs  of  powder  flasks  exposed  to  the  damp,  snap 
like  twisted  quills,  paper  becomes  soft  and  sloppy  by  the  loss  of  its  glaze, 
and  gunpowder  if  not  kept  from  the  air  refuses  to  ignite.  On  the  other 
hand,  in  North  America  where  the  south-west  winds  blow  over  large 
tracts  of  land  the  relative  moisture  is  less  than  in  Europe  ;  evaporation 
is  there  far  more  rapid  than  in  Europe  :  clothes  dry  quickly;  bread 
soon  becomes  hard,  newly  built  houses  can  be  at  once  inhabited,  European 
pianos  soon  give  way  there,  while  American  ones  are  on  this  side  very 
durable.  As  regards  the  animal  economy  the  liquids  evaporate  more 
rapidly,  by  which  the  circulation  and  the  assimilation  is  accelerated,  and 
the  whole  character  is  more  nervous.  For  evaporation  is  quicker  the 
drier  the  air,  and  the  more  frequently  it  is  renewed  ;  it  is  moreover  more 
rapid  the  higher  the  temperature,  and  the  less  th#  pressure.  This  is  not 
in  discordance  with  the  statement  that  the  quantity  of  vapour '  which 
saturates  a  given  space  is  the  same  however  this  be  filled  with  air  ;  a  cer- 
tain space  takes  up  the  same  weight  of  vapour  whether  it  is  vacuous,  or 
filled  with  rarefied  or  dense  air ;  yet  the  saturation  of  a  given  space  with 
vapour  is  more  rapid  the  smaller  the  pressure  of  the  air  and  the  less  it 
already  contains. 

'  375.  Problem  on  hyg^rometry. — To  calculate  the  weight  P  of  a 
voltime  of  moist  air  V,  the  hygrometric  state  of  which  is  E,  the  tempera- 
ture /,  and  the  pressure  H,  the  density  of  the  vapour  being  f  that  of  air. 

P 


314  On  Heat.  [375- 

From  the  second  law  of  the  mixture  of  gases  and  vapours,  it  will  be 
seen  that  the  moist  air  is  nothing  more  than  a  mixture  of  V  cubic  inches 
of  dry  air  at  /°,  under  the  pressure  H  minus  that  of  the  vapour,  and  of  V 
cubic  inches  of  vapour  at  t°  and  the  tension  given  by  the  hygrometric 
state  ;  these  two  values  must,  therefore,  be  found  separately. 

The  formula/=  F  x  E  (366)  gives  the  tension /of  the  vapour  in  the  air, 
for  E  has  been  determined,  and  F  is  found  from  t'he  tables.  The  tension 
/being  known,  if/  is  the  tension  of  the  air,/+/  =  H,  from  which/  =  H 
-/=H-FE. 

The  question  consequently  resolves  itself  into  calculating  the  weight  of 
V  cubic  inches  of  dry  air  at  /°,  and  the  pressure  H  -FE,  and  then  that  of 
"V  cubic  inches  of  aqueous  vapour  also  at  /°,  but  under  the  pressure  FE. 

Now  V  cubic   inches  of  dry  air  under  the  given  conditions  weigh 

—^, ^  ,  ~ - — '-,  and  we  readily  see  from  problem  III.  art.  359,  that  V 

(I  +  a/)  760     '  ^  ^  ^^^ 

cubic  inches  of  vapour  at*/°  and  the  pressure  FE,  weigh  ^  x    '^  j^    —     . 
Adding  these  two  weights,  and  reducing,  we  get 
p_o-3iV(H-f  FE) 
(l  +a/)  760 
If  the  air  were  saturated  we  should  have  E  =  i,  and   the  formula  would 
thus  be  changed  into  that  already  found  for  the  mixture  of  gases  and 
saturated  vapours  (359). 

This  formula  contains,  besides  the  weight  P,  many  variable  quantities 
y,  E,  H,  and  /,  and  consequently,  by  taking  successively  each  of  these 
/juantities  as  unknown,  as  many  different  problems  might  be  proposed. 
^N.   /         376'  Correction   for  the  loss  of  iveigrht   experienced    by    bodies 
^(^^  weigrbed  in  the  air.— It  has  been  seen  in  speaking  of  the  balance,  that 
^^    nhe  weight  which  it  indicates  is  only  an  apparent  weight,  and  is  less  than 
the  real  weight.     The  latter  may  be  deduced  from  the  former  when  it  is 
remembered  that  every  body  weighed  in  the  air  loses  a  weight  equal  to 
that  of  the  displaced  air  (176).     This  problem  is,  however,  very  compli- 
cated, for  not  only  does  the  weight  of  the  displaced  air  vary  with  the 
temperature,  the  pressure,  and  the  hygrometric  state,  but  the  volume  of 
the  body  to  be  weighed,  and  that  of  the  weights,  vary  also  with  the  tem- 
perature ;  so  that  a  double  correction  has  to  be  made  ;  one  relative  to  the 
weights,  the  other  to  the  body  weighed. 

Correction  I'elative  to  the  weights. — In  order  to  make  this  correction  let 
P  be  their  w- eight  in  ain  and  n  their  real  weight  in  vacuo  ;  further,  let  V 
be  the.  volume  of  these  weights  at  0°,  D  the  density  of  the  substance  of 
w^hich  they  are  made,  and  K  its  coefficient  of  linear  expansion. 

The  volume  V  becomes  V  (i  +  3K/)  at  t°,  hence  this  is  the  volume  of 
air  displaced  by  the  weights.  If  jx  be  the  weight  of  a  cubic  inch  of  air  at 
/,  and  the  pressure  H  at  the  time  of  weighing,  we  have 

P  =  n-/iV(i+3K/). 
From  the  formula  P  =  VD  (122)  V  may  be  replaced  by -^,    and    the 
formula  becomes 


-377]  Conductivity  of  Solids.  3 1 5 

P-n  [.,  -!lii3K£)]  .  (,j 

which  gives  the  value,  in  air,  of  a  weight  IT,  when  //  is  replaced  by  its 
value.  But  since  \x  is  the  weight  of  a  cubic  inch  of  air  more  or  less  moist, 
at  the  temperature  t  and  the  pressure  H,  its  value  may  be  calculated  by 
means  of  the  formula  in  the  foregoing  paragraph. 

Correction  relative  to  the  body  weighed. — Let  p  be  the  apparent  weight 
of  the  body  to  be  weighed,  -k  its  real  weight  in  vacuo,  d  its  density,  k  its 
coefficient  of  expansion,  and  /  its  temperature,  by  the  same  reasoning  as 
above  we  have 

^=^["-^^^^^]  •     •     •     •     (^) 

By  using  the  method  of  double  weighing,  and  of  a  counterpoise  whose 
apparent  weight  is/',  the  real  weight  tt',  the  density  ^',  and  the  coefficient 
k\  and  assuming  that  the  pressure  does  not  change,  which  is  usually  the 
case,  we  have  again 

,^  =  .[:-.(i^].        ...         (3) 

If  a  and  b  are  the  two  arms  of  the  beam,  we  have  in  the  first  weighing 
ap=^bp  ;  and  in  the  second  aV  =  bp,  whence  /  =  P.  Replacing  P  and  p  by 
their  values  deduced  from  the  above  equations,  we  have 

.[:-'^^3^]  =  n[.-Kl^)] 
whence  7r  =  n 


D 


(1+3/'/) 


which  solves  the  probl^. 


CHAPTER   VII. 

CONDUCTIVITY  OF  SOLIDS,   LIQUIDS,   AND   GASES. 

377.  Transmission  of  heat.  — When  we  stand  at  a  little  distance  from 
a  fire  or  other  source  of  heat  we  experience  the  sensation  of  warmth.  The 
heat  is  not  transmitted  by  the  intervening  air  ;  it  passes  through  it  with- 
out raising  its  temperature,  for  if  we  place  a  screen  before  the  fire  the 
sensation  ceases  to  be  felt.  The  heat  from  the  sun  reaches  us  in  the  same 
manner.  The  heat,  which,  as  in  this  case,  is  transmitted  to  a  body  from 
the  source  of  heat  without  affecting  the  temperature  of  the  intervening 
medium,  is  said  to  be  radiated. 

Heat  is  transmitted  in  another  way.  When  the  end  of  a  metal  bar  is 
heated,  a  certain  increase  of  temperature  is  presently  observed  along  the 
bar.     Where  the  heat  is  transmitted  in  the  mass  of  the  body  itself,  as  in 


3i6 


On  Heat. 


[377- 


this  case,  it  is  said  to  be  conducted.  We  shall  first  consider  the  trans- 
mission of  heat  by  conduction. 

378.  Conductivity  of  solids. — Bodies  conduct  heat  with  different 
degrees  of  facility.  Good  conductors  are  those  which  readily  transmit 
heat,  such  as  are  the  metals  ;  while  bad  conductors,  to  which  class  belong 
the  resins,  glass,  wood,  and  more  especially  liquids  and  gases,  offer  a 
greater  or  less  resistance  to  the  transmission  of  heat. 

In  order  to  compare  roughly  the  conducting  power  or  co7idnctivity  of 
different  solids,  Ingenhaus  constructed  the  apparatus  which  bears  his 
name,  and  which  is  represented  in  fig.  288. 
It  is  a  metal  trough,  in  which,  by  means  of 
tubulures  and  corks,  are  fixed  rods  of  the 
same  dimensions,  but  of  different  materials  ; 
for  instance,  iron,  copper,  wood,  glass.  These 
rods  extend  to  a  slight  distance  in  the  trough, 
and  the  parts  outside  are  coated  with  wax, 
which  melts  at  61°.  The  box  being  filled 
with  boiling  water,  it  is  observed  that  the  wax 
melts  to  a  certain  distance  on  the  metaUic 
^'^'  ^^^'  rods,  while  on  the  others  there  is  no  trace  of 

fusion.  The  conducting  power  is  evidently  greater  in  proportion  as  the 
wax  has  fused  to  a  greater  distance.  The  experiment  is  sometimes' 
modified  by  attaching  glass  balls  or  marbles  to  the  ends  of  the  rods  by 
means  of  wax.  As  the  wax  melts,  the  balls  drop  oft",  and  this  in  the 
order  of  their  respective  conductivities.  The  quickness  with  which 
melting  takes  place,  is  however  only  a  measure  of  the  conducting  power,  in 
case  the  metals  have  the  same  or  nearly  the  same  specific  heat. 

M.  Despretz  has  compared  the  conducting  powers  of  solids  by  means  of 
the  apparatus  represented  in  fig.  289.     It  is  a  bar  in  which  small  cavities 


are  made  at  intervals  of  4  inches  :  these  cavities  contain  mercury,  and  a 
delicate  thermometer  is  placed  in  each  of  them.     This  bar  is  exposed  at 


I 


378] 


Conductivity  of  Solids  and  L  iquids. 


317 


one  end  to  a  constant  source  of  heat ;  the  thermometers  gradually  rise 
until  they  indicate  fixed  temperatures,  which  are  less  according  as  the 
thermometers  are  farther  from  the  source  of  heat.  By  this  method 
Despretz  verified  the  following  law  :  If  the  distances  from  the  source  of 
heat  increase  in  arithmetical  prog7'ession,  the  excess  of  the  temperatiire  over 
that  of  the  surrounding  air  decreases  in  geometrical  progressiofi. 

This  law,  however,  only  prevails  in  the  case  of  very  good  conductors, 
such  as  gold,  platinum,  silver  and  copper  ;  it  is  only  approximately  true 
for  iron,  zinc,  lead,  and  tin,  and  does  not  apply  at  all  to  non-metallic 
bodies,  such  as  marble,  porcelain,  etc. 

Taking  the  conducting  power  of  gold  at  1000,  Despretz  has  constructed 
the  following  table  of  conductivities  : — 


Platinum 
Silver     . 
Copper  . 
Iron 
Zinc 


.  981 

Tin 

■     973 

Lead     . 

.     897 

Marble  . 

•     374 

Porcelain 

.     363 

Brick  earth  . 

304 
179 

23 

12 
II 


\ 


Wiedemann  and  Franz  have  made  some  valuable  investigations  on  the 
conductivity  of  heat  in  metals.  By  making  cavities  in  the  bars,  as  in 
Despretz's  method,  their  form  is  altered,  and  the  continuity  partially  de- 
stroyed. Wiedemann  and  Franz  have  avoided  this  source  of  error  by 
measuring  the  temperature  of  the  bars  in  different  places  by  applying  to 
them  the  junction  of  a  thermo-electric  couple  (385). 

The  metal  bars  were  made  as  regular  as  possible  ;  one  of  the  ends 
was  heated  to  100°,  the  rest  of  the  bar  being  surrounded  by  air  at  a  con- 
stant temperature.  The  thermo-electric  couple  was  of  small  dimensions, 
in  order  not  to  abstract  too  much  heat. 

By  this  method  Wiedemann  and  Franz  obtained  results  which  differ 
considerably  from  those  of  Despretz.  Representing  the  conductivity  of 
silver  by  100°,  they  found  for  the  other  metals  the  following  numbers  : 

Silver 
Copper  . 
Gold       . 
Tin 
Iron 

Organic  substances  conduct  heat  badly.  De  la  Rive  and  de  Candolle 
have  shown  that  woods  conduct  better  in  the  direction  of  their  fibres 
than  in  a  transverse  direction  ;  and  have  remarked  upon  the  influence 
which  this  feeble  conducting  power,  in  a  transverse  direction,  exerts  in 
preserving  a  tree  from  sudden  changes  of  temperature,  enabling  it  to 
resist  alike  a  sudden  abstraction  of  heat  from  within,  and  the  sudden  ac- 
cession of  heat  from  without.  Tyndall  has  also  shown  that  this  tendency 
is  aided  by  the  low  conducting  power  of  the  bark,  which  is  in  all  cases  less 
than  that  of  the  wood. 

Cotton,  wool,  straw,  bran,  etc.,  are  all  bad  conductors. 

It  has  been  attempted  to  determine  the  absolute  quantity  of  heat  which 


loo-o 

Steel 

II-6 

73-6 

Lead 

8-5 

53-2 

Platinum 

8-4 

14-5 

Rose's  alloy 

2-8 

11-9 

Bismuth 

1-8 

3i8 


Ofi  Heat. 


[378 


traverses  in  a  second  a  plate  of  a  substance  a  metre  square  and  a  milli- 
metre in  thickness,  the  two  sides  being  kept  at  a  constant  difference  of  i°; 
this  is  called  the  cocffi,cie?it  of  conductivity,  k.  The  mean  values  are 
approximately  obtained  if  Wiedemann's  numbers  are  increased  by  |  and 
divided  by  lo.  Thus  the  coefficient  of  copper  is  9-81.  If  the  thickness  of  a 
body  in  millimetres  is  d,  and  its  two  opposed  faces  are  at  the  temperatures 

/  and  tj,  the  quantity  of  heat  passing  through  is  k^^. 

379.  Senarmont's  experiment. — It  is  only  in  homogeneous  bodies 
that  heat  is  conducted  with  equal  facility  in  all  directions.  If  an  aper- 
ture be  made  in  a  circular  piece  of  ordinary  glass  covered  with  a  thin 
layer  of  wax,  and  a  platinum  wire  ignited  by  a  voltaic  current  be  held 
through  the  aperture,  the  wax  will  be  melted  round  the  hole  in  a  circular 
form.  Senarmont  has  made,  on  this  principle,  a  series  of  experiments  on 
the  conductivity  of  heat  in  crystals.  A  plate  cut  from  a  crystal  of  the 
regular  system  was  covered  with  wax,  and  a  heated  metal  point  was 
held  against  it.  The  part  melted  had  a  circular  form  ;  but  when  plates  of 
crystals  belonging  to  other  systems  were  investigated  in  a  similar  manner, 
it  was  found  that  the  form  of  the  line  of  egnal  temperature,  that  is,  the 
limit  of  the  melted  part,  varied  with  the  different 
systems  and  with  the  position  of  the  axes.  In 
plates  of  uniaxial  crystals  cut  parallel  to  the 
principal  axis  it  was  an  ellipse,  the  major  axis  of 
which  was  in  the  direction  of  the  principal  axis. 
In  plates  cut  perpendicular  to  the  principal  axis 
it  was  a  circle.  In  biaxial  crystals  the  line  was 
always  an  ellipse. 

380.  Conductivity  of  liquids. — The  conduc- 
tivity of  liquids  is  very  small,  as  is  seen  from  the 
following  experiment  :  A  delicate  thermoscope 
B,  consisting  of  two  glass  bulbs,  joined  by  a  tube, 
w,  in  which  there  is  a  small  index  of  coloured 
liquid,  is  placed  in  a  large  cylindrical  glass  ves- 
sel, D  (fig.  290).  This  vessel  is  filled  with  water 
at  the  ordinary  temperature,  and  a  tin  vessel.  A, 
containing  oil  at  a  temperature  of  two  or  three 
hundred  degrees,  is  dipped  in  it.  The  bulb  near  the  vessel  A  is  only  very 
slightly  heated,  and  the  index  /«  moves  through  a  very  small  distance. 
Other  liquids  give  the  same  result.  That  liquids  conduct  very  badly  is 
also  demonstrated  by  a  simpler  experiment.  A  long  test  tube  is  half  filled 
with  water  and  some  ice  so  placed  in  it  that  it  cannot  rise  to  the  surface. 
By  inclining  the  tube  and  heating  the  surface  of  the  hquid  by  means  of  a 
spirit  lamp,  the  liquid  at  the  top  may  be  made  to  boil,  while  the  ice  at  the 
bottom  remains  unmelted. 

Despretz  made  a  series  of  experiments  with  an  apparatus  analogous  to 
that  which  has  been  described,  but  he  maintained  the  liquid  in  the  vessel, 
A,  at  a  constant  temperature,  and  arranged  a  series  of  thermometers  one 
below  the  other  in  the  vessel  D.     In  this  manner  he  found  that  the  con- 


Fig.  290. 


-381] 


CondiLctivity  of  L  iquids. 


319 


ductivity  of  heat  in  liquids  obeys  the  same  laws  as  in  solids,  but  is  much 
more  feeble.     For  example,  the  conductivity  of  water  is  g\  that  of  copper. 

Paalzow  states  that  in  regard  to  conducting  power  the  following  liquids 
stand  in  the  order  given  of  their  decreasing  conductivity  for  heat  :  Mer- 
cury, water,  solution  of  sulphate  of  copper,  sulphuric  acid,  solution  of  sul- 
phate of  zinc,  solution  of  comm.on  salt. 

Guthrie  has  examined  the  conductivity  of  liquids  in  the  following 
manner.  Two  hollow  brass  cones  are  placed  near  each  other  so  that  the 
top  of  one  points  upwards,  that  of  the  other  downwards.  The  distance  of 
the  bases,  which  are  of  platinum  can  be  regulated  by  a  micrometer  screw. 
Between  the  bases  the  liquid  to  be  examined  was  introduced  by  means  of 
a  pipette.  The  lower  cone  was  fitted  with  a  glass  tube  which  dipped  in 
a  coloured  liquid,  and  thus  constituted  an  air  thermometer.  The  base  of 
the  upper  cone  was  kept  at  a  constant  temperature  by  means  of  a  current 
of  hot  water  ;  it  thus  warmed  the  liquid,  and  the  base  of  the  lower  cone,  in 
consequence  of  which  the  air  in  the  interior  was  expanded  and  the  column 
of  liquid  in  the  stem  depressed. 

The  bases  of  the  cones  were  first  brought  in  contact  and  the  depres- 
sion of  the  column  of  liquid  was  observed.  A  column  of  Hquid  of  a  given 
thickness  was  then  interposed  and  the  depression  observed  after  a  certain 
time.  The  same  thickness  of  other  liquids  were  then  introduced  and  the 
corresponding  depressions  noted.  The  difference  of  the  depressions  was 
a  measure  for  the  resistance  which  the  liquid  offered  to  the  passage  of 
heat.  The  following  numbers  give  the  ratios  of  the  resistance  of  the 
respective  liquids  to  that  of  an  equal  thickness  of  water  : 


Water 

.     J-oo 

Alcohol  . 

.  .       9-08 

Glycerine  . 

•     3-84 

Oil  of  turpentine    . 

.     1175 

Sperm  oil  . 

.     3-85 

Chloroform     . 

1210 

It  was  also  observed  that  water  conducts 
better  the  hotter  it  is  ;  and  any  salt  dissolved 
increases  the  conductivity. 

381.  Manner  in  wbich  liquids  are 
beated. — When  a  column  of  liquid  is  heated 
at  the  bottom,  ascending  and  descending 
currents  are  produced.  It  is  by  these  that 
heat  is  mainly  distributed  through  the  liquid, 
and  not  by  its  conductivity.  These  currents 
arise  from  the  expansion  of  the  inferior  layers, 
which,  becoming  less  dense,  rise  in  the  liquid, 
and  are  replaced  by  colder  and  denser  layers. 
They  may  be  made  visible  by  projecting  bran 
or  wooden  shavings  into  water,  which  rise 
and  descend  with  the  currents.  The  experi- 
ment is  arranged  as  shown  in  fig.  291.  The 
mode  in  which  heat  is  propagated  in  liquids 
and  in  gases  is  said  to  be  by  convection. 


B'ig.  291. 


320  On  Heat.  [382- 

382.  Conductivity  of  grases. — It  is  a  disputed  question  whether  gases 
have  a  true  conductivity  ;  but  certainly  when  they  are  restrained  in  their 
motion  their  conductivity  is  very  small.  All  substances,  for  instance, 
between  whose  particles  air  remains  stationary,  offer  great  resistance  to 
the  propagation  of  heat.  This  is  well  seen  in  straw,  eider  down,  and  furs. 
The  propagation  of  heat  in  a  gaseous  mass  is  effected  by  means  of  the 
ascending  and  descending  currents  formed  in  it,  as  is  the  case  with 
liquids. 

The  following  experiment  originally  devised  by  Grove  is  considered 
to  prove  that  gases  have  a  certain  conductivity.  In  a  glass  vessel  pro- 
vided with  delivery  tubes  by  which  any  gases  can  be  introduced,  or  by 
which  it  can  be  exhausted,  is  a  platinum  wire  which  can  be  heated  to 
redness  by  a  voltaic  battery.  When  the  vessel  is  exhausted  the  platinum 
wire  is  gradually  raised  to  a  bright  redness  ;  on  then  allowing  air  to 
enter,  the  luminosity  is  greatly  diminished,  and  if  the  vessel  be  exhausted 
and  then  hydrogen  admitted,  the  luminosity  quite  disappears.  This 
greater  chilling  of  the  wire  in  hydrogen  than  in  air  is  considered  by 
Magnus  to  be  an  effect  of  conduction  ;  while  Tyndall  ascribes  it  to  the 
greater  mobihty  of  the  particles  of  hydrogen. 

383.  Applications. — The  greater  or  less  conductivity  of  bodies  meets 
with  numerous  applications.  If  a  liquid  is  to  be  kept  warm  for  a  long 
time,  it  is  placed  in  a  vessel  and  packed  round  with  non-conducting  sub- 
stances, such  as  shavings,  straw,  bruised  charcoal.  For  this  purpose 
water  pipes  and  pumps  are  wrapped  in  straw  at  the  approach  of  frost. 
The  same  means  are  used  to  hinder  a  body  from  becoming  heated. 
Ice  is  transported  in  summer  by  packing  it  in  bran,  or  folding  it  in 
flannel. 

Double  walls  constructed  of  thick  planks  having  between  them  any 
finely  divided  materials,  such  as  shavings,  sawdust,  dry  leaves,  etc.,  retain 
heat  extremely  well ;  and  are  likewise  advantageous  in  hot  countries,  for 
they  prevent  its  access.  During  the  night  the  windows  are  opened,  while 
during  the  day  they  are  kept  close.  Pure  silica  in  the  state  of  rock  crystal 
is  a  better  conductor  than  lead,  but  in  a  state  of  powder  it  conducts  very 
badly.  If  a  layer  of  asbestos  is  placed  on  the  hand  a  red-hot  iron  ball 
can  be  held  without  inconvenience.  Red-hot  cannon  balls  can  be 
wheeled  to  the  gun's  mouth  in  wooden  barrows  partially  filled  with  sand. 
Lava  has  been  known  to  flow  over  a  layer  of  ashes  underneath  which 
was  a  bed  of  ice,  and  the  non-conducting  power  of  the  ashes  has  prevented 
the  ice  from  fusion. 

The  clothes  which  we  wear  are  not  warm  in  themselves  ;  they  only 
hinder  the  body  from  losing  heat,  in  consequence  of  their  spongy  texture 
and  the  air  they  enclose.  The  warmth  of  bed  covers  and  of  counterpanes 
is  explained  in  a  similar  manner.  Double  windows  are  frequently  used  in 
cold  climates  to  keep  a  room  warm — they  do  this  by  the  non-conducting 
layer  of  air  interposed  between  them.  It  is  for  the  same  reason  that  two 
shirts  are  warmer  than  one  of  the  same  material  but  of  double  the  thick- 
ness.    Hence  too  the  warmth  of  furs,  eider-down,  etc. 

The  small  conducting  power  of  felt  is  used  in  the  North  of  Europe  in 


-385]  Radiation  of  Heat.  321 

the  construction  of  the  Norwegian  stove,  which  consists  merely  of  a 
wooden  box  with  a  thick  hning  of  felt  on  the  inside.  In  the  centre  is 
a  cavity  in  which  can  be  placed  a  stew-pan  provided  with  a  cover.  On 
the  top  of  this  is  a  lid,  also,  made  of  felt,  so  that  the  pan  is  surrounded 
by  a  very  badly  conducting  envelope.  Meat,  with  water  and  suitable 
additions,  is  placed  in  the  pan,  and  the  contents  are  then  raised  to 
boiling.  The  whole  is  then  enclosed  in  the  box  and  left  to  itself ;  the 
cooking  will  go  on  without  lire,  and  after  the  lapse  of  several  hours  it 
will  be  quite  finished.  The  cooHng  down  is  very  slow,  owing  to  the  bad 
conducting  power  of  the  lining  ;  at  the  end  of  three  hours  the  temperature 
is  usually  not  found  to  have  sunk  more  than  from  10°  to  15°. 

That  water  boils  more  rapidly  in  a  metallic  vessel  than  in  one  of  porce- 
lain of  the  same  thickness  ;  that  a  burning  piece  of  wood  can  be  held 
close  to  the  burning  part  with  the  naked  hand,  while  a  piece  of  iron 
heated  at  one  end  can  only  be  held  at  a  great  distance,  are  easily  ex- 
plained by  reference  to  their  various  conductivities. 

The  sensation  of  heat  or  cold  which  we  feel  when  in  contact  with 
certain  bodies  is  materially  influenced  by  their  conductivity.  If  their 
temperature  is  lower  than  ours,  they  appear  colder  than  they  really  are, 
because  from  their  conductivity  heat  passes  away  from  us.  If,  on  the 
contrary,  their  temperature  is  higher  than  that  of  our  body,  they  appear 
warmer  from  the  heat  which  they  give  up  at  different  parts  of  their  mass. 
Hence  it  is  clear  why  carpets,  for  example,  are  warmer  than  wooden 
floors,  and  why  the  latter  are  warmer  than  stone  floors. 


CHAPTER  VIII. 

RADIATION   OF   HEAT. 


384.  Radiant  heat.— It  has  been  already  stated  (377)  that  heat  could 
be  transmitted  from  one  body  to  another  without  altering  the  temperature 
of  the  intervening  medium.  If  we  stand  in  front  of  a  fire  we  experience 
a  sensation  of  warmth  which  is  not  due  to  the  temperature  of  the  air,  for 
if  a  screen  be  interposed  the  sensation  immediately  disappears,  which 
would  not  be  the  case  if  the  surrounding  air  had  a  high  temperature. 
Hence  bodies  can  send  out  rays  which  excite  heat,  and  which  penetrate 
through  the  air  without  heating  it,  as  rays  of  light  through "  transparent 
bodies.  Heat  thus  propagated  is  said  to  be  radiated;  and  we  shall  use 
the  terms  ray  of  heat,  or  therjnal,  or  calorific  ray,  in  a  similar  sense  to  that 
in  which  we  use  the  term  ray  of  light  or  luminous  ray. 

We  shall  find  that  the  property  of  radiating  heat  is  not  confined  to 
luminous  bodies,  such  as  a  fire  or  a  red-hot  ball,  but  that  bodies  of  all 
temperatures  radiate  heat.  It  will  be  convenient  to  make  a  distinction 
between  luminous  and  obscure  rays  of  heat. 

385.  Detection  and  measurement  of  radiant  heat. — In  demon- 
strating the  phenomena  of  radiant  heat,  very  delicate  thermometers  are 

P3 


322 


On  Heat. 


[386- 


required,  and  the  thermo-electrical  multiplier  of  Melloni  is  used  for  this 
purpose  with  great  advantage  ;  for  it  not  only  indicates  minute  differences 
of  temperature,  but  it  also  measures  them  with  accuracy. 

This  instrument  cannot  be  properly  understood  without  a  knowledge  of 
the  principles  of  thermo-electrity,  for  which  Book  X.  must  be  consulted. 
It  may,  however,  be  stated  here,  that  when  two  different  metals  A  and  B 
are  soldered  together  at  one  end  (fig.  292),  the  free  ends  being  joined  by 


a  wire,  when  the  soldering  c  is  heated,  a  current  of  electricity  circulates 
through  the  system  ;  if,  on  the  contrary,  the  soldering  be  cooled,  a  current 
is  also  produced,  but  it  circulates  in  exactly  the  opposite  directions.  If 
a  number  of  such  pairs  be  alternately  soldered  together,  as  represented 
in  fig.  293,  the  intensity  of  the  current  produced  by  heating  the  ends  is 
increased ;  or,  what  amounts  to  the  same  thing,  a  smaller  degree  of  heat 
will  produce  the  same  effect.  Such  an  arrangement  of  a  number  of 
thermo-electric  pairs  is  called  a  thermo-electric  battery  ox  pile. 

Melloni's  thermo-multiplier  consists  of  a  thermo-electric  pile  connected 
with  a  delicate  galvanometer.     The  thermo-electric  pile  is  constructed  of 


Fig.  294. 

a  number  of  minute  bars  of  bismuth  and  antimony  soldered  together 
alternately,  though  kept  insulated  from  each  other,  and  contained  in  a 
rectangular  box  P,  fig.  294.  The  terminal  bars  are  connected  with  two 
binding  screws  ?«  and  ?/,  which  in  turn  are  connected  with  the  galvano- 
meter G  by  means  of  the  wires  a  and  b. 


-387]  Radiation  of  Heat.  323 

The  galvanometer  consists  of  a  quantity  of  fine  insulated  copper  wire 
coiled  round  a  frame,  in  the  centre  of  which  a  delicate  magnetic  needle 
is  suspended  by  means  of  a  silk  "thread.  When  an  electric  current  is 
passed  through  this  coil,  the  needle  is  deflected  through  an  angle  which 
depends  on  the  intensity  of  the  current.  This  angle  is  measured  on  a 
dial  by  an  index  connected  with  the  needle. 

It  may  then  be  sufficient  to  state  that  the  thermo-electric  pile  being 
connected  with  the  galvanometer  by  means  of  the  wires  a  and  b,  an  excess 
of  temperature  at  one  end  of  the  pile  causes  the  needle  to  be  deflected 
through  an  angle  which  depends  on  the  extent  of  this  excess  ;  and 
similarly  if  the  temperature  be  depressed  below  that  of  the  other  end,  a 
corresponding  deflection  is  produced  in  the  opposite  direction.  By 
arrangemenfs  of  this  kind  Melloni  was  able  to  measure  differences  of 
temperature  of  50^00^^  ^^  ^  degree. 

The  object  of  the  conical  part  C  is  to  concentrate  the  thermal  rays  on 
the  face  of  the  pile. 

386.  ]Laws  of  Radiation. — The  radiation  of  heat  is  governed  by  three 
laws  : — 

I.  Radiation  fakes  place  in  all  directions  round  a  body.  If  a  thermo- 
meter be  placed  in  different  positions  round  a  heated  body,  it  indicates 
everywhere  a  rise  in  temperature. 

I I.  In  a  homogeiieoiis  medium.,  radiation  takes  place  in  a  right  line. 
For,  if  a  screen  be  placed  in  a  right  line  which  joins  the  source  of  heat 
and  the  thermometer,  the  latter  is  not  affected. 

But  in  passing  obliquely  from  one  medium  into  another,  as  from  air 
into  glass,  calorific  like  luminous  rays  become  deviated,  an  effect 
known  as  refraction.  The  laws  of  this  phenomenon  are  the  same  for 
heat  as  for  light,  and  they  will  be  more  fully  discussed  under  the  latter 
subject. 

III.  Radiant  heat  is  propagated  in  vacuo  as  well  as  in 
air.     This  is  demonstrated  by  the  following  experiment  : — 

In  the  bottom  of  a  glass  flask  a  thermometer  is  fixed  in 
such  a  manner  that  its  bulb  occupies  the  centre  of  the  flask 
(fig.  295).  The  neck  of  the  flask  is  carefully  narrowed  by 
means  of  the  blowpipe,  and  then  the  apparatus  having  been 
suitably  attached  to  an  air  pump,  a  vacuum  is  produced  in 
the  interior.  This  having  been  done,  the  tube  is  sealed  at 
the  narrow  part.  On  immersing  this  apparatus  in  hot  water, 
or  on  bringing  near  it  some  hot  charcoal,  the  thermometer 
is  at  once  seen  to  rise.  This  could  only  arise  from  radia- 
tion through  the  vacuum  in  the  interior,  for  glass  is  so  bad 
a  conductor,  that  the  heat  could  not  travel  with  this  rapidity 
through  the  sides  of  the  flask  and  the  stem  of  the  thermo- 
meter. ^'^-  ^95- 

387.  Causes  wbicli  modify  the  intensity  of  radiant  beat. — By  the 
intensity  of  radiant  hmt  is  understood  the  quantity  of  heat  received  on 
the  unit  of  surface.  Three  causes  are  found  to  modify  this  intensity  ; 
the  temperature  of  the  source  of  heat,  its  distance,  and  the  obliquity  of 


324 


On  Heat 


[387- 


Fig.  296. 


or   30^ 


the  caloric  rays  in  reference  to  the  surface  which  emits  them.  The  laws 
which  regulate  these  modifications  may  be 
thus  stated: 

I .  The  intensity  of  radiant  heat  is  propor- 
tional to  the  tejnperature  of  the  source. 

I I .  The  inie?tsity  is  inversely  as  the  square 
of  the  distance. 

III.  The  intensity  is.  less ^  the  greater  the 
obliquity  of  the  rays  with  respect  to  the  radi- 
atiftg  surface. 

The  first  law  is  demonstrated  by  placing 
a  metal  box  containing  water  at  10°,  20°, 
successively  at  equal  distances  from  the  bulb  of  a  diiferential 
thermometer.  The  temperatures  indicated  by  the  latter  are  then  found 
to  be  in  the  same  ratio  as  those  of  the  box  :  for  instance,  if  the  temper- 
ature of  that  corresponding  to  the  box  at  10°  be  2°,  those  of  others  will 
be  4°  and  6°  respectively. 

The  truth  of  the  second  law  follows  from  the  geometrical  principle  that 
the  surface  of  a  sphere  increases  as  the  square  of  its  radius.  Suppose  a 
hollow  sphere,  ab  (fig.  296),  of  any  given  radius,  and  a  source  of  heat,  C, 
in  its  centre  ;  each  unit  of  surface  in  the  interior  receives  a  certain 
quantity  of  heat.  Now,  a  sphere,  ef  of  double  the  radius  will  present  a 
surface  four  times  as  great  :  its  internal  surface  contains,  therefore,  four 
times  as  many  units  of  surface,  and  as  the  quantity  of  heat  emitted  is 
the  same,  each  unit  can  only  receive  one-fourth  the  quantity. 

To  demonstrate  the  same  law  experimentally,  a  narrow  tin  plate  box 
is  taken  (fig.  297),  filled  with  hot  water,  and  coated  on   one  side  with 


Fig.  297. 

lampblack.     The  thermo-battery  with  its  conical  reflector  is  placed  so  that 
its  face  is  at  a  certain  definite  distance,  co,  say  9  inches,  from  this  box, 


-387] 


Radiation  of  Heat. 


325 


and  the  cover  having  been  lowered,  the  needle  of  the  galvanometer  is 
observed  to  be  deflected  through  80°,  for  example. 

If  now  the  battery  is  removed  to  a  distance,  CO,  double  that  of  (Tt*,  the 
deflection  of  the  galvanometer  remains  the  same,  which  shows  that  the 
battery  receives  the  same  amount  of  heat  ;  the  same  is  the  case  if  the 
battery  is  removed  to  three  or  four  times  the  distance.  This  result, 
though  apparently  in  opposition  to  the  second  law,  really  confirms  it. 
For  at  first  the  battery  only  receives  heat  from  the  circular  portion  ab  of 
the  side  of  the  box,  while,  in  the  second  case,  the  circular  portion  AB 


radiates  towards  it.  But,  as  the  two  cones  ACB  and  acb  are  similar,  and 
the  height  of  ACB  is  double  that  of  acb^  the  diameter  AB  is  double  that  ot 
ab^  and  therefore  the  area  AB  is  four  times  as  great  as  that  of  ab^  for  the 
areas  of  circles  are  proportional  to  the  squares  of  the  radii.  But  since 
the  radiating  surface  increases  as  the  square  of  the  distance,  while  the 
galvanometer  is  stationary,  the  heat  received  by  the  battery  must  be  in- 
versely as  this  same  square. 

The  third  law  is  demonstrated  by  means  of  the  following  experiment, 
which  is  a  modification  of  one  originally  devised  by  Leslie  (fig.  299).     P 


A 

in. 

M 

-"'  0   0 

c 

,''' 

71 

da' 

— 

—    i 

N 

Fig.  299. 

represents   the  thermo-multiplier  which  is  connected  with  its  galvano- 
meter, and   A,  a  metal  cube  full  of  hot  water.     The  cube  being  first 


326  On  Heat.  [387- 

placed  in  such  a  position,  A,  that  its  front  face  ac  is  vertical,  the  deflection 
of  the  galvanometer  is  noted.  Supposing  it  amounts  to  45°,  this  repre- 
sents the  radiation  from  ac.  If  this  now  be  turned  in  the  direction  repre- 
sented by  A',  the  galvanometer  is  still  found  to  mark  45°. 

The  second  surface  is  larger  than  the  first,  and  it  therefore  sends  more 
rays  to  the  mirror.  But  as  the  action  on  the  thermometer  is  no  greater 
than  in  the  first  case,  it  follows  that  in  the  second  case,  where  the  rays 
are  oblique,  the  intensity  is  less  than  in  the  first  case,  where  they  are 
perpendicular. 

In  order  to  express  this  in  a  formula,  let  /  be  the  intensity  of  the  rays 
emitted  perpendicularly  to  the  surface,  and  i'  that  of  the  oblique  rays. 
These  intensities  are  necessarily  inversely  as  the  surfaces  ac  and  a'c',  for 
the  effect  is  the  same  in  both  cases,  and  therefore  i'  x  surface  a'c'  =  z  x 

surface  ac;  hence  /'  =  z  -— .J— ^/,  =i  ^  =i  cos  aoa' ;  which  signifies  that 
.  surf,  rt  r         a'c 

the  intensity  of  oblique  rays  is  proportional  to  the  cosine  of  the  angle  which 
these  rays  form  with  the  normal  to  the  surface  ;  for  this  angle  is  equal  to 
the  angle  aoa'.  This  law  is  known  as  the  law  of  the  cosine ;  it  is  how- 
ever, not  general  ;  MM.  Desains  and  De  la  Provostaye  have  shown  that 
it  is  only  true  within  very  narrow  limits,  that  is  only  with  bodies  which, 
like  lampblack,  are  entirely  destitute  of  reflecting  power  (396). 

388.  Mobile  equilibrium.  Theory  of  excbang^es. — Prevost  of  Geneva 
suggested  the  following  hypothesis  in  reference  to  radiant  heat,  known  as 
Prevost's  theory  of  exchanges,  which  is  now  universally  admitted.  All 
bodies,  whatever  their  temperatures,  constantly  radiate  heat  in  all  direc- 
tions. If  we  imagine  two  bodies  at  different  temperatures  placed  near 
one  another,  the  one  at  a  higher  temperature  will  experience  a  loss  of 
heat,  its  temperature  will  sink,  because  the  rays  it  emits  are  of  greater 
intensity  than  those  it  receives  ;  the  colder  body,  on  the  contrar)^,  will 
rise  in  temperature  because  it  receives  rays  of  greater  intensity  than 
those  which  it  emits.  Ultimately  the  temperature  of  bcth  bodies  becomes 
the  same,  but  heat  is  still  exchanged  between  them,  only  each  receives  as 
much  as  it  emits,  and  the  temperature  remains  constant.  This  state  is 
called  the  mobile  equilibrium  of  temperature. 

389.  irewton's  law  of  cooling:. — A  body  placed  in  a  vacuum  is  only 
cooled  or  heated  by  radiation.  In  the  atmosphere  it  becomes  cooled  or 
heated  by  its  contact  with  the  air  according  as  the  latter  is  colder  or 
hotter  than  the  radiating  body.  In  both  cases  the  velocity  of  cooling  or 
of  heating— that  \s,  the  quantity  of  heat  lost  or  gained  in  a  second — is 
greater  according  as  the  difterence  of  temper?"-"-"  is  greater. 

Newton  has  enunciated  the  following  law  m  leference  to  the  cooling 
or  heating  of  a  body  :  The  quantity  of  heat  lost  or  gained  by  a  body  in  a 
second  is  proportional  to  the  difference  between  its  temperature  and  that  of 
the  surrounding  medium.  Dulong  and  Petit  have  proved  that  this  law  is 
not  so  general  as  Newton  supposed,  and  only  applies  where  the  differences 
of  temperature  do  not  exceed  1 5°  to  20°.  Beyond  that,  the  quantity  of 
heat  lost  or  gained  is  greater  than  that  required  by  this  law. 

Two  consequences  follow  from  Newton's  law  : 


-391]  Reflection  of  Heat.  327 

i.  When  a  body  is  exposed  to  a  constant  source  of  heat,  its  temperature 
does  not  increase  indefinitely,  for  the  quantity  which  it  receives  in  the^ 
same  time  is  always  the  same  ;  while  that  which  it  loses  increases  with 
the  excess  of  the  temperature  over  that  of  the  surrounding  medium.  Con- 
sequently a  point  is  reached  at  which  the  quantity  of  heat  emitted  is  equal 
to  that  absorbed,  and  the  temperature  then  remains  stationary. 

ii.  Newton's  law,  as  appHed  to  the  differential  thermometer,  shows  that 
its  indications  are  proportional  to  the  quantities  of  heat  which  it  receives. 
If  one  of  the  bulbs  of  a  differential  thermometer  receives  rays  of  heat 
frorp  a  constant  source,  the  instrument  exhibits  first  increasing  tempera- 
tures, but  afterwards  becomes  stationary.  In  this  case,  the  quantity  of 
heat  which  it  receives  is  equal  to  that  which  it  emits.  But  the  latter  is 
proportional  to  the  excess  of  the  temperature  of  the  bulb  above  that  of 
the  surrounding  atmosphere,  that  is,  to  the  number  of  degrees  indicated 
by  the  thermometer  ;  consequently,  the  temperature  indicated  by  the 
differential  thermometer  is  proportional  to  the  quantity  of  heat  it  re- 


REFLECTION   OF   HEAT. 

390.  Ijaws  of  reflection. — When  thermal  rays  fall  upon  a  body  they 
are,  speaking  generally,  divided  into  two  parts,  one  of  which  penetrates  the 
body,  while  the  other  rebounds  as  if  repelled  j^ 

from  the  surface  like  an  elastic  ball.     This  is 
said  to  be  reflected. 

If  mn  be  a  plane  reflecting  surface  (fig. 
300),  CB  an  incident  ray,  BD  a  line  perpen- 
dicular to  the  surface  called  the  norjnal,  and 
BA   the   reflected  ray ;    the  angle   CBD  is       "  b 

called  the  attgle  of  incidence,  and  D  B A  the  Fig.  300. 

angle  of  reflection.     The  reflection  of  heat,  like  that  of  light,  is  governed 
by  the  two  following  laws  : — 

I.  The  angle  of  reflection  is  eqtial  to  the  angle  of  incidence. 

II.  Both  the  incident  and  the  reflected  ray  are  iti  the  same  plane  with 
the  normal  to  the  reflecting  surface. 

39 1.  Experimental  demonstration  of  tbe  la^irs  of  reflection  of  beat. 
— This  may  be  effected  by  means  of  Melloni's  thermo-pile  and  also  by 
the  conjugate  mirrors  (393).  Figure  301  represents  the  arrangement 
adopted  in  the  former  case.  MN  is  a  horizontal  bar,  about  a  metre  in 
length  graduated  in  millimetres,  on  which  slide  various  parts,  which  can 
be  clamped  by  means  of  screws.  The  source  of  heat,  S,  is  a  platinum 
spiral,  kept  at  a  white  heat  in  a  spirit  lamp.  A  screen  K,,when  raised, 
cuts  off  the  radiation  from  the  source  ;  a  second  screen,  F,  with  an  aper- 
ture in  the  centre,  gives  the  rays  a  parallel  direction.  At  the  other  end 
is  an  upright  rod,  I,  with  a  graduated  dial,  the  zero  of  which  is  in  the 
direction  of  MN,  and  therefore  parallel  to  the  pencil  S;«.  In  the  centre 
of  the  dial  is  an  aperture,  in  which  turns  an  axis  which  supports  a 
metallic  mirror  m.     About  this  axis  turns  an  index,  R,  on  which  is  fixed 


328 


On  Heat, 


[391- 


the  thermo-battery,  P,  in  connection  with  the  galvanometer,  G.  H  is  a 
screen,  the  object  of  which  is  to  cut  off  any  direct  radiation  from  the 
source  of  heat  towards  the  battery.  In  order  not  to  mask  the  battery,  it 
is  not  represented  in  the  position  it  occupies  in  the  experiment. 

By  lowering  the  screen  K,  a  pencil  of  parallel  rays,  passing  through  the 
aperture  F,  falls  upon  the  mirror  m,  and  is  there  reflected.     If  the  index 


Fig.  301. 

R  is  not  in  the  direction  of  the  reflected  pencil,  this  latter  does  not 
impinge  on  the  pile,  and  the  needle  of  the  galvanometer  remains  sta- 
tionary ;  but  by  slowly  turning  the  index  R,  a  position  is  found  at  which 
the  galvanometer  attains  its  greatest  deviation,  which  is  the  case  when 
the  battery  receives  the  reflected  pencil  perpendicularly  to  its  surface. 
Reading  off  then  on  the  dial  the  position  of  a  small  needle  perpendicular 
to  the  mirror,  it  is  observed  that  this  bisects  the  angle  formed  by  the 
incident  and  the  reflected  pencil,  which  demonstrates  the  first  law. 

The  second  law  is  also  proved  by  the  same  experiment,  for  the  various 
pieces  of  the  apparatus  are  arranged  so  that  the  incident  and  reflected 
ray  are  in  the  same  horizontal  plane,  and  therefore  at  right  angles  to  the 
reflecting  surface,  which  is  vertical. 

392.  Reflection  from  concave  mirrors. — Concave  mirrors  or  re- 
flectors are  polished  spherical  or  parabolic  surfaces  of  metal  or  cf  glass, 
which  are  used  to  concentrate  luminous  or  calorific  rays  in  the  same 
point. 

We  shall  only  consider  the  case  of  spherical  mirrors.  Fig.  303  repre- 
sents two  of  these  mirrors  ;  fig.  302  gives  a  medial  section,  which  is 
called  the  principal  section.  The  centre  C  of  the  sphere  to  which  the 
mirror  belongs  is  called  the  centre  of  curvature  ;  the  point  A,  the  middle 
of  the  reflector,  is  the  centre  of  the  figure  ;  the  straight  line  AB  passing 
through  these  points,  is  the  principal  axis  of  the  mirror. 

In  order  to  apply  to  spherical  mirrors  the  laws  of  reflection  from  plane 
surfaces,  they  are  considered  to  be  composed  of  an  infinite  number  of  in- 


-393]         Reflection  of  Heat  from  Concave  Mirrors.  329 

finitely  small  plane  surfaces,  each  belonging  to  the  corresponding  tangent 
plane  ;  the  normals  to  these  small  surfaces  are  all  radii  of  the  same  sphere,- 
and  therefore  meet  at  its  centre,  the  centre  of  curvature  of  the  mirror. 

Suppose  now,  on  the  axis  AB  of  the  mirror  MM,  a  source  of  heat  so 
distant  that  the  rays  EK,  PH  .  .  .  .  which  emanate  from  it  may  be 
considered  as  a  parallel.  From  the  hypothesis  that  the  mirror  is  com- 
posed of  an  infinitude  of  small  planes,  the  ray  EK  is  reflected  from  the 
plane  K  just  as  from  a  plane  mirror  ;  that  is  to  say,  CK  being  the 
normal  to  this  plane,  the  reflected  ray  takes  a  direction  such  that  the 

angle  CKF  is  equal  to  the  angle  CKE.     The  other  rays,  PH,  GI 

are  reflected  in  the  same  manner,  and  all  converge  approximately  towards 
the  same  point  F,  on  the  line  AC.     There  is  then  a  concentration  of  the 


Fig.  302. 

rays  in  this  point,  and  consequently  a  higher  temperature  than  at  any 
other  point.  This  point  is  called  the  focus,  and  the  distance  from  the 
focus  to  the  mirror  at  A  is  Xhe  focal  distance. 

In  the  above  figure  the  heat  is  propagated  along  the  lines  EKF,  LDF, 
in  the  direction  of  the  arrows  ;  but,  conversely,  if  the  heated  body  be 
placed  at  F,  the  heat  is  propagated  along  the  lines  FKE,  FDL,  so  that 
the  rays  emitted  from  the  focus  are  nearly  parallel  after  reflection. 

393.  Verification  of  tbe  laws  of  reflection.— The  following  experi- 
ment, which  was  made  for  the  first  time  by  Pictet  and  Saussure,  and 
which  is  known  as  the  experiment  of  the  conjugate  mirrors,  demonstrates 
not  only  the  existence  of  the  foci,  but  also  the  laws  of  reflection.  Two 
reflectors,  M  and  N  (fig.  303),  are  arranged  at  a  distance  of  4  to  5  yards, 
and  so  that  their  axes  coincide.  In  the  focus  of  one  of  them,  A,  is  placed 
a  small  wire  basket  containing  a  red-hot  iron  ball.  In  the  focus  of  the 
other  is  placed  B,  an  inflammable  body,  such  as  gun-cotton  or  phosphorus. 
The  rays  emitted  from  the  focus  A  are  first  reflected  from  the  mirror  M, 
in  a  direction  parallel  to  the  axis  (392),  and  impinging  on  the  other 
mirror,  N,  are  reflected  so  that  they  coincide  in  the  focus  B.  That  this 
is  so,  is  proved  by  the  fact  that  the  gun-cotton  in  this  point  takes  fire, 
which  is  not  the  case  if  it  is  above  or  below  it. 

The  experiment  also  serves  to  show  that  fight  and  heat  are  reflected  in 
the  same  manner.  For  this  purpose  a  lighted  candle  is  placed  in  the 
focus  of  A,  and  a  ground-glass  screen  in  the  focus  of  B,  when  a  luminous 
focus  is  seen  on  it  exactly  in  the  spot  where  the  gun-cotton  ignites. 
Hence  the   luminous  and  the  calorific   foci  are  produced  at  the  same 


330 


On  Heat, 


[393- 


point,  and  the  reflection  takes  place  in  both  cases  according  to  the  same 
laws,  for  it  will  be  afterwards  shown  that  for  light  the  angle  of  reflection 
is  equal  to  the  angle  of  incidence,  and  that  both  the  incident  and  the 
reflected  rays  are  in  the  same  plane  perpendicular  to  the  plane  reflecting 
surface. 

In  consequence  of  the  high  temperature  produced  in  the  foci  of  con- 
cave mirrors  they  have  been  called  burning  mirrors.     It  is  stated  that 


Fig.  303- 

Archimedes  burnt  the  Roman  vessels  before  Syracuse  by  means  of  such 
mirrors.  Buffon  constructed  burning  mirrors  of  such  power  as  to  prove 
that  the  feat  attributed  to  Archimedes  was  possible.  The  mirrors  were 
made  of  a  number  of  silvered  plane  mirrors  about  8  inches  long  by  5 
broad.  They  could  be  turned  independently  of  each  other  in  such  a 
manner  that  the  rays  reflected  from  each  coincided  in  the  same  point. 
With  128  mirrors  and  a  hot  summer's  sun  Buffon  ignited  a  plank  of 
tarred  wood  at  a  distance  of  70  yards. 

394.  Reflection  in  a  vacuum. — Heat  is  reflected  in  a  vacuum  as  well 
as  in  air,  as  is  seen  from  the  following  experiment  (fig.  304),  due  to  Sir 
Humphry  Davy.  Two  small  concave  reflectors  were  placed  opposite  each 
other  under  the  receiver  of  an  air  pump.  In  the  focus  of  one  was  placed 
a  delicate  thermometer,  and  in  the  focus  of  the  other  a  platinum  wire 
made  incandescent  by  means  of  a  galvanic  current.  The  thermometer 
was  immediately  seen  to  rise  several  degrees,  which  could  only  be  due  to 
reflected  heat,  for  the  thermometer  did  not  show  any  increase  of  tempera- 
ture if  it  were  not  exactly  in  the  focus  of  the  second  reflector. 

395.  Apparent  reflection  of  cold. — If  two  mirrors  are  arranged  as  re- 
presented in  fig.  304,  and  a  piece  of  ice  is  placed  in  one  of  the  foci  instead 


.  396]  Reflecting  Pozver  of  Bodies  for  Heat. 


331 


Fig.  304. 


of  the  red-hot  ball,  the  surrounding  temperature  being  greater  than  zero, 
a  differential  thermometer  placed  in  the  focus  of  the  second  reflector 
would  exhibit  a  decrease  in  temperature  of  several  degrees.  This  appears 
at  first  to  be  caused  by  the  emission  of  frigorific  rays  from  ice.  It  is, 
however,  easily  explained  from  what 
has  been  said  about  the  mobile  equili- 
brium of  temperature  (388).  There  is 
still  an  exchange  of  temperature,  but 
here  the  thermometer  is  the  warmest 
body.  As  the  rays  which  the  thermo- 
meter emits  are  more  intense  than 
those  emitted  by  the  ice,  the  former 
gives  out  more  heat  than  it  receives, 
and  hence  its  temperature  sinks. 

The  sensation  of  cold  experienced 
when  we  stand  near  a  plaster  or  a  stone 
wall  whose  temperature  is  lower  than 
that  of  our  body,  or  when  we  stand  in 
front  of  a  wall  of  ice,  is  explained  in 
the  same  way. 

396.  Reflecting-  power. — The  re- 
flecting power  of  a  substance  is  its 
property  of  throwing  off  a  greater  or 
less  proportion  of  incident  heat. 

This  power  varies  in  different  substances.  In  order  to  study  this 
power  in  different  bodies  without  having  recdurse  to  as  many  reflectors, 
Leslie  arranged  his  experiments  as  shown  in  fig.  305.  The  source  of 
heat  is  a  cubical  canister,  M,  now  known  as  Leslie'' s  cube,  filled  with  hot 
water.  A  plate,  a,  of  the  substance  to  be  experimented  upon  is  placed 
on  the  axis  of  a  reflecting  mirror  between  the  focus  and  the  mirror.  In 
this  manner  the  rays  emitted  by  the  source  are  first  reflected  from  the 
mirror  and  impinge  on  the  plate  a,  where  they  are  again  reflected  and 
converge  to  a  focus  between  the  plate  and  the  mirror,  at  which  point  a 
differential  thermometer  is  placed.  The  reflector  and  the  thermometer 
are  always  in  the  same  position,  and  the  water  of  the  cube  is  always  kept 
at  100°,  but  it  is  found  that  the  temperature  indicated  by  the  thermometer 
varies  with  the  nature  of  the  plate.  This  method  gives  a  means  of 
determining,  not  the  absolute  reflecting  power  of  a  body,  but  its  power 
relatively  to  that  of  some  body  taken  as  a  standard  of  comparison.  For 
from  what  has  been  said  on  the  application  of  Newton's  law  to  the 
differential  thermometer,  the  temperatures  which  this  instrument  indicates 
are  proportional  to  the  quantities  of  heat  which  it  receives.  Hence,  if  in 
the  above  experiment,  a  plate  of  glass  causes  the  temperature  to  rise  1°, 
and  a  plate  of  lead  6°,  it  follows  that  the  quantity  of  heat  reflected  by  the 
latter  is  six  times  as  great  as  that  reflected  by  the  former.  For  the  heat 
emitted  by  the  source  remains  the  same,  the  concave  reflector  receives 
the  same  portion,  and  the  difference  can  only  arise  from  the  reflecting 
power  of  the  plates  a. 


332 


On  Heat. 


[396- 


By  this  method  Leslie  determined  the  reflecting  powers  of  the  following 
substances,  relatively  to  that  of  brass,  taken  as  loo  : — 


Polished  brass 

lOO 

Indian  ink 

n 

Silver      . 

.         .       90 

Amalgamated  tin    . 

10 

Polished  tin    . 

.       80 

Glass       .... 

10 

Steel 

.       70 

Oiled  glass     . 

^ 

Lead       . 

.       60 

Lampblack     .         . 

0 

The  numbers  only  represent  the  relative  reflecting  power  as  compared 
with  that  of  brass.     Their  absolute  power  is  the  relation  of  the  quantity 


Fig.  305. 

of  heat  reflected  to  the  quantify  of  heat  received.  Melloni  first  determined 
the  absolute  reflecting  power  of  a  certain  number  of  bodies.  Desains  and 
De  la  Provostaye,  who  also  examined  it  for  certain  metals,  obtained  the 
following  results  by  means  of  Melloni's  thermo-multiplier  (385),  the  heat 
being  reflected  at  an  angle  of  50°: — 

Silver  plate   ....  0-97  Steel 0-82 

Gold 0-95  Zinc o-8i 

Brass 0-93  Iron      .....  077 

Platinum       .         .         ...  0-83  Cast  iron       ....  074 

We  shall  presently  see  (400)  what  are  the  causes  which  modify  the 
reflecting  power. 

397.  Absorbing:  power. — The  absorbing  poiuer  of  a  body  is  its  pro- 
perty of  allowing  a  greater  or  less  quantity  of  incident  heat  to  pass  into 
its  mass.  Its  absolute  value  is  the  ratio  of  the  quantity  of  heat  absorbed 
to  the  quantity  of  heat  received. 


-398]  Radiating  Poiucr.  333 

The  absorbing  power  of  a  body  is  always  inversely  as  its  reflecting 
power:  a  body  which  is  a  good  absorbent  is  a  bad  reflector,  and  vice  versa. 
It  was  formerly  supposed  that  the  two  powers  were  exactly  complemen- 
tary, that  the  sum  of  the  reflected  and  absorbed  heat  was  equal  to  the 
total  quantity  of  incident  heat.  This  is  not  the  case  ;  it  is  always  less  : 
the  incident  heat  is  divided  into  three  parts — ist,  one  which  is  absorbed; 
2nd,  another  which  is  reflected  regularly — that  is,  according  to  laws  pre- 
viously demonstrated  (390) ;  and  a  third,  which  is  irregularly  reflected  in 
all  directions,  and  which  is  called  scattered  or  diffused  heat. 

In  order  to  determine  the  absorbing  power  of  bodies,  Leslie  used  the 
apparatus  which  he  employed  in  determining  the  reflecting  powers  (396). 
But  he  suppressed  the  plate  a\  and  placed  the  bulb  of  the  thermometer  in 
the  focus  of  the  reflector.  This  bulb  being  then  covered  successively 
with  lampblack,  or  varnish,  or  with  gold,  silver,  or  copper  foil,  etc.,  the 
thermometer  exhibited  a  higher  temperature  under  the  influence  of  the 
source  of  heat,  M,  according  as  the  substance  with  which  the  bulb  was 
covered  absorbed  more  heat.  Leshe  found  in  this  way  that  the  absorb- 
ing power  of  a  body  is  greater  the  less  its  reflecting  power.  In  these 
experiments,  however,  the  relation  of  the  absorbing  powers  cannot  be 
deduced  from  that  of  the  temperatures  indicated  by  the  thermometer,  for 
Newton's  law  is  not  exactly  applicable  in  this  case,  as  it  only  prevails  for 
bodies  whose  substance  does  not  vary,  and  here  the  covering  of  the  bulb 
varied  with  each  observation.  But  we  shall  presently  show  (399)  how 
the  comparative  absorbing  powers  may  be  deduced  from  the  ratios  of  the 
emissive  powers. 

Taking  as  a  source  of  heat  a  canister  filled  with  water  at  100°,  Mellon 
found  by  means  of  the  thermo-multiplier  the  following  relative  absorbing 
powers : — 

Lampblack     .         .         .         .100       Indian  ink       .         .         .         .85 

White  lead     .         .         .         .100       Shellac 72 

Isinglass         ....       91       Metals 13 

398.  Radiating:  power. — The  radiating  or  emissive  power  of  a  body 
is  its  capability  of  emitting  at  the  same  temperature  and  with  the  same 
extent  of  surface  greater  or  less  quantities  of  heat. 

The  apparatus  represented  in  fig.  305  was  also  used  by  Leslie  in  deter- 
mining the  radiating  power  of  bodies.  For  this  purpose  the  bulb  of  the 
thermometer  was  placed  in  the  focus  of  the  reflector,  and  the  faces  of  the 
canister  M  were  formed  of  difl"erent  metals,  or  covered  with  different 
substances,  such  as  lampblack,  paper,  etc.  The  cube  being  filled  with 
hot  water,  at  100°,  and  all  other  conditions  remaining  the  same,  Leslie 
turned  each  face  of  the  cube  successively  towards  the  reflectors,  and  noted 
the  temperature  each .  time.  That  face  which  was  coated  with  lamp- 
black caused  the  greatest  elevation  of  temperature,  and  the  metal  faces 
the  least.  Applying  Newton's  law,  and  representing  the  heat  emitted 
by  lampblack  as  100,  Leslie  formed  the  following  table  of  radiating 
powers  : — 


334 

On  Heat. 

[398- 

Lampblack     . 

.       lOO 

Isinglass . 

.    80 

White  lead     . 

.       lOO 

Tarnished  lead 

.    45 

Paper     . 

.    98 

Mercury  . 

.     20 

Sealing  wax   . 

. 

•      95 

Polished  lead  . 

.     19 

Ordinary  white 

glass 

.      90 

Polished  iron  . 

.     15 

Indian  ink 

T^    --   -ll     1-  _     __ 

.       88 

Tin,  gold,  silver, 

copper. 

etc   .     12 

It  will  be  seen  that,  in  this  table,  the  order  of  the  bodies  is  exactly  the 
reverse  of  that  in  the  tables  of  reflecting  powers. 

The  radiating  powers  of  several  substances  were  determined  by 
Melloni  by  the  same  method  as  that  of  Leslie,  but  using  the  thermo- 
multiplier  instead  of  the  differential  thermometer.  This  has  also  since 
been  done  more  exactly  by  Dessains  and  De  la  Provostaye,  who  used  the 
same  instrument,  but  avoided  certain  sources  of  error  incidental  to  previous 
methods.  They  found  in  this  manner  the  following  numbers  compared 
with  lampblack  as  100  : — 


Platinum  foil 

lO'So 

Pure  silver  laminated    . 

3-00 

Burnished  platinum     . 

9-50 

„              burnished    . 

2-50 

Silver  deposited  chemically 

5-36 

„              deposited  chemi- 

Copper foil  .... 

4-90 

cally  and  bur- 

Gold leaf     .         .         . 

4-28 

nished    . 

2-25 

It  appears,  therefore,  that  the  radiating  power  found  by  Leslie  for  the 
metals  is  too  large. 

399.  Identity  of  the  absorbing:  and  radiating-  powers. — The  absorb- 
ing power  of  a  body  cannot  be  accurately  deduced  from  its  reflecting 
power,  because  the  two  are  not  exactly  complementary.  But  the  absorb- 
ing power  would  be  determined  if  it  could  be  shown  that  in  the  same  body 
it  is  equal  to  the  radiating  power.  This  conclusion  has  been  drawn  by 
Dulong  and  Petit  from  the  following  experiments  :— In  a  large  glass  globe, 
blackened  on  the  inside,  was  placed  a  thermometer  at  a  certain  tempera- 
ture, 15°  for  example  ;  the  globe  was  kept  at  zero  by  surrounding  it  with 
ice,  and  having  been  exhausted  by  means  of  a  tubulure  connected  with 
the  air  pump,  the  time  was  noted  which  elapsed  while  the  thermometer 
fell  through  5°.  The  experiment  was  then  made  in  the  contrary  direction, 
that  is,  the  sides  of  the  globe  were  heated  to  1 5°,  while  the  thermometer 
was  cooled  to  zero  :  the  time  was  then  observed  which  the  thermometer 
occupied  in  rising  through  5°  It  was  found  that  this  time  was  exactly 
the  same  as  that  which  the  thermometer  had  ta..c".  in  sinking  through  5°, 
and  it  was  thence  concluded  that  the  radiating  power  is  equal  to  the 
absorbing  power  for  the  same  body,  and  for  the  same  difference  between 
its  temperature  and  the  temperature  of  the  surrounding  medium,  because 
the  quantities  of  heat  emitted  or  absorbed  in  the  same  time  are  equal. 

This  point  may  also  be  demonstrated  by  means  of  the  following  appa- 
ratus devised  by  Ritchie.  Fig.  306  represents  what  is  virtually  a  differen- 
tial thermometer,  the  two  glass  bulbs  of  which  are  replaced  by  two  cylin- 
drical reservoirs  B  and  C,  of  metal,  and  full  of  air.  Between  them  is  a 
third  and  larger  one  A,  which  can  be  filled  with  hot  water  by  means  of  a 
tubulure.     The  faces  of  B  and  A,  which  face  the  right,  are  coated  with 


-400] 


Radiant  Heat. 


335 


lampblack ;  those  of  C  and  A,  which  face  the  left,  are  either  painted 

white,  or  are  coated  with  silver  foil.     Tiius  of  the  two  faces  opposite  each 

other,  one  is  black  and  the  other  white;  hence  when  the  cylinder  A  is 

filled  with  hot  water,  its  white  face  radiates  towards  the  black  face  of  B, 

and  its  black  face  towards  the  white  face  of 

C.     Under  these  circumstances  the  liquid  in 

the  stem  does  not  move,  indicating  that  the 

two  reservoirs  are  at  the  same  temperature. 

On  the  one  hand,  the  greater  emissive  power 

of  the  black  face  of  A  is  compensated  by  the 

smaller  absorptive  power  of  the  white  face  of 

C ;   while,  on  the   other   hand,  the  feebler 

radiating  power  of  the  white  face  of  A  is 

compensated  by  the  greater  absorbing  power 

of  the  black  face  of  B. 

The  experiment  may  be  varied  by  re- 
placing the  two  white  faces  by  discs  of  paper, 
glass,  porcelain,  &c. 

400.  Causes  wbicli  modify  tbe  reflect- 
ing:, absorbing-,  and  radiating:  po-wers. — 
As  the  radiating  and  absorbing  powers  are 
equal,  any  cause  which  affects  the  one  affects 
the  other  also.  And  as  the  reflecting  power 
varies  in  an  inverse  manner,  whatever  in- 
creases it  diminishes  the  radiating  and  absorbing  powers,  and  vice  versa. 

It  has  been  already  stated  that  these  different  powers  vary  with  different 
bodies,  and  that  metals  have  the  greatest  reflecting  power,  and  lampblack 
the  feeblest.  In  the  same  body  these  powers  are  modified  by  the  degree 
of  poHsh,  the  density,  the  thickness  of  the  radiating  substance,  the  obli- 
quity of  the  incident  or  emitted  rays,  and,  lastly,  by  the  nature  of  the 
source  of  heat. 

It  has  been  usually  assumed  that  the  reflecting  power  increases  with 
the  polish  of  the  surface,  and  that  the  other  powers  diminish  therewith. 
But  Melloni  showed  that  by  scratching  a  polished  metallic  surface  its 
reflecting  power  was  sometimes  diminished  and  sometimes  increased. 
This  phenomenon  lie  attributed  to  the  greater  or  less  density  of  the  re- 
flecting surface.  If  the  plate  had  been  originally  hammered,  its  homo- 
geneity would  be  destroyed  by  this  process,  the  molecules  would  be  closer 
together  on  the  surface  than  in  the  interior,  and  the  reflecting  power  would 
be  increased.  But  if  the  surface  is  scratched,  the  internal  and  less  dense 
mass  becomes  exposed,  and  the  reflecting  power  diminished.  On  the 
contrary,  in  a  plate  which  has  not  been  hammered,  and  which  is  homo- 
geneous, the  reflecting  power  is  increased  when  the  plate  is  scratched, 
because  the  density  at  the  surface  is  increased  by  the  scratches. 

The  experiments  of  Leslie,  Rumford,  and  Melloni  further  prove,  that 
the  thickness  of  the  radiating  substance  also  modifies  its  emissive  power. 
The  latter  philosopher  found  that  when  the  faces  of  a  cube  filled  with 
water  at  a  constant  temperature  were  varnished,  the  emissive  power  in 


336 


071  Heat. 


[400- 


creased  with  the  number  of  layers  up  to  i6  layers,  and  that  above  that 
point  it  remained  constant,  whatever  the  number.  He  calculated  that 
the  thickness  of  the  i6  layers  was  0-04  of  a  millimetre.  With  reference 
to  metals,  gold  leaves  of  o-oo8, 0-004,  a-^d  0-002  of  a  millimetre  in  thickness, 
having  been  successively  applied  on  the  sides  of  a  cube  of  glass,  the  dimi- 
nution of  radiant  heat  was  the  same  in  each  case.  It  appears  therefore 
that,  between  certain  Hmits,  the  thickness  of  the  radiating  layer  of  metal 
is  without  influence. 

The  absorbing  power  varies  with  the  inclination  of  the  incident  rays. 
It  is  greatest  at  the  normal  incidence,  that  is,  at  right  angles ;  and  it  di- 
minishes in  proportion  as  the  incident  rays  deviate  from  the  normal. 
This  is  one  of  the  reasons  why  the  sun  is  hotter  in  summer  than  in  winter, 
because,  in  the  former  case,  the  solar  rays  are  less  oblique. 

The  radiating  power  of  gaseous  bodies  in  a  state  of  combustion  is  very 
weak,  as  is  seen  by  bringing  the  bulb  of  a  thermometer  near  a  hydrogen 
flame,  the  temperature  of  which  is  very  high.  But  if  a  platinum  spiral  be 
placed  in  this  flame,  it  assumes  the  temperature  of  the  flame,  and  radiates 
a  considerable  quantity  of  heat,, as  is  indicated  by  the  thermometer.  It  is 
for  an  analogous  reason  that  the  flames  of  oil  and  of  gas  lamps  radiate 
more  than  a  hydrogen  flame,  in  consequence  of  the  excess  of  carbon  which 
they  contain,  and  which,  not  being  entirely  burned,  becomes  incandescent 
in  the  flame. 

401.  Melloni's  researcbes  on  radiant  beat. — For  our  knowledge  of 
-the  phenomena  of  the  reflection,  emission,  and  absorption  of  heat  which 
have  up  to  now  been  described,  science  is  indebted  mainly  to  Leslie.  But 
since  his  time  the  discovery  of  other  and  far  more  delicate  modes  of  de- 


Fig.  307 


Fig.  309. 


Fig.  310. 


tecting  and  measuring  heat  has  not  only  extended  and  corrected  our  pre- 
vious knowledge,  but  has  lead  to  the  discovery  of  other  phenomena  of 
radiant  heat,  which  without  such  improved  means  must  have  remained 
unknown. 

This  advance  in  science  is  due  to  an  Italian  philosopher,  Melloni,  who 
first  applied  the  thermo-electric  pile,  invented  by  Nobili,  to  the  measure- 


-402]  Radiant  Heat.  337 

ment  of  very  small  differences  of  temperature  ;  a  method  of  which  a  pre- 
liminary account  has  already  been  given. 

In  his  experiments  Melloni  used  five  sources  of  heat — ist,  a  Locatelli's 
lamp— one,  that  is,  without  a  glass  chimney,  but  provided  with  a  reflector 
(fig.  307) ;  2nd,  an  Argand  lamp,  that  is,  one  with  a  chimney  and  a  double 
draught ;  3rd,  a  platinum  spiral,  kept  red  hot  by  a  spirit  lamp  (fig,  308)  ; 
4th,  a  blackened  copper  plate,  kept  at  a  temperature  of  about  400  degrees 
by  a  spirit  lamp  (fig.  309)  ;  5th,  a  copper  tube,  blackened  on  the  outside 
and  filled  with  water  at  100°  (fig.  310). 

402.  Bynamical  theory  of  Heat.— Before  describing  the  results  ar- 
rived at  by  Melloni  and  others,  it  will  be  convenient  to  explain  here  the 
view  now  generally  taken  as  to  the  mode  in  which  heat  is  propagated. 
For  additional  information  the  chapter  on  the  Mechanical  Theory  of  Heat 
and  the  book  on  Light  should  be  read.  According  to  what  has  been 
already  stated,  a  hot  body  is  nothing  more  than  one  whose  particles  are 
in  a  state  of  vibration.  The  higher  the  temperature  of  the  body  the  more 
rapid  are  these  vibrations,  and  a  diminution  in  temperature  is  but  a 
diminished  rapidity  of  vibration  of  the  particles.  The  propagation  of  heat 
through  a  bar  is  due  to  a  gradual  communication  of  this  vibratory  motion 
from  the  heated  part  to  the  rest  of  the  bar.  A  good  conductor  is  one  which 
readily  takes  up  and  transmits  the  vibratory  motion  from  particle  to 
particle,  while  a  bad  conductor  is  one  which  takes  up  and  transmits  the 
motion  with  difficulty.  But  even  through  a  good  conductor  the  propaga- 
tion of  this  motion  is  comparatively  slow  ;  how  then  are  we  to  explain  the 
instantaneous  perception  of  heat  experienced  when  a  screen  is  removed 
from  a  fire,  or  when  a  cloud  is  drifted  from  the  face  of  the  sun  ?  In  this 
case,  the  heat  passes  from  one  body  to  another  without  affecting  the  tem- 
perature of  the  medium  which  transmits  it.  In  order  to  explain  these 
phenomena,  it  is  imagined  that  all  space,  the  interplanetary  spaces  as  well 
as  the  interstices  in  the  hardest  crystal  or  the  heaviest  metal,  in  short, 
matter  of  any  kind,  is  permeated  by  a  medium  having  the  properties  of  a 
fluid  of  infinite  tenuity  called  ether.  The  particles  of  a  heated  body 
being  in  a  state  of  intensely  rapid  vibration,  communicate  their  motion  to 
the  ether  around  them,  throwing  it  into  a  system  of  waves  which  travel 
through  space  and  pass  from  one  body  to  another  with  the  velocity  of 
light.  When  the  undulations  of  the  ether  reach  a  given  body,  the  motion 
is  again  delivered  up  to  the  particles  of  that  body,  which  in  turn  begin  to 
vibrate,  that  is,  the  body  becomes  heated.  This  passage  of  motion 
through  the  hypothetical  ether  is  termed  radiation,  and  a  so-called  ray  of 
heat  is  merely  the  direction  of  the  motion  of  one  series  of  waves. 

It  will  facilitate  the  understanding  of  this  to  consider  the  analogous 
mode  in  which  sound  is  produced  and  propagated.  A  sounding  body  is 
one  whose  entire  mass  is  in  a  state  of  vibration  ;  the  more  rapid  the  rate 
of  vibration,  the  more  acute  the  sound  ?  the  slower  the  rate  of  vibration, 
the  deeper  the  sound.  This  vibratory  motion  is  communicated  to  the 
,  surrounding  air,  by  means  of  which  the  vibrations  reach  the  auditory 
nerve  and  there  produce  the  sensation  of  sound.  If  a  metal  ball  be  heated, 
say  to  the  temperature  of  boiling  water,  we  can  ascertain  that  it  radiates 

Q 


338  .     On  Heat.       '  [402- . 

heat,  although  we  cannot  see  any  luminosity ;  and  if  its  temperature  be 
gradually  raised,  we  see  it  become  successively  of  a  dull  red,  bright  red, 
and  dazzling  white.  Here  it  is  assumed  that  at  each  particular  temperature 
the  heated  body  emits  waves  of  a  definite  length  ;  in  other  words,  its  par-  • 
tides  vibrate  in  a  certain  period.  As  its  temperature  rises  it  sends  out 
other  and  more  rapid  undulations,  which  coexist  however  with  all  those- 
which  it  had  previously  emitted.  Thus  the  motion  at  each  successive 
temperature  is  compounded  of  all  preceding  ones. 

It  has  been  seen  that  vibrations  of  the  air  below  and  above  a  certain 
rate  do  not  affect  the  auditory  nerve  ;  it  can  only  take  up  and  transmit  to 
the  brain  vibrations  of  a  certain  periodicity.  So  too  with  the  vibrations 
Avhich  produce  heat.  The  optic  nerve  is  insensible  to  a  large  number  of 
wave  lengths.  It  can  apprehend  only  those  waves  that  form  the  visible 
spectrum.  If  the  rate  of  undulation  be  slower  than  the  red  or  faster 
than  the  violet,  though  intense  motion  may  pass  through  the  humours 
of  the  eye  and  fall  upon  the  retina,  yet  we  shall  be  utterly  unconscious 
of  the  fact,  for  the  optic  nerve  cannot  take  up  and  respond  to  the  rate  of 
vibrations  which  exist  beyond  the  visible  spectrum  in  both  directions. 
Hence  these  are  termed  invisible  or  obscure  rays.  A  vast  quantity  of 
these  obscure  rays  are  emitted  by  flames  which,  though  intensely  hot, 
are  yet  almost  non-luminous,  such  as  the  oxy-hydrogen  flame,  or  that  ot 
a  Bunsen's  burner  ;  for  the  vibrations  which  these  emit,  though  capable 
in  part  of  penetrating  the  media  of  the  eye,  are  incapable  of  exciting  in 
the  optic  nerve  the  sensation  of  light. 

403.  Tbernial  analysis  of  solar  Ugrbt. — When  a  solar  ray  (fig.  311), 
admitted  through  an  aperture  in  a  dark  room^  is  concentrated  on  a  prism 


of  rock  salt  by  means  of  a  lens  of  the  same  material,  and  then  after 
emerging  from  the  prism  is  received  on  a  screen,  it  will  be  found  to 
present  a  band  of  colours  in  the  following  order  :  red,  orange,  yellow 
green,  blue,  and  violet.     This  is  called  the  spectrum. 

If  now  a  narrow  and  delicate  thermo-pile  be  placed  successively  on  the 
space  occupied  by  each  of  the  colours,  it  will  be  scarcely  affected  on  the 
violet,  but  in  passing  over  the  other  colours  it  will  indicate  a  gradual 
i-ise  of  temperature,  which  is  greatest  at  the  red.     Painters  thus,  guided 


-104]  Radiant  Heat,       ^  339 

by  a  correct  but  unconscious  feeling,  always  speak  of  blue  and  green 
colours  as  cold,  and  of  red  and  orange  as  warm  tones.  If  the  pile  be  now 
moved  in  the  same  direction  beyond  the  limits  of  the  luminous  spectrum, 
the  temperature  will  gradually  rise  up  to  CP,  at  which  it  attains  its 
maximum.  From  this  point  the  pile  indicates  a  decrease  of  temperature 
until  it  reaches  a  point,  O,  where  it  ceases  to  be  affected.  This  point  is 
about  as  distant  from  R  as  the  latter  is  from  V  ;  that  is,  there  is  a  region 
in  which  thermal  effects  are  produced  extending  as  far  beyond  the  red 
end  of  the  spectrum  in  one  direction  as  the  entire  length  of  the  visible 
spectrum  is  in  the  other.  In  accordance  with  what  we  have  stated,  the 
sun's  light  consists  of  rays  of  different  rates  of  vibration  ;  by  their  pas- 
sage through  the  prism  they  are  unequally  broken  or  refracted  ;  those  of 
greatest  wave  length  or  slowest  vibrating  period  are  least  bent  aside,  or 
are  said  to  be  the  least  refrangible,  while  those  with  shorter  wave  lengths 
are  the  most  refrangible. 

These  non-luminous  rays  outside  the  red  are  called  the  extra  or  ultra- 
red  rays,  or  sometimes  the  Herschelian  rays,  from  Sir  W.  Herschel,  who 
first  discovered  their  existence. 

If  in  the  above  case  prisms  of  other  materials  than  rock  salt  be  used,' 
the  position  of  maximum  heat  will  be  found  to  vary  with  the  nature  of 
the  prism,  a  fact  first  noticed  by  Seebeck.  Thus  with  a  prism  of  water 
it  is  in  the  yellow ;  with  one  of  crown  glass,  in  the  middle  of  the  red,  and 
so  on.  These  changes  are  due,  as  Melloni  subsequently  found,  to  the 
circumstance  that  prisms  of  different  materials  absorb  rays  of  different 
refrangibility  to  unequal  extents.  But  rock  salt  practically  allows  heats 
of  all  kinds  to  pass  with  equal  facility,  and  thus  gives  a  normal  spectrum. 

404.  Tyndall's  researcbes. — Tyndall  has  recently  investigated 
the  spectrum  produced  by  the  electric  light,  and  has  arrived  at  some 
highly  important  results.  His  mode  of  experimenting  was  as  follows  : — 
The  electric  light  was  produced  between  charcoal  points  by  a  Grove's 
battery  of  fifty  cells.  The  beam,  rendered  parallel  by  a  double  rock  salt 
lens,  was  caused  to  pass  through  a  narrow  slit,  and  then  through  a  second 
lens  of  rock  salt  ;  the  slices  of  white  light  thus  obtained  being  decomposed 
by  a  prism  of  the  same  material.  To  investigate  the  thermal  conditions 
of  the  spectrum  a  linear  thermo-electric  pile  was  used  ;  that  is,  one  con- 
sisting of  a  number  of  elements  arranged  in  a  Hne,  and  in  front  of  which 
was  a  slit  that  could  be  narrowed  to  any  extent.  The  instrument  was 
mounted  on  a  movable  bar  connected  with  a  fine  screw,  so  that  by 
turning  a  handle  the  pile  could  be  pushed  forward  through  the  smallest 
space.  On  placing  this  apparatus,  originally  devised  by  Melloni  for  his 
researches  on  the  solar  spectrum,  successively  in  each  part  of  the  spectrum 
of  the  electric  light,  the  heating  effected  at  various  points  near  each 
other  was  determined  by  the  indications  of  a  very  delicate  galvanometer. 
As  in  the  case  of  the  solar  spectrum,  the  heating  effect  gradually  in- 
creased from  the  violet  end  towards  the  red,  and  was  greatest  in  the  dark 
space  beyond  the  red.  The  position  of  the  greatest  heat  was  about  as 
far  from  the  limit  of  the  visible  red  as  the  latter  was  from  the  green,  and 

Q2 


340 


On  Heat. 


[404- 


the  total  extent  of  the  invisible  spectrum  was  found  to  be  twice  that  of 
the  visible. 

The  increase  of  temperature  in  the  dark  space  is  very  considerable. 
If  thermal  intensities  are  represented  by  perpendicular  lines  of  propor- 
tionate length,  erected  at  those  parts  of  the  spectrum  to  which  they 
correspond,  on  passing  beyond  the  red  end  these  lines  increase  rapidly* 
and  greatly  in  length,  reach  a  maximum,  and  then  fall  somewhat  more 
suddenly.  If  these  Hnes  are  connected,  they  form  a  curve  (fig.  312), 
which  beyond  the  red  represents  a  massive  peak,  which  quite  dwarfs  by 
its  magnitude  that  of  the  visible  spectrum.     In  fig.   313  the  dark  parts  at 


9 

C 

/ 

/N^ 

1 

HI^HHlM 

V   ^-      8.     y       0. 

1 

^ 

Fig.  i 

2. 

the  end  represent  the  obscure  radiation.  The  curve  is  based  in  the  manner 
above  stated,  on  the  results  obtained  by  Tyndall  with  the  electric  light. 
The  upper  curve  in  fig.  313,  represents  the  spectrum  of  solar  light  from 


the  experiments  of  Miiller  with  a  rock  salt  prism,  while  the  lower  curve 
represents  the  results  obtained  with  the  use  of  a  flint  glass  prism,  which 
is  thus  seen  to  absorb  some  of  the  ultra-red  radiation. 

Tyndall  found   that   by  interposing  various  substances,  more  espe- 
cially water,  in  certain  thicknesses,  in  the  path  of  the  electric  light,  the 


-405]  Radiant  Heat.      "JVt*^  )  1  m  ^  »'?^ '. 34 1 

ultra-red  radiation  was  greatly  diminished,  the  peak  was  not  so  lofty. 
Now  aqueous  vapour  would,  like  water,  absorb  the  obscuie  rays.  And-- 
most  probably  the  reason  why  the  obscure  part  of  the  spectrum  of  the 
solar  light  is  not  so  intense  as  in  the  case  of  the  electric  light,  is  that  the 
obscure  rays  have  been  already  partially  absorbed  by  the  aqueous  vapour 
of  the  atmosphere.  If  a  solar  spectrum  could  be  produced  outside  the 
atmosphere,  it  doubtless  would  give  a  spectrum  more  like  that  of  the 
electric  light,  which  is  uninfluenced  by  the  atmospheric  absorption. 

This  has  been  remarkably  confirmed  in  other  ways.  Melloni  observed 
that  the  position  of  the  maximum  in  the  solar  spectrum  differs  on  differ- 
ent days  ;  which  is  probably  due  to  the  varying  absorption  of  the  atmo- 
sphere, in  consequence  of  its  varying  hygrometric  state.  Recently, 
Secchi,  in  Rome,  has  found  the  same  shifting  of  the  maximum  to  occuf 
in  the  different  seasons  of  the  year  ;  for  in  winter,  when  there  is  least 
moisture  in  the  atmosphere,  the  maximum  is  farther  from  the  red  than 
in  summer,  when  the  aqueous  vapour  in  the  air  is  most  abundant.  An 
important  observation  on  the  luminous  rays  has  also  been  made  by  Cooke, 
in  America,  who  found  that  the  faint  black  Hnes  in  the  solar  spectrum 
attributed  to  the  absorption  of  light  by  our  atmosphere  (see  book  on 
Optics)  are  chiefly  caused  by  the  presence  of  aqueous  vapour, 

405.  Ituminous  and  obscure  radiation. — It  has  been  stated  that 
the  radiation  from  a  luminous  object,  a  gas  flame  for  example,  is  of 
a  composite  character ;  a  portion  consists  of  what  we  term  light,  but 
a  far  greater  part  consists  of  heat  rays,  which  are  insensible  to  our 
eyes,  being  unable  to  affect  the  optic  nerve.  When  this  mixed  radiatfon 
falls  upon  the  blackened  face  of  a  thermo-electric  pile,  the  whole  of  it 
is  taken  to  be  absorbed,  the  light  by  this  act  being  converted  into  heat, 
and  affecting  the  instrument  proportionally  with  the  purely  calorific  rays. 
The  total  radiation  of  a  luminous  source,  expressed  in  units  of  heat  or 
force,  can  thus  be  measured.  By  introducing  into  the  path  of  the  rays 
a  body  capable  of  stopping  either  the  luminous  or  the  obscure  radiation 
we  can  ascertain  by  the  comparative  action  on  the  pile  the  -relative 
quantities  of  heat  and  light  radiated  from  the  source.  Melloni  sought 
to  do  this  by  passing  a  luminous  beam  through  a  layer  of  water  con- 
taining alum  in  solution ;  a  liquid  which  he  found  in  previous  experi- 
ments absorbed  all  the  radiation  from  bodies  heated  under  incandescence. 
Comparing  the  transmission  through  this  liquid^— which  allowed  the 
luminous  part  of  the  beam  to  pass,  but  quenched  the  obscure  portion — 
with  the  transmission  through  a  plate  of  rock  salt — which  affected 
neither  the  luminous  nor  the  obscure  radiation,  but  gave  the  loss  due  to 
reflection — Melloni  revealed  the  astonishing  fact  that  90  per  cent,  of  the 
radiation  from  an  oil  flame  and  99  per  cent,  of  the  radiation  from  an 
alcohol  flame  consist  of  invisible  calorific  rays.  This  proportion  has  been 
still  further  increased  by  the  recent  experiments  of  Tyndall,  who  em- 
ployed a  liquid  free  from  the  objections  which  have  caused  a  shght 
error  in  Melloni's  method.  Tyndall  discovered  that  iodine,  whilst 
opaque  to  light,  is  transparent  to  the  obscure  heat  rays.  Dissolving  this 
substance  in   bisulphide  of  carbon,  a  solution  was  obtained  which  was 


342  On  Heat,  [405- 

impervioiis  to  the  most  intense  light,  but  wonderfully  pervious  to  radiant 
heat  ;  only  a  slight  absorption  being  effected  by  the  bisulphide.  By 
successively  comparing  the  transmission  through  the  transparent  liquid, 
and  the  transmission  through  the  same  liquid  rendered  opaque  by  iodine, 
the  value  of  the  luminous  radiation  from  various  sources  was  found  to  be 
as  follows  : — 


Source 

Luminous 

Obscure' 

Red-hot  spiral 

O 

lOO 

Hydrogen  flame  . 

o 

lOO 

Oil  flame     .         .         •         . 

3 

97 

Gas  flame    .... 

4 

96 

White-hot  spiral , 

.        .      .    4-6 

95*4 

Electric  light 

lO 

90 

Here  by  direct  experiment  the  ratio  of  luniinous  to  obscure  rays  in 
the  electric  light  is  found  to  be  10  per  cent,  of  the  total  radiation.  By 
prismatic  analysis,  the  curve  shown  in  fig.  312  was  obtained,  graphi- 
cally representing  the  proportion  of  luminous  to  obscure  rays  in  the 
electric  light ;  by  calculating  the  areas  of  the  two  spaces  in  the  dia- 
gram, the  obscure  portion  is  found  to  be  nearly  10  times  as  large  as  the 
luminous. 

406.  Transmutation  of  obscure  rays. — We  shall  find,  in  speaking  of 
the  luminous  spectrum,  that  beyond  the  violet  there  are  rays  which  are 
invisible  to  the  eye,  but  which  are  distinguished  by  their  chemical  action, 
and  are  spoken  of  as  the  actinic  or  chemical  rays  ;  they  are  also  known  as 
the  Ritteric  rays,  from  the  philosopher  who  first  discovered  their  existence. 

As  we  shall  also  see  in  the  book  on  Optics,  Stokes  has  succeeded  in 
converting  these  rays  into  rays  of  lower  refrangibility,  which  then  become 
visible  ;  so  Tyndall  has  recently  effected  the  corresponding  but  inverse 
change,  and  has  increased  the  refrangibility  of  the  Herschelian  or  extra 
red  rays,  and  thus  rendered  them  visible.  V 

Tyndall  worked  with  the  electric  light.  The  chkrcoal  points  were 
placed  in  front  of  a  concave  silvered  glass  mirror  in  such  a  manner  that 
the  rays  from  the  points  after  reflection  were  concentrated  to  a  focus 
about  6  inches  distant.  On  the  path  of  the  beam  was  interposed  a  cell 
full  of  a  solution  of  iodine  in  bisulphide  of  carbon,  which,  as  we  have 
seen,  has  the  power  of  completely  stopping  all  luminous  radiation,  but 
gives  free  passage  to  the  non-luminous  rays.  On  now  placing  in  the 
focus  of  the  beam  thus  sifted  a  piece  of  platinum,  this  was  raised  to 
incandescence  by  the  impact  of  perfectly  invisible  rays.  In  like  manner 
a  piece  of  charcoal  in  vacuo  was  heated  to  redness. 

By  a  proper  arrangement  of  the  charcoal  points  a  metal  may  be  raised 
to  whiteness,  and  the  light  now  emitted  by  the  metal  yields  on  prismatic 
analysis  a  brilliant  luminous  spectrum,  which  is  thus  entirely  derived  from 
the  invisible  rays  beyond  the  red. 

To  the  new  phenomena  here  described,  this  transmutation  of  non- 
luminous  into  luminous  heat,  Tyndall  has  applied  the  term  calorescence. 

When  the  eye  was  cautiously  placed  in  the  focus,  guarded  by  a  small 


407] 


Radiant  Heat. 


343 


hole  being  pierced  in  a  metal  screen,  so  that  the  converged  rays  should 
only  enter  the  pupil  and  not  affect  the  surrounding  part  of  the  eye,  no 
impression  of  light  was  produced,  and  there  was  scarcely  any  sensation 
of  heat.  A  considerable  portion  was  absorbed  by  the  humours  of  the 
eye,  but  yet  a  powerful  beam  undoubtedly  reached  the  retina  ;  for,  as 
Tyndal  showed  by  a  separate  experiment,  about  i8  per  cent,  of  the 
obscure  radiation  from  the  electric  light  passed  through  the  humours  of 
an  ox's  eye. 

407.  Transmutation  of  tliermal  rays. — Melloni  was  the  first  who 
examined  extensively  and  accurately  the  absorption  of  heat  by  solids 
and  Hquids.  The  apparatus  he  employed  is  represented  in  the  annexed 
figure  (314),  where  A  B  is  the  thermo-electric  pile ;  ^  is  a  support  for  the 


Fig.  314. 

source  of  heat,  in  this  case  a  Locatelli's  lamp  ;  F  and  E  are  screens,  and 
C  is  a  support  for  the  body  experimented  upon  ;  while  in  is  the  pile,  and 
D  the  galvanometer. 

The  various  sources  of  heat  used  by  Melloni  in  his  experiments  have 
been  already  (401)  enumerated. 

To  express  the  power  which  bodies  have  of  transmitting  heat,  Melloni 
used  the  term  diathermancy  :  diathermancy  bears  the  same  relation  to 
radiant  heat  that  transparency  does  to  light ;  and  in  like  manner  the 
power  of  stopping  radiant  heat  is  called  athermancy^  which  thus  corre- 
sponds to  opacity  for  light.  In  experimenting  on  the  diathermancy  of 
liquids,  Melloni  used  glass  troughs  with  parallel  sides,  the  thickness  of 
the  liquid  layer  being  0-3^  in.  The  radiant  heat  of  an  Argand  lamp  with 
a  glass  chimney  was  first  allowed  to  fall  directly  on  the  face  of  the  pile, 
and  the  deflection  produced  in  the  galvanometer  taken  as  the  total  radia- 
tion ;  the  substance  under  examination  was  then  interposed,  and  the 
deflection  noted.  This  corresponded  to  the  quantity  of  heat  transmitted 
by  the  substance.  If  /  indicate  this  latter  number,  and  t'  the  total  radia- 
tion, then 

f  :  / ::  100  :  .r, 


344  On  Heat.  [407- 

which  is  the  percentage  of  rays   transmitted.     Thus,  calhng  the  total 
radiation  loo,  Melloni  found  that 


Bisulphide  of  carbon  transmitted 
Olive  oil  „ 

Ether  „ 

Sulphuric  acid  „ 

Alcohol  „ 

Solution  of  alum  or  sugar  „ 
Distilled  water  „ 


63 

21 
17 
15 
12 


In  experimenting  with  solids  the  substances  were  cut  into  plates  ot 
inch  in  thickness,  and  it  was  found  that  of  every  100  rays  there  was 
transmitted  by 


Rock  salt         .... 

92 

Selenite   .         .         .         . 

.     20 

Iceland  spar  and  plate  glass   . 

62 

Alum        .         .         .         . 

.     12 

Smoky  quartz  .... 

67 

Sulphate  of  copper  . 

0 

Transparent  carbonate  of  lead 

52 

The  transmission  of  heat  through  hquids  has  been  re-examined  by 
Tyndall  in  the  following  way  : — Instead  of  employing  a  glass  vessel  to 
hold  the  liquids  under  examination,  he  made^  use  of  a  little  cell  whose 
ends  were  stopped  by  parallel  plates  of  rock  salt.  The  plates  were 
separated  by  a  ring  of  brass,  with  an  aperture  on  the  top  through  which 
the  li6[uid  could  be  poured.  As  this  plate  could  be  changed  at  will, 
liquid  layers  of  various  thicknesses  were  easily  obtainable,  the  apparatus 
being  merely  screwed  together  and  made  hquid  tight  by  paper  washers. 
The  instrument  was  mounted  on  a  support  before  an  opening  in  a  brass 
screen  placed  in  front  of  the  pile.  The  source  of  heat  employed  was  a 
spiral  of  platinum  wire  raised  to  incandescence  by  an  electric  current  ; 
the  spiral  being  enclosed  in  a  small  glass  grSbe  with  an  aperture  in  front 
Lthrough  which  the  radiation  passed  unchanged  in  its  character,  a  point  of 
essential  importance  overlooked  by  Melloni.  The  table  at  top  of  p.  345 
contains  the  results  of  experiments  made  with  liquids  in  the  various 
thicknesses  indicated,  the  numbers  expressing  the  absorption  per  cent,  of 
the  total  radiation.  The  transjnission  per  cent,  can  be  found  in  each 
case  by  subtracting  the  absorption  from  100.  Thus  a  layer  of  water  0*2 
inch  thick  absorbs  807  and  transmits  19-3  per  cent,  of  the  radiation  from 
a  red  hot  spiral. 

It  appears  from  these  tables,  that  there  is  no  connection  between  dia- 
thermancy and  transparency.  The  liquids,  except  olive  oil,  are  all  colour- 
less and  transparent,  and  yet  vary  as  much  as  75  per  cent,  in  the  amount 
of  heat  transmitted.  Among  the  solids,  smoky  quartz,  which  is  nearly 
opaque  to  hght,  transmits  heat  very  well ;  while  alum,  which  is  perfectly 
transparent,  cuts  off  88  per  cent,  of  heat  rays.  As  there  are  different 
degrees  of  transparency,  so  there  are  different  degrees  of  diathermancy  ; 
and  the  one  cannot  be  predicated  from  the  other. 

By  studying  the  transmission  of  heat  from  different  parts  of  the  spec- 
trum separately,  the  connection  between  light  and  heat  becomes  manifest. 
With  this  view  Masson  and  Jamin  received  the  spectrum  of  the  solar 


-408] 


Radiant  Heat. 


345 


Absorption  of  heat  by  liquids. 

i 

Liquid 

Thickness  of  liquid  in  parts  of  an  inch 

0'02 

0*04 

0*07 

0-14 

0-27 

Bisulphide  of  carbon  . 

S'S 

8-4 

12-5 

15-2 

17-3 

1  C  hloroform 

1 6-6 

25-0 

ZS'^ 

40*0 

44-8 

1  I  odide  of  methyl 

36-1 

46-5 

sy^ 

65-2 

68-6 

1  I  odide  of  ethyl 

38-2 

507 

59-0 

69-0 

7VS 

Benzole 

43*4 

557 

62-5 

71-5 

ly^ 

Amylene 

58-3 

65-2 

73-6 

777 

82-3 

Ether  . 

63-3 

7ys 

76-1 

78-6 

85-2 

Acetic  ether 

74'o 

78-0 

82-0 

86-1 

Formic  ether 

65-2 

76-3 

79-0 

84-0 

87-0 

Alcohol 

67-3 

78-6 

83-6 

85-3 

89-1 

Water  . 

807 

86-1 

88-8 

91-0 

91-0 

i:~-Lx      : 1-  .           _  • 

r 

1       li 

_      T-1 

; J     J        •,! 

light  given  by  a  prism  of  rock  salt  on  a  movable  screen  provided  with 
an  aperture,  so  that  by  raising  or  lowering  the  screen  the  action  of  any 
given  part  of  the  spectrum  on  different  plates  could  be  investigated.  They 
thus  found — 

That  glass,  rock  crystal,  ice,  and  generally  substances  transparent  for 
light,  are  also  diathermanous  for  all  kinds  of  luminous  heat ; 

That  a  coloured  glass,  red,  for  instance,  which  only  transmits  the  red 
rays  of  the  spectrum,  and  extinguishes  the  others,  also  extinguishes  every 
kind  of  luminous  heat,  excepting  that  of  the  red  rays  ; 

That  glass  and  rock  crystal,  which  are  diathermanous  for  luminous 
heat,  also  transmit  the  obscure  heat  near  the  red,  that  is,  the  most  re- 
frangible, but  extinguish  the  extreme  obscure  rays,  or  those  which  are  the 
least  deflected  by  the  prism.  * 

Alum  extinguishes  a  still  greater  proportion  of  the  obscure  spectrum, 
and  ice  stops  it  altogether. 

408.  Influence  of  the  nature  of  the  heat. — The  diathermanous  power 
differs  greatly  with  the  heat  from  different  sources,  as  Melloni  made 
evident  from  the  following  table,  in  which  the  numbers  express  what  pro- 
portion of  every  100  rays  from  the  different  sources  of  heat  incident 
on  the  plates  is  transmitted  : — 


Locatelli's 
lamp 

Incandescent 
platinum  wire 

Copper  at  400° 

Copper  at  100° 

Rock  salt     . 

92 

92 

92 

92 

Fluor  spar   . 

J 

78 

69 

42 

Zl 

Plate  glass  . 

39 

24 

6 

0 

Black  glass .   . 

26 

55 

12 

0 

Selenite 

14 

5 

0 

0 

Alum   . 

2 

0 

0 

Ice       . 

.     ^ 

o'S 

0 

0 

Q3 


346 


On  Heat. 


[408 


These  different  sources  of  heat  correspond  to  light  from  different  sources. 
Rock  salt  is  here  stated  to  transmit  all  kinds  of  heat  with  equal  facility, 
and  to  be  the  only  substance  which  does  so.  It  is  analogous  to  white 
glass,  which  is  transparent  for  light  from  all  sources.  Fluor  spar  trans- 
mits 78  per  cent,  of  the  rays  from  a  lamp,  but  only  33  of  those  from  a 
blackened  surface  at  100°.  A  piece  of  plate  glass  only  one-tenth  of  an 
inch  thick,  and  perfectly  transparent  to  light,  is  opaque  to  all  the  radiation 
from  a  source  of  100°,  transmits  only  6  per  cent,  of  the  heat  from  a  source 
at  400°,  and  but  39  of  the  radiation  from  the  lamp.  Black  glass,  on  the 
contrary,  though  it  cuts  off  all  heat  from  a  source  at  100°,  allows  12  per 
cent,  of  the  heat  at  400°  to  pass,  and  is  equally  transparent  to  the  heat 
from  the  spiral,  but  on  account  of  its  blackness  is  more  opaque  to  the  heat 
from  the  lamp.  As  we  have  already  seen,  every  luminous  ray  is  a  heat 
ray  ;  now  as  several  of  the  substances  in  this  table  are  pervious  to  all  the 
luminous  rays,  and  yet,  as  in  the  case  of  ice,  transmit  about  6  per  cent,  of 
luminous  heat,  we  have  an  apparent  anomaly  ;  which,  however,  is  only  a 
confirmation  of  the  remarkably  small  proportion  which  the  luminous  rays 
of  a  lamp  bear  to  the  obscure. 

From  these  experiments  Melloni  concluded  that  as  the  temperature 
of  the  source  rose,  more  heat  was  transmitted.  This  may  be  taken  as 
a  general  law,  which  has  been  recently  confirmed  by  some  refined  ex- 
periments of  Tyndall.  The  platinum  lamp,  previously  described,  was 
used  as  the  source,  the  temperature  of  which  Tyndall  was  enabled 
to  vary  from  a  dark  to  a  brilliant  white  heat,  without  disturbing  in  any 
way  the  position  of  the  apparatus  ;  the  gradations  of  temperature  being 
obtained  by  a  gradual  augmentation  of  the  strength  of  the  electric  current 
which  heated  the  platinum  spiral.  Instead  of  liquids,  vapours  were 
chosen  as  the  subject  of  experiment,  and  examined  in  a  manner  to  be 
described  subsequently  ;  the  measurements  are  given  in  the  following 
itable  :— 

Absorption  of  heat  by  vapour's. 


Name  of  vapour 

1 

1 

Source,  platinum  spiral 

Barely  visible 

Bright  red 

White  hot 

Near  fusion 

Bisulphide  of  carbon 
Chloroform 
Iodide  of  methyl 
Iodide  of  ethyl 
!  Benzole    .... 
Amylene  .... 
Ether       .         . 
Formic  ether   . 
Acetic  ether     . 

6-5 
9-1 

12-5 
2T-3 

1       26-4 
35-8 
43-4 
45-2 
49-6 

47 
6-3 
9-6 

177 

20'6 

27-5 

3'-4 
31-9 
34-6 

2-9 
5-6 
7-8 

12-8 

16-5 
227 
25-9 
25-1 

27-2 

2-5 
3'9 

i 

237 
21-3 

The  percentage  of  rays  absorbed  is  here  seen  to  diminish  in  each  case 
as  the  temperature  of  the  source  rises.     M-ere  elevation  of  temperature 


-409]  Radiant  Heat.  347 

does  not,  however,  invariably  produce  a  high  penetrative  power  in  the 
rays  emitted  ;  for  Tyndall  has  shown  that  the  rays  from  sources  of 
far  higher  temperature  than  any  of  the  foregoing  are  more  largely  ab- 
sorbed by  certain  substances  than  are  the  rays  emitted  from  any  one  of 
the  sources  as  yet  mentioned.  Thus  it  was  found  that  the  radiation  from 
a  hydrogen  flame  was  completely  intercepted  by  a  layer  of  water  only  0*27 
of  an  inch  thick,  the  same  layer  transmitting  9  per  cent,  of  the  radiation 
from  the  red-hot  spiral,  a  source  of  much  lower  temperature.  The  expla- 
nation of  this  is,  that  those  rays  which  heated  water  emits  (and  water,  the 
product  of  combustion,  is  the  main  radiant  in  a  hydrogen  flame)  are  the 
very  ones  which  this  substance  most  largely  absorbs.  This  statement, 
which  will  become  clearer  after  reading  the  analogous  phenomena  m  the 
case  of  light,  was  strikingly  exemplified  by  the  powerful  absorption  of  the 
heat  from  a  carbonic  oxide  flame  by  carbonic  acid  gas.  It  will  be  seen 
presently  (411)  that  of  the  rays  from  a  heated  plate  of  copper  olefiant  gas 
absorbs  10  times  the  quantity  intercepted  by  carbonic  acid,  whilst  of  the 
rays  from  a  carbonic  oxide  flame  Tyndall  found  carbonic  acid  ab- 
sorbed twice  as  much  as  olefiant  gas.  A  tenth  of  an  atmosphere  of  carbonic 
acid  enclosed  in  a  tube  4  feet  long,  absorbs  60  per  cent,  of  the  radiation 
from  a  carbonic  oxide  flame.  Radiant  heat  of  this  character  can  thus  be 
used  as  a  delicate  test  for  the  presence  of  carbonic  acid,  the  amount  of 
which  can  even  be  accurately  measured  by  the  same  means.  This  has 
been  done  by  Prof  Barrett,  who,  in  this  way,  has  made  ?i  physical  analysis 
of  the  human  breath.  In  one  experiment  the  quantity  of  carbonic  acid 
contained  in  breath  physically  analysed  was  found  to  be  4"56  per  cent., 
whilst  the  same  breath  chemically  analysed  gave  4*66,  a  difference  of 
only  one-tenth  per  cent, 

409.  influence  of  tbe  tbickness  and  nature  of  screens.— It  will  be 
seen  from  the  table  (408)  that  of  every  100  rays  rock  salt  transmits  92. 
The  other  8  may  either  have  been  absorbed  or  reflected  from  the  surface 
of  the  plate.  According  to  Melloni,  the  latter  is  the  case  ;  for  if,  instead 
of  on  one  plate,  heat  be  allowed  to  fall  on  two  or  more  plates  whose  total 
thickness  does  not  exceed  that  of  the  one,  the  quantity  of  heat  arrested 
will  be  proportional  to  the  number  of  reflecting  surfaces.  He  therefore 
concluded  rock  salt  to  be  quite  diathermanous. 

The  experiments  of  MM.  Provostaye  and  Desains,  of  Balfour 
Stewart,  and  those  of  Tyndall,  show  that  this  conclusion  is  not 
strictly  correct ;  rock  salt  does  absorb  a  very  small  proportion  of  obscure 
rays. 

The  quantity  of  heat  transmitted  through  rock  salt  is  practically  the 
same,  whether  the  plate  be  i,  2,  or  4  millimetres  thick.  But  with  other 
bodies  absorption  increases  with  the  thickness,  although  by  no  means  in 
direct  proportion.  This  is  seen  to  be  the  case  in  the  table  of  absorption 
by  liquids  at  different  thicknesses.  The  following  table  tells  what  pro- 
portion of  1,000  rays  from  a  Locatelli's  lamp  pass  through  a  glass  plate 
of  the  given  thickness  : — 

Thickness  in  millimetres     .0-512345678 

Rays  transmitted        .         .  775  733  682  653  634  620  609. 600  592  , 


348  On  Heat.  [409- 

The  absorption  takes  place  in  the  first  layers  ;  the  rays  which  have 
passed  these  possess  the  property  of  passing  through  other  layers  in  a 
higher  degree,  so  that  beyond  the  first  layers  the  heat  transmitted  ap- 
proaches a  certain  constant  value.  If  a  thin  glass  plate  be  placed 
behind  another  glass  plate  a  centimetre  thick,  the  former  diminishes 
the  transmission  by  little  more  than  the  reflection  from  its  surface.  But 
if  a  plate  of  alum  were  placed  behind  the  glass  plate,  the  result  would  be 
different,  for  the  latter  is  opaque  for  much  of  the  heat  transmitted  by 
glass. 

Heat,  therefore,  which  has  traversed  a  glass  plate  traverses  another 
plate  of  the  same  material  with  very  slight  loss,  but  is  very  greatly 
diminished  by  a  plate  of  alum.  Of  loo  rays  which  had  passed  through 
green  glass  or  tourmaline,  only  5  and  7  were  respectively  transmitted  by 
the  same  plate  of  alum.  A  plate  of  blackened  rock  salt  only  transmits 
obscure  rays,  while  alum  extinguishes  them.  Consequently,  when  these 
two  substances  are  superposed,  a  system  impervious  to  light  and  heat  is 
obtained. 

These  phenomena  find  their  exact  analogies  in  the  case  of  light.  The 
different  sources  of  heat  correspond  to  flames  of  different  colours,  and  the 
various  screens  to  glasses  of  different  colours.  A  red  flame  looked  at 
through  a  red  glass  appears  quite  bright,  but  through  a  green  glass  it 
appears  dim  or  is  scarcely  visible.  So  in  like  manner  heat  which  has 
traversed  a  red  glass  passes  through  another  red  glass  with  little  diminu- 
tion, but  it  is  almost  completely  stopped  by  a  green  glass.  Rock  salt  at 
150°  emits  only  one  kind  of  heat;  it  is  monothermal  just  as  sodium 
vapour  is  monochromatic. 

Different  luminous  rays  being  distinguished  by  their  colours,  to  these 
different  obscure  calorific  rays  Melloni  gave  the  name  of  therniocrose  or 
heat  colouration.  The  invisible  portion  of  the  spectrum  is  accordingly 
mapped  out  into  a  series  of  spaces,  each  possessing  its  own  peculiar 
feature,  corresponding  to  the  coloured  spaces  which  are  seen  in  that 
portion  of  the  spectrum  visible  to  our  eyes. 

Besides  thickness  and  colour,  the  polish  of  a  substance  influences  the 
transmission.  Glass  plates  of  the  same  size  and  thickness  transmit  more 
heat  as  their  surface  is  more  polished.  Bodies  which  transmit  heat  of 
any  kind  very  readily  are  not  heated.  Thus  a  window  pane  is  not  much 
heated  by  the  strongest  sun's  heat ;  but  a  glass  screen  held  before  a 
common  fire  stops  most  of  the  heat,  and  is  itself  heated  thereby.  The 
reason  of  this  is  that  by  far  the  greater  part  of  the  heat  from  a  fire  is 
obscure,  and  to  this  kind  of  heat  glass  is  opaque. 

410.  Diffusion  of  beat. — When  a  ray  of  light  falls  upon  an  unpolished 
surface  in  a  definite  direction,  it  is  decomposed  into  a  variety  Of  rays 
which  are  reflected  from  the  surface  in  all  directions.  This  irregular  re- 
flection is  called  diffusion,  and  it  is  in  virtue  of  it  that  bodies  are  visible 
when  light  falls  upon  them.  A  further  peculiarity  is,  that  all  solar  rays 
are  not  equally  diffused  from  the  surface  of  bodies.  Certain  bodies  diffuse 
certain  rays  and  absorb  others,  and  accordingly  appear  coloured.  The 
red  colour  of  a  geranium  is  caused  by  its  absorbing  all  the  rays,  excepting 


-411]  Radiant  Heat.  349 

the  red,  which  are  irregularly  reflected.  Just  as  is  the  case  with  trans- 
•mitted  light  in  transparent  bodies,  so  with  diffused  light  in  opaque  ones, 
for  if  a  red  body  is  illuminated  by  red  light  it  appears  of  a  bright  red 
colour,  but  if  green  light  fall  upon  it  it  is  almost  black.  We  shall  now 
see  that  here  again  analogous  phenomena  prevail  with  heat. 

Various  substances  diffuse  different  thermal  rays  to  a  different  extent ; 
each  possesses  a  peculiar  thermocrose  or  heat  tint.  Melloni  placed  a 
number  of  strips  of  brass  foil  between  the  source  of  heat  and  the  thermo- 
pile. They  were  coated  on  the  side  opposite  to  the  pile  with  lampblack, 
and  on  the  other  side  with  the  substances  to  be  investigated.  Represent- 
ing the  quantity  of  heat  absorbed  by  the  lampblack  at  100,  the  absorption 
of  the  other  bodies  was  as  follows  : — 


Incandescent 

Copper 

Copper 

platinum 

at  400° 

at  100° 

Lampblack 

.       100 

100 

\oo 

White  lead 

.            -          56 

89 

100 

Isinglass 

.       54 

64 

91 

Indian  ink 

•      95 

87 

85 

Shellac  . 

.      47 

70 

72 

PoHshed  meta 

1       .        .     13-5 

13 

13 

Hence,  white  lead  absorbs  far  less  of  the  heat  radiated  from  incan- 
descent platinum  than  lampblack,  but  it  absorbs  the  obscure  rays  from 
copper  at  100°  as  completely  as  lampblack.  Indian  ink  is  the  reverse  of 
this  ;  it  absorbs  obscure  rays  less  completely  than  luminous  rays.  Lamp- 
black absorbed  the  heat  from  all  sources  in  equal  quantities,  and  very 
nearly  completely.  In  consequence  of  this  property  all  thermoscopes 
which  are  used  for  investigating  radiant  heat  are  covered  with  lamp- 
black, as  it  is  the  best  known  absorbent  of  heat.  The  behaviour  of  metals 
is  the  reverse  of  that  of  lampblack.  They  reflect  the  heat  of  different 
sources  in  che  same  degree.  They  are  to  heat  what  white  bodies  are  to 
light. 

As  coloured  light  is  altered  by  diffusion  from  several  bodies,  so  Knob- 
lauch has  shown  that  the  different  kinds  of  heat  are  altered  by  reflection 
from  different  surfaces.  The  heat  of  an  Argand  lamp  diffused  from 
white  paper  passes  more  easily  through  calcspar  than  when  it  has  been 
diffused  from  black  paper. 

The  rays  of  heat,  like  the  rays  of  light,  are  susceptible  of  polarisation 
and  double  refraction.  These  properties  will  be  better  understood  after 
treating  of  light. 

411.  Relation  of  g:a8es  and  vapours  to  radiant  heat. — For  a  long 
time  it  was  believed  that  gaseous  bodies  were  as  permeable  to  heat  as  a 
vacuum  ;  and  though  subsequently  this  was  disproved,  yet  down  to  a 
recent  period  it  was  thought  that  whatever  absorption  such  bodies  might 
exercise  was  slight  and  similar  in  degree.  The  whole  subject  has,  how- 
ever, been  investigated  by  Tyndall  in  a  series  of  laborious  experiments, 
the  apparatus  used  in  which  is  represented,  in  its  essential  features,  in 
the  adjacent  figure  ;  the  arrangement  being  looked  upon  from  above, 

A  is  a  cylinder  about  4  feet  in  length  and  2^  inches  in  diameter,  placed 


350  On  Heat.  [411- 

horizontally,  the  ends  of  which  can  be  closed  with  rock  salt  plates  :  by 
means  of  a  lateral  tube  at  r  it  can  be  connected  with  an  air  pump  and 
exhausted  ;  while  at  /  is  another  tube  which  serves  for  the  introduction  of 
gases  and  vapours.  T  is  a  sensitive  thermo-pile  connected  with  an 
extremely  delicate  galvanometer  M. 

The  deflections  of  this  galvanometer  were  proportional  to  the  degrees 
of  heat  up  to  about  30°  ;  beyond  this  point  the  proportionality  no  longer 


Fig  315. 

held  good,  and  accordingly  for  the  higher  degrees  a  table  was  empirically 
constructed,  in  which  the  value  of  the  higher  deflections  was  expressed 
in  units  ;  the  unit  being  the  amount  of  heat  necessary  to  move  the  needle 
through  one  of  the  lower  degrees. 

C  is  a  source  of  heat,  which  usually  was  either  a  Leslie's  cube  filled 
with  boiling  water,  or  else  a  sheet  of  blackened  copper  heated  by  gas. 
Now  when  the  source  of  heat  was  permitted  to  radiate  through  the  ex- 
hausted tube,  it  caused  the  needle  to  assume  a  very  high  deflection  ;  and 
in  this  position  a  very  considerable  degree  of  absorption  would  have  been 
needed  to  produce  an  alteration  of  1°  of  the  galvanometer.  And  if  to 
lessen  this  deflection  a  lower  source  of  heat  had  been  used,  the  fraction 
absorbed  would  be  correspondingly  less,  and  might  well  have  been  in- 
sensible. Hence  Tyndall  adopted  the  following  device,  by  which  he  was 
enabled  to  use  a  powerful  flux  of  heat,  and  at  the  same  time  discover 
small  variations  in  the  quantity  falling  on  the  pile. 

The  source  of  heat  at  C  was  allowed  to  radiate  through  the  tube  at  the 
end  of  which  the  pile  was  placed ;  a  deflection  was  produced  of,  say  70° ; 
a  second  source  of  heat,  D,  was  then  placed  near  the  other  face  of  the 
pile,  the  amount  of  heat  falling  on  the  pile  from  this  compensating  cube 
being  regulated  by  means  of  a  movable  screen  S.  When  both  faces  of 
the  pile  are  warmed,  two  currents  are  produced,  which  are  in  opposite 
directions,  and  tending  therefore  to  neutralise  each  other :  when  the  heat 
on  both  faces  is  precisely  equal  the  neutralisation  is  perfect,  and  no  current 
at  all  is  produced,  however  high  may  be  the  temperature  on  both  sides. 
In  the  arrangement  just  described,  by  means  of  the  screen  S,  the  radia- 
tion from  the  compensating  cube  was  caused  to  neutralise  exactly  the 
radiation  from  the  source  C  ;  the  needle  consequently  was  brought  down 
from  70°  to  zero,  and  remained  there  so  long  as  both  sources  were  equal. 
If  now  a  gas  or  vapour  be  admitted  into  the  exhausted  tube,  any  power  ot 
absorption  it  may  possess  will  be  indicated  by  the  destruction  of  this 
equilibrium,  and  preponderance  of  the  radiation  from  the  compensating 
cube,  by  an  amount  corresponding  to  the  heat  cut  oif  by  the  gas.     Ex- 


-412]  Radiant  Heat,  3  5  r 

amined  in  this  way,  air,  hydrogen,  and  nitrogen,  when  dried  by  passing 
through  sulphuric  acid,  were  found  to  exert  an  almost  inappreciable  effect ; 
their  presence  as  regards  radiant  heat  being  but  Httle  different  to  a 
vacuum.  But  with  olefiant  and  other  complex  gases  the  case  was  entirely 
different.  Representing  by  the  number  i  the  quantity  of  radiant  heat 
absorbed  by  air,  olefiant  gas  absorbs  970  times,  and  ammoniacal  gas  1 195 
times  this  amount.  In  the  following  table  is  given  the  absorption  of 
obscure  heat  by  various  gases,  referred  to  air  as  unity  : — 

Name  of  sras  Absorption  under 

M  ame  ot  gas  ^^  -^^^^^^  pressure. 

Air I 

Oxygen         i 

Nitrogen i 

Hydrogen i 

Chlorine 39 

Hydrochloric  acid 62 

Carbonic  acid .         .90 

Nitrous  oxide 355 

Marsh  gas 403 

Sulphurous  acid 710 

Olefiant  gas 970 

Ammonia 1195 

If  instead  of  comparing  the  cases  at  a  common  pressure  of  one  atmo- 
sphere, they  are  compared  at  a  common  pressure  of  an  inch,  their  differ- 
ences in  absorption  are  still  more  strikingly  seen.  Thus  assuming  the 
absorption  by  i  inch  of  dry  air  to  be  i,  the  absorption  by  i  inch  of  olefiant 
gas  is  7,950,  and  by  the  same  amount  of  sulphurous  acid  8,800. 

412.  Influence  of  pressure  and  tbickness  on  tbe  absorption  of 
beat  by  g:ases. — The  absorption  of  heat  by  gases  varies  with  the  pressure ; 
this  variation  cannot  be  seen  in  the  case  of  air,  as  the  total  absorption  is 
so  small,  but  in  the  case  of  those  gases  which  have  considerable  absorp- 
tive power  it  is  easily  shown.  Taking  the  total  absorption  by  atmo- 
spheric air  under  ordinary  pressure  at  unity,  the  numbers  of  olefiant  gas 
under  a  pressure  of  i,  3,  5,  7,  and  10  inches  of  mercury  are  respectively 
90  142,  168,  182,  and  193.  Thus  one-thirtieth  of  an  atmosphere  of 
olefiant  gas  exerts  90  times  the  absorption  of  an  entire  atmosphere  of  air. 
And  the  absorption,  it  is  seen,  increases  with  the  density,  though  not  in 
a  direct  ratio.  Tyndall  showed,  however,  by  special  experiments,  that 
for  very  low  oressures  the  absorption  does  increase  with  the  density. 
Employing  as  a  unit  volume  of  the  gas  a  quantity  which  measured  only 
^^^th  of  a  cubic  inch,  and  admitting  successive  measures  of  olefiant  gas  into 
the  experimental  tube,  it  was  found  that  up  to  15  measures  the  absorption 
was  directly  proportionate  to  the  density  in  each  case. 

In  these  experiments  the  length  of  the  experimental  tube  remained  the 
same  whilst  the  pressure  of  the  gas  within  it  was  caused  to  vary ;  in  other 
subsequent  experiments  the  pressure  of  the  gas  was  kept  constant,  whilst 
the  length  of  the  tube  was,  by  suitable  means,  varied  fromo-oi  of  an  inch 


352  On  Heat.  [412- 

up  to  50  inches.  The  source  was  a  heated  plate  of  copper ;  of  the  total 
radiation  from  this  nearly  2  per  cent,  were  absorbed  by  a  film  of  olefiant 
gas  -oi  of  an  inch  thick,  upwards  of  9  per  cent,  by  a  layer  of  the  same  gas 
o-i  of  an  inch  thick,  33  per  cent,  by  a  layer  2  inches  thick,  68  per  cent, 
by  a  column  20  inches  long,  and  ^'j  per  cent,  by  a  column  rather  more 
than  4  feet  long. 

413.  Absorptive  power  of  vapours. — Great  as  is  the  absorptive 
power  of  olefiant  gas,  it  is  exceeded,  as  Tyndall  found,  by  that  of  several 
vapours.  The  mode  of  experimenting  was  analogous  to  that  with  the 
gases.  The  liquid  from  which  the  vapours  were  to  be  derived  was  en- 
closed in  a  small  flask,  which  could  be  attached  with  a  stopcock  to  the 
exhausted  experimental  tube.  The  absorption  was  then  determined  after 
admitting  the  vapours  into  the  tube  in  quantities  measured  by  the  pressure 
of  the  barometer  gauge  attached  to  the  air  pump. 

The  following  table  shows  the  absorption  of  vapours  under  pressures 
varying  from  o-i  to  vo  inch  of  mercury  : — 

T.T  c  Absorption  under  pressure 

Name  of  vapours  j^  f^^^es  of  mercury 


O-I 

0-5 

i-o 

Bisulphide  of  carbon 

.         .       15 

47 

62 

Benzole            .... 

.       66 

182 

267 

Chloroform      .... 

.         .       85 

182 

236 

Ether       ..... 

.     300 

710 

870 

Alcohol 

.     325 

622 

Acetic  ether    .... 

.     590 

980 

1 195 

These  numbers  refer  to  the  absorption  of  a  whole  atmosphere  of  dry 
air  as  their  unit,  and  it  is  thus  seen  that  a  quantity  of  bisulphide  of  car- 
bon vapour,  the  feeblest  absorbent  yet  examined,  which  only  exerts  a 
pressure  of  ^^^th  of  an  inch  of  mercury,  or  the  gl^th  of  an  atmosphere,  gave 
15  times  the  absorption  of  an  entire  atmosphere  of  air ;  and  j^^th  of  an  inch 
of  acetic  ether  590  times  as  much.  Comparing  air  at  a  pressure  of  o-i 
with  acetic  ether  of  the  same  pressure,  the  absorption  of  the  latter  would 
be  more  than  17,500  times  as  great  as  that  of  the  former. 

The  absorption  by  the  infinitesimally  small  quantity  of  matter  consti- 
tuting a  perfume  can  never  be  measured ;  for  Tyndall  found  that  the 
odours  from  the  essential  oils  exercised  a  marked  influence  on  radiant 
heat.  Perfectly  dry  air  was  allowed  to  pass  through  a  tube  containing 
dried  paper  impregnated  with  various  essential  oils,  and  then  admitted 
into  the  experimental  tube.  Taking  the  absorption  of  dry  air  as  unity, 
the  following  were  the  numbers  respectively  obtained  for  air  scented  with 
various  oils  :— PatchouH  31,  otto  of  roses  37,  lavender  60,  thyme  68,  rose- 
mary 74,  cassia  109,  aniseed  372.  Thus  the  perfume  of  a  flower-bed 
absorbs  a  large  percentage  of  the  heat  of  low  refrangibility  emitted 
from  it. 

Ozone  prepared  by  electrolysing  water  was  also  found  to  have  a  re- 
markable absorptive  effect.  The  small  quantity  of  ozone  present  in  elec- 
trolytic oxygen  was  found  in  one  experiment  to  exercise  136  times  the 
absorption  of  the  entire  mass  of  the  oxygen  itself. 


-415]  Radiant  Heat.  353 

But  the  most  important  results  which  Tyndall  has  obtained  are  those 
which  follow  from  his  experiments  on  the  behaviour  of  aqueous  vapour 
to  radiant  heat.  The  experimental  tube  was  filled  with  air,  dried  as 
perfectly  as  possible,  and  the  absorption  it  exercised  was  found  to  be 
one  unit.  Exhausting  the  tube,  and  admitting  the  ordinary  undried,  but 
not  specially  moist,  air  from  the  laboratory,  the  absorption  now  rose  to 
72  units.  The  difference  between  dried  and  undried  air  can  only  be 
ascribed  to  the  aqueous  vapour  the  latter  contains.  Thus  on  a  day  of 
average  humidity  the  absorptive  effect  due  to  the  transparent  aqueous 
vapour  present  in  the  atmosphere  is  72  times  as  great  as  that  of  the  air 
itself,  though  in  quantity  the  latter  is  about  200  times  greater  than  the 
former.  Analogous  results  were  obtained  on  different  days,  and  with 
specimens  of  air  taken  from  various  localities.  When  air  which  had 
been  specially  purified  was  allowed  to  pass  through  a  tube  filled  with 
fragments  of  moistened  glass  and  examined,  it  was  found  to  exert  an 
absorption  90  times  that  of  pure  air. 

In  some  other  experiments  Tyndall  suppressed  the  use  of  rock  salt 
plates  in  his  experimental  tube,  and  even  the  tube  itself,  and  yet  in  every 
case  the  results  were  such  as  to  show  the  great  power  which  aqueous 
vapour  possesses  as  an  absorbent  of  radiant  heat. 

The  absorptive  action  which  the  aqueous  vapour  in  the  atmosphere 
exerts  on  the  sun's  heat  has  been  established  by  a  series  of  actinometrical 
observations  made  by  Soret  at  Geneva  and  on  the  summit  of  Mont 
Blanc;  he  finds  that  the  intensity  of  the  solar  heat  on  the  top  of  Mont 
Blanc  is  f  ths  of  that  at  Geneva ;  in  other  words,  that  of  the  heat  which  is 
radiated  at  the  height  of  Mont  Blanc,  about  |th  is  absorbed  in  passing 
through  a  vertical  layer  of  the  atmosphere  14,436  feet  in  thickness.  The 
same  observer  has  found  that  with  virtually  equal  solar  heights  there  is 
the  smallest  transmission  of  heat  on  those  days  on  which  the  tension 
of  aqueous  vapour  is  greatest,  that  is,  when  there  is  most  moisture  in 
the  atmosphere. 

414.  Radiating-  power  of  g-ases. — Tyndall  also  examined  the  ra- 
diating power  of  gases.  A  red-hot  copper  ball  was  placed  so  that  the 
current  of  heated  air  which  rose  from  it  acted  on  one  face  of  a  thermo- 
pile ;  this  action  was  compensated  by  a  cube  of  hot  water  placed  in 
front  of  the  opposite  face.  On  then  allowing  a  current  of  dry  olefiant 
gas  from  a  gasholder  to  stream  through  a  ring  burner  over  the  heated 
ball  and  thus  supplant  the  ascending  current  of  hot  air,  it  was  found 
that  the  gas  radiated  energetically.  By  comparing  in  this  manner  the 
action  of  many  gases  it  was  discovered  that,  as  is  the  case  with  solids, 
those  gases  which  are  the  best  absorbers  are  also  those  which  radiate 
most  freely. 

415.  Bynamic  radiation  and  absorption. — To  another  class  of  phe- 
nomena which  Tyndall  discovered  he  gives  the  name,  dynainic  radiation 
and  absorption. 

A  gas  when  permitted  to  enter  an  exhausted  tube  is  heated  in  conse- 
quence of  the  collision  of  its  particles  against  the  sides  of  the  vessel ;  it  thus 
becomes  a  source  of  heat,  which  is  perfectly  capable  of  being  measured. 


354  On  Heat.  [415- 

Tyndall  calls  this  dynamic  heating.  In  like  manner,  when  a  tube  full  of 
gas  or  vapour  is  rapidly  exhausted,  a  chilling  takes  place  owing  to  the 
loss  of  heat  in  the  production  of  motion;  this  he  calls  dynamic  chilling 
or  absorption. 

He  could  thus  determine  the  radiation  or  absorption  of  a  gas  without 
any  source  of  heat  external  to  the  gas  itself.  An  experimental  tube  was 
taken,  one  end  of  which  was  closed  with  a  polished  metal  plate,  and  the 
other  with  a  plate  of  rock  salt ;  in  front  of  the  latter  was  the  face  of  the 
pile.  The  needle  being  at  zero,  and  the  tube  exhausted,  a  gas  was  allowed 
quickly  to  enter  until  the  tube  was  full,  the  effect  on  the  galvanometer 
being  noted.  This  being  only  a  transitory  effect  the  needle  soon  returned 
to  zero  ;  the  tube  was  then  rapidly  pumped  out,  by  which  a  sudden 
chilling  was  produced,  and  the  needle  exhibited  a  deflection  in  the  opposite 
direction. 

Comparing  in  this  way  the  dynamic  heating  and  chilling  of  various 
gases,  it  was  found  that  those  gases  which  are  the  best  absorbers  are  in 
like  manner  the  best  radiators. 

Metallic  surfaces  when  poHshed  are,  as  we  have  seen  (398),  bad  radi- 
ators, but  radiate  freely  when  covered  with  varnish.  Now  Tyndall 
made  the  curious  experiment  of  varnishing  a  metallic  surface  by  a  film  of 
gas.  A  LesHe's  cube  was  placed  with  its  polished  metal  side  in  front  of 
the  pile,  and  its  effect  neutralised  by  a  second  cube  placed  before  the 
other  face  of  the  pile.  On  allowing,  by  a  special  arrangement,  a  stream 
of  olefiant  or  coal  gas  to  flow  from  a  gasholder  over  the  metallic  face  of 
the  first  cube,  a  copious  radiation  from  that  side  was  produced  as  long  as 
the  flow  of  gas  continued.  Acting  on  the  principle  indicated  in  the  foregoing 
experiment,  Tyndall  determined  the  dynamic  radiation  and  absorption  of 
vapours.  The  experimental  tube  containing  a  vapour  under  a  small 
known  pressure,  air  was  allowed  to  enter  until  the  pressure  inside  the 
tube  was  the  same  as  that  of  the  atmosphere.  In  this  way  the  entering 
air  by  its  impact  against  the  tube  became  heated  ;  and  its  particles 
mixing  with  those  of  the  minute  quantity  of  vapour  present,  each  of  them 
became,  so  to  speak,  coated  with  a  layer  of  the  vapour.  The  entering 
air  was  in  this  case  a  source  of  heat,  just  as  in  the  above  experiments 
the  Leslie  cube  was.  Here,  however,  one  gas  varnished  another  ;  the 
radiation  and  subsequently  the  absorption  of  various  vapours  could  thus 
be  determined. 

It  was  found  that  vapours  differed  very  materially  in  their  power  of 
radiating  under  these  circumstances:  of  those  which  were  tried  bisul- 
phide of  carbon  vapour  was  the  worst  and  boracic  ether  the  best  radiator. 
And  in  all  cases  those  which  were  the  best  absorbents  were  also  the  best 
radiators.  By  this  method  Tyndall  was  able  to  observe  a  definite  radia- 
tive power  with  the  more  powerful  vapours  when  the  quantity  present  was 
immeasurably  small. 

416.  Relation  of  absorption  to  molecular  state.  — Up  to  a  recent 
period  it  was  considered  that  the  absorption  of  heat  was  mainly  dependent 
upon  the  physical  condition  of  the  body  examined.  This  led  to  the 
belief  that  it  was  impossible  for  substances  of  such  tenuity  as  gases  and 


-416]  Radiant  Heat.  355 

vapours  to  absorb  any  sensible  amount  of  heat  ;  and  that  the  absorption 
by  bodies  when  in  a  hquid  state  would  be  unlike  the  same  bodies  when 
solid ;  moreover,  that  if  all  solid  bodies  were  reduced  to  an  equally  fine 
state  of  division,  the  present  differences  in  their  absorbent  and  radiative 
powers  would  disappear.  A  few  experiments  made  by  Melloni  on 
atmospheric  air  supported  the  first  idea,  and  a  series  of  experiments  by 
Masson  and  Courtepee  established  the  belief  in  the  last.  But  we  have 
seen  that  TyndalFs  researches  have  revealed  the  powerful  absorption  of 
heat  by  various  gases  and  vapours,  and  we  shall  now  briefly  show  that 
the  researches  of  the  same  philosopher  have  overthrown  the  last  two 
conclusions,  giving  us  an  insight  into  the  cause  of  the  absorption  of  heat 
which  before  was  unattainable. 

After  the  examination  of  the  absorption  of  heat  by  vapours,  Tyndall 
tried  the  same  substances  in  a  liquid  form.  The  conditions  of  the  experi- 
ments were  in  both  cases  the  same  ;  the  source  of  heat  was  always  a 
spiral  of  platinum,  heated  to  redness  by  an  electric  current  of  known 
strength  ;  and  plates  of  rock  salt  were  invariably  employed  to  contain 
both  vapours  and  liquids.  Finally,  the  absorption  by  the  vapours  was  re- 
measured  ;  in  this  case  introducing  into  the  experimental  tube,  not  as 
before  equal  quantities  of  vapour,  but  amounts  proportional  to  the  density 
of  the  liquid.  When  this  last  condition  had  been  attained,  it  was  found 
that  the  order  of  absorption  by  a  series  of  liquids,  and  by  the  same  series 
when  turned  into  vapour,  was  precisely  the  same.  Thus  the  substances 
tried  stood  in  the  following  order  as  liquid  and  as  vapour,  beginning  with 
the  feeblest  absorbent,  and  ending  with  the  most  powerful  : — 

Liquids  Vapours 

Bisulphide  of  carbon       ....  Bisulphide  of  carbon. 

Chlorofprm Chloroform. 

Iodine  of  ethyl Iodine  of  ethyl. 

Benzole Benzole. 

Amylene  .        .      ■  .         .         .         .  Amylene. 

Ether      .         .  ....  Ether. 

Acetic  ether Acetic  ether. 

Alcohol Alcohol. 

Water. 

A  direct  determination  of  the  proportional  amount  of  the  vapour  of 
water  could  not  be  made,  on  account  of  the  lowness  of  its  tension,  and 
the  hygroscopic  nature  of  the  plates  of  the  rock  salt.  But  the  remarkable 
and  undeviating  regularity  of  the  absorption  by  all  the  other  substances 
in  the  list,  when  as  liquid  and  vapour,  establishes  the  fact,  which  is  cor- 
roborated by  the  experiments  we  have  already  mentioned,  that  aqueous 
vapour  is  one  of  the  most  energetic  absorbents  of  heat. 

In  this  table  it  will  be  noticed  that  those  substances  which  have  the 
simplest  chemical  constitution  stand  first  in  the  Hst,  with  one  anomalous 
exception,  namely  that  of  water.  In  the  absorption  of  heat  by  gases, 
Tyndall  found  that  the  elementary  gases  were  the  feeblest  absorbents, 
while  the  gases  of  most  complex  constitution  were  the  most  powerful 


356  On  Heat.  [416- 

absorbers.  Thus  it  may  be  inferred  that  absorption  is  mainly  dependent 
on  chemical  constitution  ;  that  is  to  say,  that  absorption  and  radiation 
are  molecular  acts  independent  of  the  physical  condition  of  the  body. 

But  this  conclusion  appeared  to  be  contradicted  by  the  experiments 
of  Masson  and  Courtepde  on  powders.  Tyndall  has  therefore  repeated 
these  experiments,  and  found  them  to  be  entirely  incorrect.  Avoiding 
the  source  of  error  into  which  the  French  experimenters  had  fallen, 
Tyndall  has  discovered  that  the  radiation  of  powders  is  similar  to  that 
of  the  solids  from  which  they  were  derived,  and  therefore  differs  greatly 
inter  se.  The  absorbent  power  of  powders  was  also  found  to  correspond 
with  their  radiative  power — as  we  have  shown  to  be  the  case  with  solids 
and  gases,  and,  though  as  yet  we  have  no  experiments  on  the  subject,  is 
doubtless  also  true  for  liquids.  The  powders  were  attached  to  the  tin 
surfaces  of  a  Leslie's  cube,  in  such  a  manner  that  radiation  took  place 
from  the  surface  of  the  powder  alone.  The  following  table  gives  the 
radiation  in  units  from  some  of  the  powders  examined  by  Tyndall ;  the 
metal  surface  of  the  cube  giving  a  deflection  of  1 5  units  : — 

Radiation  from  powders. 


Rock  salt 

•     35-3 

Sulphate  of  calcium 

.     777 

Biniodide  of  mercury 

.     397 

Red  oxide  of  iron . 

.     78-4 

Sulphur 

•   .     40-6 

Hydrated  oxide  of  zinc 

.     80-4 

Chloride  of  lead    . 

•     55-4 

Black  oxide  of  iron 

.     81-3 

Carbonate  of  calcium 

.      •  .     70-2 

Sulphide  of  iron  . 

.     817 

Red  oxide  of  lead 

•     74-0 

Lampblack   . 

.     84-0 

It  will  be  noticed  that  these  substances  are  of  various  colours.  Some 
are  white,  such  as  rock  salt,  chloride  of  lead,  carbonate  and  sulphate  of 
calcium,  and  hydrated  oxide  of  zinc  ;  some  are  red,  such  as  biniodide  of 
mercury  and  oxide  of  lead  ;  whilst  others  are  black,  as  sulphide  of  iron 
and  lampblack  :  we  have  besides  other  colours.  The  colours  therefore 
have  no  influence  on  the  radiating  power  :  for  example,  rock  salt  is  the 
feeblest  radiator,  and  hydrated  oxide  of  zinc  one  of  the  most  powerful 
radiators.  The  views  of  Tyndall  therefore,  instead  of  being  overthrown, 
were  confirmed  by  these  his  latest  experiments. 

Nearly  a  century  ago  Franklin  made  experiments  on  coloured  pieces 
of  cloth,  and  found  their  absorption,  indicated  by  their  sinking  into  snow 
on  which  they  were  placed,  to  increase  with  the  darkness  of  the  colour. 
But  all  the  cloths  were  equally  powerful  absorbents  of  obscure  heat,  and 
the  effects  noticed  were  only  produced  by  their  relative  absorptions  of 
light.  In  fact,  the  conclusions  to  be  drawn  from  FrankHn's  experiment 
only  holds  good  for  luminous  heat,  especially  sunlight,  such  as  he  em- 
ployed. 

417.  Applicationss. — The  properties  which  bodies  possess  of  absorb- 
ing, emitting,  and  reflecting  heat,  meets  with  numerous  applications  in 
domestic  economy  and  in  the  arts.  Leslie  stated  in  a  general  manner 
that  white  bodies  reflect  heat  very  well,  and  absorb  very  little,  and  that 
the  contrary  is  the  case  with  black  substances.     As  we  have  seen,  this 


-417]  Radiant  Heat.  357- 

principle  is  not  generally  true,  as  Leslie  supposed  ;  for  example,  for  non- 
luminous  rays  white  lead  has  as  great  an  absorbing  power  as  lampblack 
(410).  Leslie's  principle  applies  to  powerful  absorbents  like  cloth,  cotton, 
wool  and  other  organic  substances  when  exposed  to  luminous  heat.  Ac- 
cordingly, the  most  suitable  coloured  clothing  for  summer  is  just  that 
which  experience  has  taught  us  to  use,  namely,  white,  for  it  absorbs  less 
of  the  sun's  rays  than  black  clothing,  and  hence  feels  cooler. 

The  polished  fire-irons  before  a  fire  are  cold,  whilst  the  black  fender 
is  often  unbearably  hot.  If,  on  the  contrary,  a  liquid  is  to  be  kept  hot  as 
long  as  possible,  it  must  be  placed  in  a  brightly  poHshed  metalhc  vessel, 
for  then,  the  emissive  power  being  le.ss,  the  cooling  is  slower.  It  is  for 
this  reason  advantageous  that  the-steam  pipes,  etc.,  of  locomotives  should 
be  kept  bright. 

In  the  Alps,  the  mountaineers  accelerate  the  fusion  of  the  snow  by 
covering  it  with  earth,  which  increases  the  absorbing  power. 

In  our  dwellings,  the  outsides  of  the  stoves  and  of  hot  water  apparatus 
ought  to  be  black,  and  the  insides  of  fire-places  ought  to  be  fined  with 
fire-clay,  in  order  to  increase  the  radiating  power  towards  the  apartment. 

It  is  in  consequence  of  the  great  diathermaneity  of  dry  atmospheric 
air  that  the  higher  regions  of  the  atmosphere  are  so  cold,  notwithstanding 
the  great  heat  which  traverses  them  :  whilst  the  intense  heat  of  the  sun's 
direct  rays  on  high  mountains  is  probably  due  to  the  comparative  absence 
of  aqueous  vapour  at  those  high  elevations.  / 

As  nearly  all  the  luminous  rays  of  the  sun  pass  thj^bugh  water,  and 
the  sun's  radiation  as  we  receive  it  on  the  surface  of  the  earth  consisting 
of  a  large  proportion  of  luminous  rays,  accidents  have  often  arisen  from 
the  convergence  of  these  luminous  rays  by  bottles  of  water  which  act  as 
lenses.  In  this  way  gunpowder  could  be  fired  by  the  heat  of  the  sun's 
rays  concentrated  by  a  water  lens  ;  and  the  drops  of  water  on  leaves  in 
greenhouses  have,  it  is  said,  been  found  to  act  as  lenses,  and  burn  the 
leaves  on  which  they  rest. 

Certain  bodies  can  be  used  (407),  to  separate  the  heat  and  light  radiated 
from  the  same  source.  Rock  salt  covered  with  lampblack,  or  still  better 
with  iodine  transmits  heat,  but  completely  stops  fight.  On  the  other 
hand,  alum,  either  as  a  plate  or  in  solution,  or  a  thin  layer  of  water,  is 
permeable  to  light,  but  stops  all  the  heat  from  obscure  sources.  This 
property  is  made  use  of  in  apparatus  which  are  illuminated  by  the  sun's 
rays,  in  order  to  sift  the  rays  of  their  heating  power,  and  a  vessel  full  of 
water  or  a  solution  of  alum  is  used  with  the  electric  light  when  it  is 
desirable  to  avoid  too  intense  a  heat. 

In  gardens,  the  use  of  shades  to  protect  plants  depends  partly  on  the 
diathermancy  of  glass  for  heat  from  luminous  rays  and  its  athermancy 
for  obscure  rays.  The  heat  which  radiates  from  the  sun  is  largely  of  the 
former  quality,  but  by  contact  with  the  earth  it  is  changed  into  obscure 
heat,  which  as  such  cannot  retraverse  the  glass.  This .  explains  the 
manner  in  which  greenhouses  accumulate  their  warmth,  and  also  the  great 
heat  experienced  in  summer  in  rooms  having  glass  roofs,  for  the  glass  in 
both  cases  effectually  entraps  the  solar  rays.     On  the  same  principle 


358 


On  Heat. 


[417- 


plates  of  glass  are  frequently  used  as  screens  to  protect  us  from  the  heat 
of  a  fire  :  the  glass  allows  us  to  see  the  cheerful  light  of  the  fire,  but  inter- 
cepts the  larger  part  of  the  heat  radiated  from  the  fire.  Though  the 
screens  thus  become  warm  by  the  heat  they  have  absorbed,  yet  as  they 
radiate  this  heat  in  all  directions,  towards  the  fire  as  well  as  towards  us, 
we  finally  receive  less  heat  when  they  are  interposed. 


CHAPTER   IX. 


CALORIMETRY. 


i^  >a 


418.  Calorimetry.  Thermal  unit. — The  object  of  calorimetry  is  to 
measure  the  quantity  of  heat  which  a  body  parts  with  or  absorbs  when  its 
temperature  sinks  or  rises  through  a  certain  number  of  degrees,  or  when 
it  changes  its  condition. 

Quantities  of  heat  may  be  expressed  by  any  of  its  directly  measurable 
effects,  but  the  most  convenient  is  the  alteration  of  temperature,  and 
quantities  of  heat  are  usually  defined  by  stating  the  extent  to  which  they 
are  capable  of  raising  a  known  weight  of  a  known  substance,  such  as 
water. 

The  unit  chosen  for  comparison,  and  called  the  thermal  unit,  is  not 
everywhere  the  same.  In  France  it  is  the  quantity  of  heat  necessary  to 
raise  the  temperature  of  one  kilogramme  of  water  through  one  degree 
Centigrade;  this  is  called  a  <:rt:/^r/^.  In  this  book  we  shall  adopt,  as  a 
thermal  unit,  the  quantity  of  heat  necessary  to  raise  one  pound  of  water 
th?-ough  one  degree  Centigrade  :  i  calorie  =^T2  thermal  units,  and  i  ther- 
mal unit  =  0-45  calorie. 

419.  specific  beat. — When  equal  weights  of  two  different  substances 
at  the  same  temperature  placed  in  similar  vessels  are  subjected  for  the 
same  length  of  time  to  the  heat  of  the  same  lamp,  or  are  placed  at  the 
same  distance  in  front  of  the  same  fire,  it  is  found  that  their  temperatures 
will  vary  considerably  ;  thus  mercury  will]  be  much  hotter  than  water. 
But  as,  from  the  conditions  of  the  experiment,  they  have  each  been  re- 
ceiving the  same  amount  of  heat,  it  is  clear  that  the  quantity  of  heat  which 
is  sufficient  to  raise  the  temperature  of  mercury  through  a  certain  number 
of  degrees  will  only  raise  the  temperature  of  the  same  quantity  of  water 
through  a  less  number  of  degrees  ;  in  other  words,  that  it  requires  more 
heat  to  raise  the  temperature  of  water  through  one  degree  than  it  does  to 
raise  the  temperature  of  mercury  by  the  same  extent.  Conversely,  if 
the  same  quantities  of  water  and  of  mercury  at  100°  C.  be  allowed  to  cool 
down  to  the  temperature  of  the  atmosphere,  the  water  will  require  a  much 
longer  time  for  the  purpose  than  the  mercury  :  hence,  in  cooling  through 
the  same  number  of  degrees,  water  gives  out  more  heat  than  does  mercury. 

It  is  readily  seen  that  all  bodies  have  not  the  same  specific  heat.  If  a 
pound  of  mercury  at  100°  is  mixed  with  a  pound  of  water  at  zero,  the 
temperature  of  the  mixture  will  only  be  about  3°.     That  is  to  say,  that 


,x^^ 


-420]  Calorimetry.     Specific  Heat.  359 

while  the  mercury  has  cooled  through  97°,  the  temperature  ot  the  water 
has  only  been  raised  3°.  Consequently  the  same  weight  of  water  requires 
about  32  times  as  much  heat  as  mercury  does  to  produce  the  same  eleva- 
tion of  temperature. 

If  similar  experiments  are  made  with  other  substances  it  will  be  found 
that  the  quantity  of  heat  required  to  effect  a  certain  change  of  tempera- 
ture is  different  for  almost  every  substance,  and  we  speak  of  the  specific 
heat  or  calorific  capacity  of  a  body  as  the  quantity  of  heat  which  it  absorbs 
when  its  temperature  rises  through  a  given  range  of  temperature,  from . 
zero  to  1°  for  example,  compared  with  the  quantity  of  heat  which  would 
be  absorbed  under  the  same  circumstances,  by  the  same  weight  of  water. 
In  other  words,  water  is  taken  as  the  standard  for  the  comparison  of 
specific  heats.  Thus,  to  say  that  the  specific  heat  of  lead  is  0-0314, 
means  that  the  quantity  of  heat  which  would  raise  the  temperature  of 
any  given  quantity  of  lead  through  1°  C.  would  only  raise  the  temperature 
of  the  same  quantity  of  water  through  0-0314. 

Temperature  is  the  vis  viva  of  the  smallest  particles  of  a  body  ;  in 
bodies  of  the  same  temperature  the  atoms  have  the  same  vis  viva,  the 
smaller  mass  of  the  lighter  atoms  being  compensated  by  their  greater 
velocity.  The  heat  absorbed  by  a  body  not  only  raises  its  temperature, 
that  is  increases  the  vis  viva  of  the  progressive  motion  of  the  atoms,  but 
in  overcoming  the  attraction  of  the  atoms  it  moves  them  further  apart,  and 
along  with  the  expansion  which  this  represents  some  external  pressure  is 
overcome.  In  the  conception  of  specific  heat  is  included,  not  merely  that 
amount  of  heat  which  goes  to  raise  the  temperature,  but  also  that  necessary 
for  the  internal  work  of  expansion,  and  that  required  for  the  external  work. 
If  these  latter  could  be  separated  we  should  get  the  true  heat  of  tempera- 
ture,  that  which  is  used  solely  in  increasing  the  vis  viva  of  the  atoms.  This 
is  sometimes  called  the  tn(e  specific  heat. 

Three  methods  have  been  employed  for  determining  the  specific  heats 
of  bodies  :  (i.)  the  method  of  the  melting  of  ice,  (ii.)  the  method  ot 
mixtures,  and  (iii.)  that  of  cooling.  In  the  latter,  the  specific  heat  of  a 
body  is  determined  by  the  time  which  it  takes  to  cool  through  a  certain 
temperature.  Previous  to  describing  these  methods,  it  will  be  convenient 
to  explain  the  expression  for  the  quantity  of  heat  absorbed  or  given  out 
by  a  body  of  known  weight  and  specific  heat,  when  its  temperature  rises 
or  falls  through  a  certain  number  of  degrees. 

420.  Measure  of  tbe  sensible  heat  absorbed  by  a  body. — Let  m  be 
the  weight  of  a  body  in  pounds,  c  its  specific  heat,  and  /  its  temperature. 
The  quantity  of  heat  necessary  to  raise  a  pound  of  water  through  one 
degree  being  taken  as  unity,  in  of  these  units  would  be  required  to  raise 
nt  pounds  of  water  through  one  degree,  and  to  raise  it  through  /  degrees, 
/  times  as  much,  or  7nt.  As  this  is  the  quantity  of  heat  necessary  to  raise 
through  t  degrees  in  pounds  of  water  whose  specific  heat  is  unity,  a  body 
of  the  same  weight  only  of  different  specific  heat,  would  require  intc. 
Consequently,  when  a  body  is  heated  through  /  degrees,  the  quantity  of 
heat  which  it  absorbs  is  the  product  of  its  weight  into  its  temperature 


36o 


071  Heat. 


[420- 


into  its  specific  heat.     This  principle  is  the  basis  of  all  the  formulae  for 
calculating  specific  heats. 

If  a  body  is  heated  or  cooled  from  t'  to  t  degrees,  the  heat  absorbed  or 
disengaged  will  be  represented  by  the  formula 

7Jt{f  —  t)c,  or  m(t-t')c. 

42  T  ivcethod  of  the  fusion  of  ice. — This  method  of  determining 
specific  heats  is  based  on  the  fact  that  to 
melt  a  pound  of  ice  80  thermal  units  are 
necessary,  or  more  exactly  79"25.  Black's 
calorimeter  (fig.  316)  consists  of  a  block 
of  ice  in  which  a  cavity  is  made,  and 
which  is  provided  with  a  cover  of  ice. 
The  substance  whose  specific  heat  is  to 
be  determined  is  heated  to  a  certain  tem- 
perature, and  then  placed  m  the  cavity 
which  is  covered.  After  some  time  the 
body  becomes  cooled  to  zero.  It  is  then 
opened,  and  both  the  substance  and  the  cavity  wiped  dry  with  a  sponge 
which  has  been  previously  weighed.  The  increase  of  weight  of  this 
sponge  obviously  represents  the  ice  which  has  been  converted  into  water. 
Now,  since  one  pound  of  ice  at  0°  in  melting  to  water  0°  absorbs 
80  thermal  units,  P  pounds  absorbs  80  P  units.  On  the  other  hand  this 
quantity  of  heat  is  equal  to  the  heat  given  out  by  the  body  in  cooling 
from  t°  to  zero,  which  is  uitc,  fot  it  may  be  taken  for  granted  that  in 


Fig.  317- 


Fig.  318. 


cooling  from  t^  to  zero  a  body  gives  out  as  much  heat  as  it  absorbs  in 
being  heated  from  zero  to  t°.     Consequently  from 

80P 
mt' 


intc  =  80  P  we  have  c  ■■ 


-422] 


Specific  Heat. 


361 


It  is  difficult  to  obtain  blocks  of  ice  as  large  and  pure  as  those  used 
by  Black  in  his  experiments,  and  Lavoisier  and  Laplace  have  replaced 
the  block  of  ice  by  a  more  complicated  apparatus,  which  is  called  the  ice 
calorimeter.  Fig.  317  gives  a  perspective  view  of  it,  and  fig.  318  repre- 
sents a  section.  It  consists  of  three  concentric  tin  vessels  ;  in  the  central 
one  is  placed  the  body  M,  whose  specific  heat  is  to  be  determined,  while 
the  two  others  are  filled  with  pounded  ice.  The  ice  in  the  compartment 
A  is  melted  by  the  heated  body,  while  the  ice  in  the  compartment  B  cuts 
off  the  heating  influence  of  the  surrounding  atmosphere.  The  two  stop- 
cocks E  and  D  give  issue  to  the  water  which  arises  from  the  liquefaction 
of  the  ice. 

In  order  to  find  the  specific  heat  of  a  body  by  this  apparatus,  its 
weight  m  is  first  determined  ;  it  is  then  raised  to  a  given  temperature,  /, 
by  keeping  it  for  some  time  in  an  oil  or  water  bath,  or  in  a  current  of 
steam.  Having  been  quickly  brought  into  the  central  compartment,  the 
lids  are  replaced  and  covered  with  ice,  as  represented  in  the  figure.  The 
water  which  flows  out  by  the  stopcock  D  is  collected.  Its  weight,  P,  is 
manifestly  that  of  the  melted  ice.  The  calculation  is  then  made  as  in  the 
preceding  case. 

There  are  many  objections  to  the  use  of  this  apparatus.  From  its  size 
it  requires  some  quantity  of  ice,  and  a  body,  M,  of  large 
mass  ;  while  the  experiment  lasts  a  considerable  time. 
A  certain  weight  of  the  melted  water  remains  adhering  to 
the  ice,  so  that  the  water  which  flows  out  from  D  does 
not  exactly  represent  the  weight  of  the  melted  ice. 

422.  Bunsen's  ice  calorimeter. — On  the  very  con- 
siderable diminution  of  volume  which  ice  experiences  on 
passing  into  water  (323),  Bunsen  has  based  a  calorimeter 
which  is  particularly  suited  when  only  small  quantities 
of  a  substance  can  be  used  in  determinations,  A  small 
test  tube  a  (fig.  319)  intended  to  receive  the  substance 
experimented  upon  is  fused  in  the  wider  tube  B.  The 
part  ab  contains  pure  freshly  boiled-out  distilled  water,  H  Kla 
and  the  prolongation  of  this  tube  BC  together  with  the 
capillary  tube  d^  contains  pure  mercury.  This  tube  d  is 
firmly  fixed  to  the  end  of  the  tube  C  ;  it  is  graduated,  and 
the  value  of  each  division  of  the  graduation  is  specially 
determined  by  calibration.  When  the  apparatus  is  im- 
mersed in  a  freezing  mixture,  the  water  in  the  part  freezes. 
Hence,  if  afterwards  while  the  apparatus  is  protected 
against  the  access  of  heat  from  without,  a  weighed  quan- 
tity of  a  substance  at  a  given  temperature  is  introduced 
into  the  tube,  it  imparts  its  heat  to  this  in  sinking  to  zero.  ^'^-  3^9- 
In  doing  so  it  melts  a  certain  quantity  of  ice  which  is  evidenced  by  a 
corresponding  depression  of  the  mercury  in  tube  d.  Thus  the  weight  of 
ice  melted,  together  with  the  weight  and  original  temperature  of  the  sub- 
stance experimented  upon,  furnish  all  the  data  for  calculating  the 
specific  heat. 

R 


362  On  Heat.  [422- 

For  this  mode  of  determining  the  specific  heat  a  new  determination 
of  the  latent  heat  of  ice  was  made,  and  was  found  to  be  80-025.  It  was 
also  in  connection  with  these  experiments  that  Bunsen  made  his  de- 
termination of  the  specific  gravity  of  ice,  which  he  found  to  be  in  the 
mean  0-91674. 

By  the  above  method  Bunsen  determined  the  specific  heat  of  several 
of  the  rare  metals  for  which  a  weight  of  only  a  few  grains  could  be  used. 
.__  423.  Method  of  mixtures. — In  determining  the  specific  heat  of  a 
solid  body  by  this  method,  it  is  weighed  and  raised  to  a  known  tempera- 
ture, by  keeping  it,  for  instance,  for  some  time  in  a  closed  place  heated 
by  steam  ;  it  is  then  immersed  in  a  mass  of  cold  water,  the  weight  and 
temperature  of  which  are  known.  From  the  temperature  of  the  water 
after  mixture  the  specific  heat  of  the  body  is  determined. 

Let  M  be  the  weight  of  the  body,  T  its  temperature,  c  its  specific  heat ; 
and  let  m  be  the  weight  of  the  cold  water,  and  /  its  temperature. 

As  soon  as  the  heated  body  is  plunged  into  the  water,  the  temperature 
of  the  latter  rises  until  both  are  at  the  same  temperature.  Let  this  tem- 
perature be  9.  The  heated  body  has  been  cooled  by  T  -  f^  ;  it  has,  there- 
fore, lost  a  quantity  of  heat,  M(T-O)^.  The  cooHng  water  has,  on  the 
contrary,  absorbed  a  quantity  of  heat  equal  to  vi{(^-t),  for  the  specific 
heat  of  water  is  unity.  Now  the  quantity  of  heat  given  out  by  the  body  is 
manifestly  equal  to  the  quantity  of  heat  absorbed  by  the  water  ;  that  is, 
M (T  -  {))c  =  m{9  - 1),  from  which 

7n{Q-t) 
M(T-9* 

An  example  will  illustrate  the  application  of  this  formula.  A  piece  of 
iron  weighing  60  ounces,  and  at  a  temperature  of  100°  C,  is  immersed  in 
180  ounces  of  water,  whose  temperature  is  19°  C.  After  the  temperatures 
have  become  uniform,  that  of  the  cooling  water  is  found  to  be  22°  C. 
What  is  the  specific  heat  of  the  iron  } 

Here  the  weight  of  the  heated  body  M  is  60,  the  temperature  T  is  100°, 
c  is  to  be  determined  ;  the  temperature  of  mixture,  P,  is  22°,  the  weight  of 
the  cooling  water  is  180,  and  its  temperature  19°.     Therefore 

180(22-19)      9  ^Q.j 
60(100^22)     78     °''53. 

424.  Corrections. — The  vessel  containing  the  cooling  water  is  usually 
a  small  cylinder  of  silver  or  brass,  with  thin  polished  sides,  and  is  sup- 
ported by  some  badly  conducting  arrangement.  It  is  obvious  that  this 
vessel,  which  is  originally  at  the  temperature  of  the  cooling  water,  shares 
its  increase  of  temperature,  and  in  accurate  experiments  this  must  be 
allowed  for.  The  decrease  of  temperature  of  the  heated  body  is  equal  to 
the  increase  of  temperature  of  the  cooling  water,  and  of  the  vessel  in 
which  it  is  contained.  If  the  weight  of  this  latter  be  7n%  and  its  specific 
heat  c',  its  temperature,  like  that  of  the  water  is  /  :  consequently  the 
previous  equation  becomes 

M^(T  -  0)  =  m{9  -  /)  +  w  V(  --t)) 
from  which,  by  obvious  transformations, 


-425]  Specific  Heat.  363 

M(T-(;)       * 

Generally  speaking,  the  value  m'  c'  is  put  =  \i ;  that  is  to  say,  \i  is  the 
weight  of  water  which  would  absorb  the  same  quantity  of  heat  as  the 
vessel.  This  is  said  to  be  the  reduced  value  in  water  of  the  vessel,  or  the 
water  equivalent.     The  expression  accordingly  becomes 

(;y?  +  fi)(0-/) 
M(T-  )    • 

In  accurate  experiments  it  is  necessary  also  to  allow  for  the  heat  ab- 
sorbed by  the  glass  and  mercury  of  the  thermometer,  by  introducing  into 
the  equation  their  values  reduced  on  the  same  principle. 

In  order  to  allow  for  the  loss  of  heat  due  to  radiation,  a  prehminary 
experiment  is  made  with  the  body  whose  specific  heat  is  sought,  the  only 
object  of  which  is  to  ascertain  approximately  the  increase  of  temperature 
of  the  cooling  water.  If  this  increase  be  10°,  for  example,  the  tempera- 
ture of  the  water  is  reduced  by  half  this  number  — that  is  to  say  5°  below 
the  temperature  of  the  atmosphere — and  the  experiment  is  then  carried 
out  in  the  ordinary  manner. 

By  this  method  of  compensation,  first  introduced  by  Rumford,  the 

water  receives  as  much  heat  from  the  atmosphere  during  the  first  part  of 

the, experiment  as  it  loses  by  radiation  during  the  second  part. 

N.   /  425.  Reg-nault's  apparatus  for  determining'  specific  lieats. — Fig. 

/yi^  represents  one  of  the  forms  of  apparatus  used  by  M.  Regnault  in  de- 

/  termining  specific  heats  by  the  method  of  mixtures. 

The  principal  part  is  a  water-bath,  AA,  of  which  fig.  321  represents  a 
section.  It  consists  of  three  concentric  compartments  ;  in  the  central 
one  there  is  a  small  basket  of  brass  wire,  r,  containing  fragments  of  the 
substance  to  be  determined,  in  the  middle  of  which  is  placed  a  thermo- 
meter, T.  The  second  compartment  is  heated  by  a  current  of  steam 
coming  through  the  tube  ^,  from  a  boiler,  B,  and  passing  into  a  worm,  a^ 
where  it  is  condensed.  The  third  compartment,  zV,  is  an  air  chamber,  to 
hinder  the  loss  of  heat.  The  water  bath  AA  rests  on  a  chamber,  K, 
with  double  sides,  EE,  forming  a  jacket,  which  is  kept  full  of  cold  water, 
in  order  to  exclude  the  heat  from  AA  and  from  the  boiler  B.  The  central 
compartment  of  the  water  bath  is  closed  by  a  damper  r,  which  can  be 

I  opened  at  pleasure,  so  that  the  basket  c  can  be  lowered  into  the  cham- 
ber K. 
On  the  left  of  the  figure  is  represented  a  small  and  very  thin  brass 
vessel  D,  suspended  by  silk  threads  on  a  small  carriage^  which  can  be 
moved  out  of,  or  into,  the  chamber  K.  This  vessel  which  serves  as  a 
calorimeter,  contains  water,  in  which  is  immersed  a  thermometer,  t. 
^nother  thermometer  at  the  side,  ^,  gives  the  temperature  of  the  air. 
]  When  the  thermometer  T  shows  that  the  temperature  of  the  substance 
in  the  bath  is  stationary,  the  screen  h  is  raised,  and  the  vessel  D  moved 
to  just  below  the  central  compartment  of  the  water  bath.  The  damper  r 
is  then  withdrawn,  and  the  basket  c  and  its  contents  are  lowered  into  the 
water  of  the  vessel  D,  the  thermometer  T  remaining  fixed  in  the  cork. 


3^4 


Oil  Heat. 


[425- 


The  carriage  and  the  vessel  D  are  then  moved  out,  and  the  water  agi- 
tated until  the  thermometer  T  becomes  stationary.  The  temperature  which 
it  indicates  is  i).  This  temperature  known,  the  rest  of  the  calculation  is 
made  in  the  manner  described  in  art.  424,  care  being  taken  to  make  all 
the  necessary  corrections. 

In  determining  the   specific   heat   of   substances — phosphorus,   for 
instance — which^  could  not  be  heated  without  causing  them  to  melt,  or 


Fig.  320. 

undergo  some  change  which  would  interfere  with  the  accuracy  of  the 
result,  Regnault  adopted  an  inverse  process  :  he  cooled  them  down  to  a 
temperature  considerably,  below  that  of  the  water  in  the  calorimeter,  and 
then  observed  the  diminution  in  the  temperature  of  the  latter,  which 
resulted  from  immersing  the  cooled  substance  in  it. 

To  ascertain  the  specific  heat  of  bodies,  such  as  potassium,  where  the 
use  of  water  is  quite  inapplicable,  the  determination  is  made  in  another 
liquid,  such  as  turpentine  or  benzole,  the  specific  heat  of  which  is  known. 

426.  Metbod  of  coolingr. — Equal  weights  of  different  bodies  whose 
specific  heats  are  different,  will  occupy  different  times  in  cooling  through 
the  same  number  of  degrees.  Dulong  and  Petit  have  applied  this  prin- 
ciple in  determining  the  specific  heats  of  bodies  in  the  following  manner: 


-428] 


Specific  Heat  of  Liquids. 


365 


A  small  polished  silver  vessel  is  filled  with  the  substance  in  a  state  of  fine 
powder,  and  a  thermometer  placed  in  the  powder,  which  is  pressed  down. 
This  vessel  is  heated  to  a  certain  temperature,  and  is  then  introduced  into 
a  copper  vessel,  in  which  it  fits  hermetically.  This  copper  vessel  is  ex- 
hausted, and  maintained  at  the  constant  temperature  of  melting  ice,  and 
the  time  noted  which  the  substance  takes  in  falling  through  a  given  range 
of  temperature,  from  15°  to  5°  for  example.  The  times  which  equal 
weights  of  different  bodies  require  for  cooling  through  the  same  range  of 
temperature  are  directly  as  their  specific  heats. 

Regnault  has  proved  that  with  solids  this  method  does  not  give  trust- 
worthy results  ;  it  assumes,  which  is  not  quite'  the  case,  that  the  cooling 
in  all  parts  is  equal,  and  that  all  substances  part  with  their  heat  to  the 
silver  case  with  equal  facility.  The  method  may,  however,  be  employed 
with  success  in  the  determination  of  the  specific  heat  of  liquids. 

In  an  investigation  of  the  specific  heats  of  various  soils,  Pfaundler 
found  that  a  soil  of  low  specific  heat  heats  and  cools  rapidly,  while  earth 
of  higher  specific  heat  undergoes  slow  heating  and  slow  coohng ;  that 
moist  earths,  rich  in  humus,  have  a  high  specific  heat  amounting  in  the 
case  of  turf,  to  as  much  as  0-5  ;  while  dry  soils  free  from  humus,  such  as 
lime  and  sand,  have  a  low  specific  heat,  not  more  than  about  0'2. 

427.  Specific  heat  of  liquids. — The  specific  heat  of  hquids  may  be 
determined  either  by  the  method  of  cooling,  by  that  of  mixtures,  or  by 
that  of  the  ice  calorimeter.  In  the  latter  case  they  are  contained  in  a 
small  metal  vessel,  or  a  glass  tube,  which  is  placed  in  the  central  com- 
partment (fig.  318),  and  the  experiment  then  made  in  the  usual  manner. 

It  will  be  seen  from  the  following  table  that  water  and  oil  of  turpentine 
have  a  much  greater  specific  heat  than  that  of  other  substances,  and  more 
especially  than  the  metals.  It  is  from  its  great  specific  heat  that  water 
requires  a  long  time  in  being  heated  or  cooled,  and  that  for  the  same 
weight  and  temperature  it  absorbs  or  gives  out  far  more  heat  than  other 
substances.  This  double  property  is  applied  in  the  hot  water  apparatus, 
of  which  we  shall  presently  speak,  and  it  plays  a  most  important  part  in 
the/^conomy  of  nature. 
./428. 


428.  XMCean  specific  beats  of  solids  and  liquids  between  C  and  100 

/  '^^By  means  of  the  method  of  mixture  and  of  that  of  cooling,  M.  Regnault 


has  determined  the  specific  heats  of  a  number  of  bodies.  The  following 
table  contains  the  numbers  obtained  for  the  bodies  usually  met  with  in 
the  arts  : — 


Substances 

Specific 
heats 

Substances 

Specific 
heats 

Water  at  0°     . 

.     i-ooooo 

Calcined  animal  cha 

rcoal     0-26085 

„       10       . 

.     I  -00050 

Wood  charcoal 

.     0-24111 

»       15       . 

.     roo20o 

Sulphur 

.     0-20259 

mean  between 

Graphite 

.     0-20187 

„       0  and  100° 

.     I  -00500 

Thermometer  glass  . 

.     0-19768 

Turpentine  at  17°   . 

.     0-42590 

Phosphorus 

.     0-18949 

Alcohol        „  17°   . 

.     0-61500 

Diamond 

.     0-14687 

Ether 

.     0-51600 

Grey  iron 

.     0-12983 

Glycerine     „ 

.     0-55500 

Steel 

.     0-11750 

366 


On  Heat. 


[428- 


Specific 
heats 

Substances 

Specific 
heats 

0-1I379 

Tin  . 

.      0-05623 

0-10863 

Antimony 

.      0-05077 

0-10696 

Mercury  . 

.      0-03332 

0-09555 

Gold 

.      0-03244 

0-09515 

Platinum 

.      0-03244 

0-09391 

Bismuth  . 

.      0-03084 

0-05701 

Substances 

Iron 

Nickel 

Cobalt 

Zinc 

Copper 

Brass 

Silver 

These  numbers  represent  the  mean  specific  heats  between  0°  and  loo*^. 
Dulong  and  Petit's  investigations  have,  however,  shown  that  the  specific 
heats  increase  with  the  temperature.  Those  of  the  metals,  for  instance, 
are  greater  between  100°  and  200°  than  between  zero  and  100°,  and  are 
still  greater  between  200°  and  300°.  That  is  to  say,  a  greater  amount  of 
heat. is  required  to  raise  a  body  from  200°  to  250*^  than  from  100°  to  150° 
and  still  more  than  from  zero  to  50°.  For  silver,  the  mean  specific  heat 
between  0°  and  100°  is  00557,  while  between  0°  and  200°  it  is  o-o6ii. 
The  specific  heat  of  platinum  for  any  temperature  may  be  expressed  by 
the  formula  0-0328  +  0-0000042/,  where/  is  the  temperature;  and  that 
of  water  by  the  formula  i  +  0-00004/  +  o'oooooo()f^ . 

The  increase  of  specific  heat  with  the  temperature  is  greater  as  bodies 
are  nearer  their  fusing  point.  Any  action  which  increases  the  density 
and  molecular  aggregation  of  a  body,  diminishes  its  specific  heat.  The 
specific  heat  of  copper  is  diminished  by  its  being  hammered,  but  it  regains 
its  original  value  after  the  metal  has  been  again  heated. 

The  specific  heat  of  a  liquid  increases  with  the  temperature  much  more 
rapidly  than  that  of  a  solid.  Water  is,  however,  an  exception  ;  its  specific 
heat  increases  less  rapidly  than  does  that  of  solids. 

A  substance  in  the  liquid  state  has  a  greater  specific  heat  than  when  it 
is  sohd  ;  thus,  melted  tin  has  the  specific  heat  0-0637,  while  that  of  solid 
tin  is  only  005623.  The  specific  heat  of  liquid  bromine  is  o-iii,  that  of 
sohd  bromine  being  0-081.  The  difference  in  the  case  of  water  is  greater. 
Its  specific  heat  is  i,  that  of  ice,  according  to  Person,  being  0*504.  In 
the  gaseous  state  a  body  has  a  higher  specific  heat  than  in  the  liquid 
state. 

Pouillet  used  the  specific  heat  of  platinum  for  measuring  high  degrees 
of  heat.  Supposing  200  ounces  of  platinum  had  been  heated  in  a  furnace, 
and  had  then  been  placed  in  1000  ounces  of  water,  the  temperature  of 
which  it  had  raised  from  13°  to  20°.  From  the  formula  we  have  M  =200, 
m  =  1000  ;  ^  is  20,  and  /is  13.  The  specific  heat  of  platinum  is  0-033,  ^i^d 
we  have,  therefore,  from  the  equation, 

Mc(T-0  =  »2(^-0 

^  _  m{^-t)^'^C^  ^  7000  +132  ^  7132  ^  r.     o 

Wc  6-6  6-6^ 

It  is  found,  however,  that  the  specific  heat  of  platinum  at  tempera- 
tures of  about  1000  is  0-0373 ;  if  this  value,  therefore,  be  substituted  for 
c  in  the  above  equation, 

7-46 


-429]  Diilong  and  Petit' s  Law.  367 

By  this  method,  which  requires  great  skill  in  the  experimenter,  Pouillet 
determined  a  series  of  high  temperatures.  He  found,  for  example,  the 
temperature  of  melting  iron  to  be  I5cx)°  to  1600°  C. 

429.  I>ulong:  and  Petit's  law. — A  knowledge  of  the  specific  heat  of 
bodies  has  become  of  great  importance,  in  consequence  of  Dulong  and 
Petit's  discovery  of  the  remarkable  law,  that  the  product  of  the  specific 
heat  of  any  element  into  its  atomic  weight  is  a  constant  number,  a  law 
which  may  also  be  enunciated  by  saying  that  the  specific  heats  of  simple 
bodies  are  inversely  as  their  atomic  weights.  Thus,  taking  the  atomic 
weight  of  iron  at  28,  its  specific  heat  0-11379,  and  the  product  3'i86  ;  the 
atomic  weight  of  nickel  is  29-5,  its  specific  heat  0-10863,  product  3-204  ; 
the  atomic  weight  of  hydrogen  is  i,  its  specific  heat  3-2,  and  the  product 
is  3-2. 

Regnault,  who  determined  the  specific  heats  of  a  large  number  of 
elements  with  great  care,  confirmed  Dulong  and  Petit's  law,  but  he  found 
that  the  number,  instead  of  being  constant,  as  Dulong  and  Petit  had  sup- 
posed, varies  between  2*95  and  3-41.  These  variations  may  depend  partly 
on  the  difficulty  of  obtaining  the  elements  quite  pure,  and  partly  on  the 
errors  incidental  to  the  determination  of  the  specific  heats,  and  of  the 
equivalents.  But  the  specific  heats  of  bodies  vary  with  the  state  of  aggre- 
gation, and  also  with  the  limits  of  the  temperature  at  which  they  are  de- 
termined. Some,  such  as  potassium,  have  been  determined  at  tempera- 
tures very  near  their  fusing  points  ;  others,  like  platinum,  at  great  dis- 
tances from  these  points.  And,  doubtless,  the  principal  reason  of  the 
discrepancies  is  the  fact  that  the  determinations  have  not  been  made 
under  identical  physical  conditions,  and  at  temperatures  equally  distant 
from  the  fusing  point. 

The  equivalents  of  the  elements  represent  the  relative  weights  of  equal 
numbers  of  atoms  of  these  bodies,  and  the  product/^  of  the  specific  heat 
c  into  the  equivalent  p  is  the  ato7nic  specific  heat,  or  the  quantity  of  heat 
necessary  to  raise  the  temperature  of  the  same  number  of  atoms  by  one 
degree  ;  and  Dulong  and  Petit's  law  may  be  thus  expressed  :  the  sajne 
quantity  of  heat  is  needed  to  heat  a?i  atom  of  all  simple  bodies  to  the  same 
extent. 

The  atomic  heat  of  a  body,  when  divided  by  its  specific  heat,  gives  the 
equivalent  of  a  body.  Regnault  has  even  proposed  to  use  this  relation 
as  a  means  of  determining  the  equivalent,  and  it  certainly  is  of  great  ser- 
vice in  deciding  on  the  equivalent  of  a  body  in  cases  where  the  chemical 
relations  permit  a  choice  between  two  or  more  numbers. 

In  compound  bodies  the  law  also  prevails  ;  the  product  of  the  specific 
heat  into  the  equivalent  is  an  almost  constant  number,  which  varies,  how- 
ever, with  the  different  classes  of  bodies.  Thus,  for  the  class  of  oxides  of 
the  general  formula  RO,  it  is  11-30;  for  the  sesquioxides  R^O^  it  is 
27-15  ;  for  the  sulphides  RS,  it  is  18-88 ;  and  for  the  carbonates  RCO^,  it 
is  21-54. 

The  law  may  be  expressed  in  the  following  general  manner  :  With 
compounds  of  the  same  formula,  and  of  a  similar  chemical  constitution^ 


368  On  Heat.  [429- 

the  product  of  the  atomic  weight  into  the  specific  heat  is  a  constant  quan- 
tity.    This  includes  Dulong  and  Petit's  law  as  a  particular  case. 

430.  Specific  beat  of  compound  bodies. — In  order  to  deduce  the 
specific  heat  of  the  compound  from  that  of  its  elements,  M.  Woestyn  has 
made  the  following  hypothesis  :  he  assumes  that  an  element,  in  entering 
into  combination  with  others  to  form  a  compound  body,  retains  its  own 
specific  heat,  so  that  if  /,  p',  p",  ....  represent  the  atomic  weights  of 
the  elements,  and  P  that  of  the  compound  ;  c,  c',  c",  .  .  .  .  C,  the  cor- 
responding specific  heats,  while  n,  n',  n'\  ....  are  the  numbers  of  atoms 
of  these  simple  bodies  which  make  up  the  molecule  of  the  compound,  the 
relation  obtains  : 

VZ  =  npc-,n'p'c'-^n"p"c"+   .... 

M.  Wcestyn  has  found  that  the  results  obtained  by  calculating,  on  this 
hypothesis,  the  specific  heats  of  the  sulphides,  iodides,  and  bromides,  agree 
with  experimental  results. 

431.  Specific  heat  of  g-ases. — The  specific  heat  of  a  gas  may  be  re- 
ferred either  to  that  of  water  or  to  that  of  air.  In  the  former  case,  it  repre- 
sents the  quantity  of  heat  necessary  to  raise  a  given  weight  of  the  gas 
through  one  degree,  as  compared  with  the  heat  necessary  to  raise  the 
same  weight  of  water  one  degree.  In  the  latter  case  it  represents  the 
quantity  of  heat  necessary  to  raise  a  given  volume  of  the  gas  through  one 
degree,  compared  w^th  the  quantity  necessary  for  the  same  volume  of  air 
treated  in  the  same  manner. 

De  la  Roche  and  Bernard  determined  the  specific  heats  of  gases  in  refer- 
ence to  water  by  causing  known  volumes  of  a  given  gas  under  constant 
pressure,  and  at  a  given  temperature,  to  pass  through  a  spiral  glass  tube 
placed  in  water,  Fiom  the  increase  in  temperature  of  this  water,  and 
from  the  other  data,  the  specific  heat  was  determined  by  a  calculation 
analogous  to  that  given  under  the  method  of  mixtures.  The  same  physi- 
cists also  determined  the  specific  heats  of  different  gases  relatively  to  that 
of  air,  by  comparing  the  quantities  of  heat  which  equal  volumes  of  a  given 
gas,  and  of  air  at  the  same  pressure  and  temperature,  imparted  to  equal 
weights  of  water.  Subsequently  to  these  researches,  De  la  Rive  and 
Marcet  have  applied  the  method  of  cooling  to  the  same  determination  ; 
and  still  more  recently  Regnault  has  made  a  series  of  investigations  on 
the  calorific  capacities  of  gases  and  vapours,  in  which  he  has  adopted, 
but  with  material  improvements,  the  method  of  De  la  Roche  and  Bernard. 
He  has  thus  obtained  the  following  results  for  the  specific  heats  of  the 
various  gases  and  vapours,  compared  first  with  an  equal  weight  of  water 
taken  as  unity ;  secondly,  with  that  of  an  equal  volume  of  air,  referred,  as 
before,  to  its  own  weight  of  water  taken  as  unity. 

Specific  heats 
Equal 
weights 

Air    . 

f  Oxygen  . 
Simple  I  Nitrogen  . 
gases         i  Hydrogen 

I  Chlorine    . 


Equal 

Equal 

weights 

volumes 

0-2374 

0-2374 

0-2175 

0-2405 

0-2438 

0-2370 

3-4090 

0-2359 

0-I2I0 

0-2962 

-432] 


Latent  Heat  of  FiLsion. 


369 


Compound 
gases 


Vapours      ^ 


f  Binoxide  of  nitrogen 
I  Carbonic  oxide 
I  Carbonic  acid   . 

Hydrochloric  acid 

Ammonia . 

defiant  gas 
'Water 

Ether 

Alcohol     . 

Turpentine 
j  Bisulphide  of  carbon 
(^  Benzole 


Specific 

heats 

Equal 

Equal 

weights 

volumes 

0-2315 

0-2406 

0-2450 

0-2370 

0-2163 

0-3307 

0-1845 

0-2333 

0-5083 

0-2966 

0-4040 

0-4106 

0-4805 

0-2984 

0-4810 

1-2296 

0-4534 

O-717I 

0-5061 

2-3776 

0-1570 

0-4140 

0-3754 

I -01 14 

In  making  these  determinations  the  gases  were  under  a  constant  pres- 
sure, but  variable  volume ;  that  is,  the  gas  as  it  was  heated  could  expand, 
and  this  is  called  the  specific  heat  imder  constant  pressiire.  But  if  the 
gas  when  being  heated  is  kept  at  a  constant  volume,  its  pressure  or  elastic 
force  then  necessarily  increasing,  it  has  a  different  capacity  for  heat ;  this 
latter  is  spoken  of  as  the  specific  heat  under  constant  votume.  That  this 
latter  is  less  than  the  former  is  evident  from  the  following  considerations  : 

Suppose  a  given  quantity  of  gas  to  have  had  its  temperature  raised  t°, 
while  the  pressure  remained  constant,  this  increase  of  temperature  will 
have  been  accompanied  by  a  certain  increase  in  volume.  Supposing  now 
that  the  gas  is  so  compressed  as  to  restore  it  to  its  original  volume,  the 
result  of  this  compression  will  be  to  raise  its  temperature  again  to  a 
certain  extent,  say  t'°.  The  gas  will  now  be  in  the  same  condition  as 
if  it  had  been  heated,  and  not  been  allowed  to  expand.  Hence,  the  same 
quantity  of  heat  which  is  required  to  raise  the  temperature  of  a  given 
weight  of  gas,  f,  while  the  pressure  remains  constant  and  the  volume 
alters,  will  raise  the  temperature  /  +  /'  degrees  if  it  is  kept  at  a  constant 
volume  but  variable  pressure.  The  specific  heat,  therefore,  of  a  gas  at 
constant  pressure,  c^,  is  greater  than  the  specific  heat  under  constant 

C         t  4-  t' 

volume,  c,  and  they  are  to  each  other  as  /  +  /'  :  /,  that  is  -'  = . 

It  is  not  possible  to  determine  by  direct  means  the  specific  heat  of  gases 
under  constant  volume  with  even  an  approach  to  accuracy ;  and  it  has 
always  been  determined  by  some  indirect  method,  of  which  the  most  ac- 
curate is  based  on  the  theory  of  the  propagation  of  sound  (218).  The 
latest  determination  made  on  this  basis  gives  the  number  1-414  for  the 

value  of  -^. 
c 

432.  latent  heat  of  ftision.— Black  was  the  first  to  observe  that  dur- 
ing the  passage  of  a  body  from  the  solid  to  the  liquid  state,  a  quantity  of 
heat  disappears,  so  far  as  thermometric  effects  are  concerned,  and  which 
is  accordingly  said  to  become  latent. 

In  one  experiment  he  suspended  in  a  room  at  the  temperature  8-5°  two 
thin  glass  flasks,  one  containing  water  at  0°,  and  the  other  the  same  weight 

R3 


< 


370  071  Heat.  [432- 

of  ice  at  o°  At  the  end  of  half  an  hour  the  temperature  of  the  water  had 
risen  4°,  that  of  the  ice  being  unchanged,  and  it  was  lo^^  hours  before  the 
ice  had  melted  and  attained  the  same  temperature.  Now  the  temperature  of 
the  room  remained  constant,  and  it  must  be  concluded  that  both  vessels 
received  the  same  amount  of  heat  in  the  same  time.  Hence  21  times  as 
much  heat  was  required  to  melt  the  ice  and  raise  it  to  4°  as  was  sufficient 
to  raise  the  same  weight  of  water  through  4°.  So  that  the  total  quantity 
of  heat  imparted  to  the  ice  was  21  x  4  =  84,  and  as  of  this  only  4  was 
used  in  raising  the  temperature,  the  remainder,  80,  was  used  in  simply 
melting  the  ice. 

He  also  determined  this  latent  heat  by  immersing  119  parts  of  ice  at 
0°  in  135  parts  of  water  at  877°  C.  He  thus  obtained  254  parts  of  water 
at  11-6°  C.  Taking  into  account  the  heat  received  by  the  vessel  in  which 
the  liquid  was  placed,  he  obtained  the  number  79-44  as  the  latent  heat  of 
liquidity  of  ice. 

We  may  thus  say  : 

Water  at  0°  =  Ice  at  0°  +  latent  heat  of  liquefaction. 

The  method  which  Black  adopted  is  essentially  that  which  is  now  used 
for  the  determination  of  latent  heats  of  liquids ;  it  consists  in  placing  the 
substance  under  examination  at  a  known  temperature  in  the  water  (or 
other  liquid)  of  a  calorimeter,  the  temperattire  of  which  is  sufficient  to 
melt  the  substance  if  it  is  solid,  and  to  solidify  it  if  liquid,  and  when  uni- 
formity of  temperature  is  established  in  the  calorimeter,  this  temperature 
is  determined.  Thus,  to  take  a  simple  case,  suppose  it  is  required  to  de- 
termine the  latent  heat  of  liquidity  of  ice.  Let  M  be  a  certain  weight  of 
ice  at  zero,  and  m  a  weight  of  water  at  f  sufficient  to  melt  the  ice.  The 
ice  is  immersed  in  the  water,  and  as  soon  as  it  has  melted  the  final 
temperature  b°  is  noted.  The  water,  in  cooling  from  f  to  fc°  has  parted 
with  a  quantity  of  heat,  m{t  —  ' ).  If  x  be  the  latent  heat  of  the  ice,  it 
absorbs,  in  liquefying,  a  quantity  of  heat,  M;ir;  but,  besides  this,  the  water 
which  it  forms  has  risen  to  the  temperature  f^°,  and  to  do  so  has  required 
a  quantity  of  heat,  represented  by  M^.  We  thus  get  the  equation 
M:r  +  M0  =  m{t  -  O), 

from  which  the  value  of  x  is  deduced. 

By  this  method,  and  avoiding  all  sources  of  error,  M  M.  Desains  and  De 
la  Provostaye  found  that  the  latent  heat  of  the  liquefaction  of  ice  is  79*25  ; 
that  is,  a  pound  of  ice,  in  liquefying,  absorbs  the  quantity  of  heat  which 
would  be  necessary  to  raise  7925  pounds  of  water,  1°,  or,  what  is  the  same 
thing,  one  pound  of  water  from  zero  to  79*25° 

This  method  is  thus  essentially  that  of  the  method  of  mixtures;  the 
same  apparatus  may  be  used,  and  the  same  precautions  are  required  in 
the  two  cases.  In  determining  the  latent  heat  of  liquidity  of  most  solids, 
the  different  specific  heats  of  the  substance  in  the  sohd  and  in  the  liquid 
state  require  to  be  taken  into  account.  In  such  a  case,  let  ?n  be  the  weight 
of  the  water  in  the  calorimeter  (the  water  equivalents  of  the  calorimeter 
and  thermometer  supposed  to  be  included);  M  the  weight  of  the  substance 
operated  on;  /  the  original  and  n  the  final  temperature  of  the  calorimeter ; 


-433] 


Latent  Heat  of  Vapours. 


371 


T  the  original  temperature  of  the  substance  ;  C  its  melting  (or  freezing) 
point ;  C  the  specifit  heat  of  the  substance  in  the  solid  state  between  the- 
temperature  C  and  ^  ;  c\\.s  specific  heat  in  the  liquid  state  between  the 
temperatures  T  and  %  ;  and  let  L  be  the  latent  heat  sought. 

If  the  experiment  be  made  on  a  melted  substance  which  gives  out  heat 
to  the  calorimeter  and  is  thereby  solidified  (it  is  taken  for  granted  that  a 
body  gives  out  as  much  heat  in  sohdifying  as  it  absorbs  in  liquefying),  it  is 
plain  that  the  quantity  of  heat  absorbed  by  the  calorimeter,  w(y  -  /),  is 
made  up  of  three  parts  :  first,  the  heat  lost  by  the  substance  in  cooling 
from  its  original  temperature  T  to  the  solidifying  point  % ;  secondly,  the 
heat  given  out  in  solidification,  L ;  and,  thirdly,  the  heat  it  loses  in  sink- 
ing from  its  solidifying  point  C  to  the  temperature  of  the  water  of  the 
calorimeter.     That  is : 


ni{B  -t)  =  m[^(T-E)^  +  L  +  fr  -  ^)cj 


whence, 


in{^  -  i) 


-(T-^)c-{^-h)C. 


M.  Person,  who  has  made  several  researches  on  this  subject,  has 
obtained  the  following  numbers  for  the  latent  heats  of  fusion  of  several 
bodies : 


Water 

•     79-24 

Bismuth 

.     1264 

Nitrate  of  sodium 

.     62-97 

Sulphur 

•       9-37 

Zinc      . 

.     28-13 

Lead    .... 

•       5-37 

Silver   . 

.     21-07 

Phosphorus 

•       5-03 

Tin       .         .         . 

.     14-25 

D'Arcet's  alloy     . 

.       4-50 

Cadmium 

.     13-66 

Mercury 

.       2-83 

These  numbers  represent  the  number  of  degrees  through  which  a  pound 
of  water  would  be  raised  by  a  pound  of  the  body  in  question  in  passing 
from  the  liquid  to  the  solid  state ;  or,  what  is  the  same  thing,  the  number 
of  pounds  of  water  that  would  be  raised  1°  C.  by  one  of  the  bodies  in 
solidifying. 

On  modern  views  the  heat  expended  in  melting  is  consumed  in  moving 
the  atoms  into  new  positions;  the  work,  or  its  equivalent  in  heat  required 
for  this,  the  potential  energy  they  thus  acquire,  is  strictly  comparable  to 
the  expenditure  of  work  in  the  process  of  raising  a  weight.  When  the  liquid 
solidifies,  it  reproduces  the  heat  which  had  been  expended  in  liquefying 
the  solid ;  just  as  when  a  stone  falls  it  produces  by  its  impact  against  the 
ground  the  heat,  the  equivalent  -of  which  in  work,  had  been  expended  in 
raising  it,  and  a  similar  explanation  applies  to  the  latent  heat  of 
gaseification. 

433.  determination  of  tbe  latent  beat  of  vapours. — Liquids,  as  we 
have  seen  in  passing  into  the  state  of  vapour,  absorb  a  very  considerable 
quantity  of  heat,  which  is  termed  latent  heat  of  vaporisatio7i.  In  deter- 
mining the  heat  absorbed  in  liquids,  it  is  assumed  that  a  vapour,  in 
liquefying,  gives  out  as  much  heat  as  it  had  absorbed  in  becoming  con- 
verted into  vapour. 

The  method  employed  is  essentially  the  same  as  that  for  determining 


372 


On  Heat. 


[433 


the  specific  heat  of  gases.  Fig.  322  represents  the  apparatus  used  by 
M.  Despretz.  The  vapour  is  produced  in  a  retort,  C/  where  its  tempera- 
ture is  indicated  by  a  thermometer.  It  passes  into  a  worm  immersed  in 
cold  water,  where  it  condenses,  imparting  its  latent  heat  to  the  condensing 

water  in  the  vessel  B.  The  con- 
densed vapour  is  collected  in  a 
vessel.  A,  and  its  weight  represents 
the  quantity  of  vapour  which  has 
passed  through  the  worm.  The  ther- 
mometers in  B  give  the  change  of 
temperature. 

Let  M  be  the  weight  of  the  con- 
densed vapour,  T  its  temperature 
on  entering  the  worm,  which  is 
that  of  its  boiling  point,  and  x  the 
latent  heat  of  vaporisation.  Simi- 
larly, let  ni  be  the  weight  of  the 
condensing  water  (comprising  the 
weight  of  the  vessel  B  and  of  the 
worm  SS  reduced  in  water),  let  t° 
be  the  temperature  of  the  water  at  the  beginning,  and  fe°  its  temperature 
at  the  end  of  the  experiment. 

It  is  to  be  observed  that,  at  the  commencement  of  the  experiment,  the 
condensed  vapour  passes  out  at  the  temperature  /°,  while  at  the  conclusion 
its  temperature  is  6° ;  we  may,  however,  assume  that  its  mean  temperature 


Fig.  322. 


during  the  experiment  is 


The  vapour  M  after  condensation  has 


therefore  parted  with  a  quantity  of  heat  M  (  T  —     "*"  _  j  c,  while  the  heat 

disengaged  in  liquefaction  is  represented  by  M^.  The  quantity  of  heat 
absorbed  by  the  cold  water,  the  worm  and  the  vessel  is  m{ii  —  t).   Therefore, 

M;ir  +  M^^T  -  — -^^  c  =  m(0  -  /), 

from  which  x  is  obtained.  M.  Despretz  found  that  the  latent  heat  of 
aqueous  vapour  at  100°  is  540 ;  that  is,  a  pound  of  water  at  100°  absorbs 
in  vaporising  as  much  heat  as  would  raise  540  pounds  of  water  through 
1°.  M.  Regnault  found  the  number  537,  and  MM.  Favre  and  Silbermann 
538-8. 

As  in  the  case  of  the  latent  heat  of  water  we  may  say. 

Steam  at  100°  =  Water  at  100°  + latent  heat  of  gaseification. 

In  the  conversion  of  a  body  from  the  liquid  into  the  gaseous  state,  as  in 
the  analogous  process  of  fusion,  one  part  of  the  heat  is  used  in  increasing 
the  temperature  and  another  in  internal  work.  For  vaporisation  the 
greater  portion  is  consumed  in  the  internal  work  of  overcoming  the 
reciprocal  attraction  of  the  particles  of  liquid,  and  in  removing  them  to 
the  far  greater  distances  apart  in  which  they  exist  in  the  gaseous  state.  In 


-434]  Favre  and  Silhermanii  s  Caloi^imeter.  '^'ji 

addition  to  this  there  is  the  external  work — namely,  that  required  to  over- 
come the  external  pressure,  usually  that  of  the  atmosphere ;  and  as  the 
increase  of  volume  in  vaporisation  is  considerable,  this  pressure  has  to  be 
raised  through  a  greater  distance.  Vaporisation  may  take  place  without 
having  external  work  to  perform,  as  when  it  is  effected  in  vacuo  ;  but 
whether  the  evaporation  is  under  a  high  or  under  a  low  pressure,  on  the 
surface  of  a  liquid  or  in  the  interior,  there  is"  always  a  great  consumption 
of  heat  in  internal  work. 
'  434.  Favre  and  Silbermann's  calorimeter. — The  apparatus  (fig.  323) 
furnishes  a  very  delicate  means  of  determining  the  calorific  capacity  of 
liquids,  latent  heats  of  evaporation,  and  the  heat  disengaged  in  chemical 
actions. 

The  principal  part  is  a  spherical  iron  reservoir,  A,  full  of  mercury,  of 
which  it  holds  about  50  pounds,  and  represents,  therefore,  a  volume  of  more 
than  half  a  gallon.  On  the  left  there  are  two  tubulures,  B,  in  which  are 
fitted  two  sheet-iron  tubes  or  7tiuffles,  projecting  into  the  interior  of  the 
bulb.  Each  can  be  fitted  with  a  glass  tube  for  containing  the  substance 
experimented  upon.  In  most  cases  one  muffle  and  one  glass  tube  are 
enough ;  the  two  are  used  when  it  is  desired  to  compare  the  quantities  of 
heat  produced  in  two  different  operations.  In  a  third  verticle  tubulure,  C, 
there  is  also  a  muffle,  which  can  be  used  for  determining  calorific  capacities 
by  Regnault's  method  (425),  in  which  case  it  is  placed  beneath  the  r  of 
fig.  320. 

The  tubulure  d  contains  a  steel  piston  ;  a  rod,  turned  by  a  handle,  in, 
and  which  is  provided  with  a  screw  thread,  transmits  a  vertical  motion  to 
the  piston  ;  but,  by  a  peculiar  mechanism,  gives  it  no  rotatory  motion.  In 
the  last  tubulure  is  a  glass  bulb,  a,  in  which  is  a  long  capillary  glass  tube, 
bo,  divided  into  parts  of  equal  capacity. 

It  will  be  seen  from  this  description  that  the  mercury  calorimeter  is 
nothing  more  than  a  thermometer  with  a  very  large  bulb  and  a  capillary 
stem  :  it  is  therefore  extremely  delicate.  It  differs,  however,  from  a  ther- 
mometer in  the  fact  that  the  divisions  do  not  indicate  the  temperature  of 
the  mercury  in  the  bulb,  but  the  number  of  thermal  units  imparted  to  it 
by  the  substances  placed  in  muffle. 

This  graduation  is  effected  as  follows  : — By  working  the  piston  the 
mercury  can  be  made  to  stop  at  any  point  of  the  tube,  bo,  at  which  it  is 
desired  the  graduation  should  commence.  Having  then  placed  in  the 
iron  tube  a  small  quantity  of  mercury,  which  is  not  afterwards  changed,  a 
thin  glass  tube,  e,  is  inserted,  which  is  kept  fixed  against  the  buoyancy  of 
the  mercury  by  a  small  wedge  not  represented  in  the  figure.  The  tube 
being  thus  adjusted,  the  point  of  a  bulb  tube  (see  fig.  324)  is  introduced 
containing  water,  which  is  raised  to  the  boihng  point :  turning  the  position 
of  the  pipette,  then,  as  represented  on  n',  a  quantity  of  the  liquid  flows 
into  the  test  tube. 

The  heat  which  is  thus  imparted  to  the  mercury  makes  it  expand  ;  the 
column  of  mercury  in  bo  is  lengthened  by  a  number  of  divisions,  which  we 
shall  call  n.  If  the  water  poured  into  the  test  glass  be  weighed,  and  if  its 
temperature  be  taken  when  the  column  ^^is  stationary,  the  product  of  the 


374  On  Heat.  [434- 

weight  of  the  water  into  the  number  of  degrees  through  which  it  has 
fallen  indicates  the  number  of  thermal  units  which  the  water  gives  up  to 
the  entire  apparatus  (419).     Dividing  by  71  this  number  of  thermal  units, 


Fig.  323. 

the  quotient  gives  the  number  a  of  thermal  units  corresponding  to  a 
single  division  of  the  tube  bo. 

In  determining  the  specific  heat  of  liquids,  a  given  weight  M,  of  the 
liquid  in  question  is  raised  to  the  temperature  T,  and  is  poured  in  the 
tube  C.  Calling  the  specific  heat  of  the  liquid  C,  its  final  temperature  ^, 
and  n  the  number  of  divisions  by  which  the  mercurial  column  bo  has 
advanced,  we  have 

yicij-^)=nn,  from  which  c=  --    ^^— -. 

The  boards  represented  round  the  apparatus  are  hinged  so  as  to  form  a 
box,  which  is  lined  with  eider  down  or  wadding  to  prevent  any  loss  of 
heat.  It  is  closed  at  the  top  by  a  board,  which  is  provided  with  a  suitable 
case,  also  hned,  which  fits  over  the  tubulures  </and  a.  A  small  magnifying 
gla^s  which  slides  along  the  latter  enables  the  divisions  on  scale  to  be 
id  off. 

435.  Sxaxnples. — I.  What  weight  of  ice  at  zero  must  be  mixed  with  9 
^unds  of  water  at  20°  in  order  to  cool  it  to  5°.'* 


-436] 


Steam  Engines. 


375 


Let  M  be  the  weight  of  ice  necessary  ;  in  passing  from  the  state  of  ice 
to  that  of  water  at  zero,  it  will  absorb  80 M  thermal  units  ;  and  in  order  to 
raise  it  from  zero  to  5°,  5M  thermal  units  will  be  needed.    Hence  the  total 


Fig.   124,. 

heat  which  it  absorbs  is  80M  +  5M  :^85M.  On  the  other  hand,  the  heat 
given  up  by  the  water  in  cooHng  from  20°  to  5°  is  9  x  (20-5)  =  135, 
Consequently, 

85M  =  135  ;  from  which  M  =  1-588  pounds. 

II.  What  weight  of  steam  at  loo'^  is  necessary  to  raise  the  temperature 
of  208  pounds  of  water  from  14°  to  32°.? 

Let  p  be  the  weight  of  the  steam.  The  latent  heat  of  steam  is  540°,  and 
consequently  p  pounds  of  steam  in  condensing  into  water  give  up  a 
quantity  of  heat,  540/^,  and  form/  pounds  of  water  at  100°.  But  the  tem- 
perature of  the  mixture  is  32°,  and  therefore  p  gives  up  a  further  quantity 
of  heat /( 1 00  — 32)  =  68/^,  for  in  this  case  c  is  unity.  The  208  pounds  of 
water  in  being  heated  from  14°  to  32°  absorb  208(32  —  14)  =  3744  units. 
Therefore, 

540/ +  68/ =  3744  ;  from  which/ =  6" 1 58  pounds. 


CHAPTER     X. 


STEAM   ENGINES. 


436.  Steam  engrineis. — Steam  engines  are  machines  in  which  the  elastic 
force  of  aqueous  vapour  is  used  as  motive  power.  In  the  ordinary  engines 
the  alternate  expansion  and  condensation  of  steam  imparts  to  a  piston  an 
alternating  rectilinear  motion,  which  is  changed  into  a  circular  motion  by 
means  of  various  mechanical  arrangements. 

Every  steam  engine  consists  essentially  of  two  distinct  parts  :  the  ap- 
paratus in  which  the  vapour  is  produced,  and  the  engine  proper.  We 
shall  tirst  describe  the  former. 


3;6 


On  Heat. 


[437- 


437.  Steam  boiler. — The  boiler  is  the  apparatus  in  which  steam  is 
generated.  Fig.  325  represents  a  side  view,  and  fig.  326  a  cross  section 
of  a  cylindrical  boiler,  such  as  are  used  for  fixed  engines  ;  those  of  loco- 
motives and  of  steam  vessels  are  very  different. 

It  is  a  long  wrought-iron  cyhnder,  PQ,  with  curved  ends,  beneath 
which  there  are  two  smaller  cylinders,  BB,  of  the  same  material,  and 


f'ig-  325- 

communicating  with  the  boiler  by  two  tubes.  Only  one  of  these  cylinders 
is  represented  in  the  figure.  They  are  called  heaters,  and  are  quite  full 
of  water,  while  the  boiler  is  only  about  half  full. 

In  order  to  multiply  the  heating  surface,  and  utilise  all  the  heat  carried 
off  by  the  products  of  combustion,  the  latter  are  made  to  circulate  through 
brick  conduits  which  surround  the  sides  of  the  heaters  and  of  the  boiler. 
These  conduits,  which  are  called  flues,  divide  the  furnace  into  two 
horizontal  compartments,  FF  and  DCD  (fig,  326).  The  upper  compart- 
ment is  moreover  divided  into  three  distinct  flues,  D,  C,  D,  by  two  vertical 
divisions,  which  are  not  represented  in  the  drawing,  and  which  correspond 
to  the  two  sides  of  the  boiler.  The  flame  and  the  products  of  com- 
bustion, which  first  sweep  below  the  heaters  from  back  to  front,  return  in 
the  opposite  direction  by  the  central  flues  C  ;  then,  dividing,  they  pass 
by  the  lateral  flues  into  the  chimney  K,  where  they  are  lost  in  the  at- 
mosphere. 


438] 


Steam  Engines. 


'377 


Explanation  of  Figures  325  and  326. 

E.  Float  of  the  safety  whistle,  s. 
FF.  Furnace. 

F.  Float,  to  show  the  level  of  the  water  in  the  boiler.  It  consists  of  a 
rectangular  piece  of  stone  partially  immersed  in  water,  as  seen  through 
the  space  which  is  represented  as  left  open.  The  stone,  which  is  sus- 
pended at  one  end  of  a  lever,  is  kept  poised  by  the  loss  of  weight  which 
it  sustains  by  immersion  in  the  water,  and 
by  a  weight,  «,  at  the  other  end  of  the 
lever.  As  long  as  the  water  is  at  the 
desired  height,  the  lever  whicli  sustains  the 
float  remains  horizontal  ;  but  it  sinks 
when  there  is  too  little  water,  and  rises 
in  the  contrary  direction  when  there  is 
too  much.  Guided  by  these  indications, 
the  stoker  can  regulate  the  supply  of 
water. 

K.  Chimney,    which    has    usually    a 
great  height  so  as  to  increase  the  draught. 

S.   Safety    valve,     described     under 
Papin's  digester  (347). 

T.  Man-hole,  an  aperture  by  which 
the  boiler  can  be  repaired  and  cleansed 
This  is  self-closing,  and  consists  of  a 
cover  fitting  against  the  inside  edges.  It- 
is  kept  in  position  by  a  screw,  which  also 
presses  it  strongly  against  the  sides.  Thus 
the  greater  the  internal  pressure,  the  more  firmly  is  the  cover  pressed 
against  the  sides,  and  the  more  completely  does  it  close. 

a.  Counterpoise  of  the  float. 

m.  Tube  which  leads  the  steam  to  the  tube  c  of  the  valve  chest. 

n.  Tube  for  the  admission  of  feed  water  for  the  boiler. 

s.  Safety  whistle — so  called  because  it  gives  a  whistle  when  there  is 
not  enough  water  in  the  boiler  ;  a  circumstance  which  might  produce  an 
accident.  As  long  as  the  level  of  the  water  is  not  too  low  in  the  boiler, 
the  steam  does  not  pass  into  the  whistle  ;  but  if  the  level  sinks  below  a 
certain  point,  a  small  float,  E,  which  closes  the  bottom  of  the  whistle 
sinks,  and  the  steam  escapes  ;  in  so  doing  it  grazes  against  the  edge  of  a 
thin  metal  plate,  which  it  sets  in  vibration,  and  produces  a  sharp  and 
loud  sound.  This  steam  whistle  is  the  sound  frequently  heard  upon 
railways  ;  it  is  used  as  a  signal  in  locomotives. 

438.  Double  action,  or  "Watt's  engrine. — In  the  double  acting  steam 
engine,  the  steam  acts  alternately  above  and  below  the  piston.  It  is  also 
known  as  Waffs  engine,  from  its  illustrious  inventor. 

We  shall  first  give  a  general  idea  of  this  engine,  and  shall  then  describe 
each  part  separately.     On  the  left  of  the  fig.  327  is  the  cylinder  which 


Fig.  326. 


378 


071  Heat, 


[438- 


receives  the  steam  from  the  boiler.  A  'part  of  its  side  is  represented 
as  being  left  open,  and  a  piston,  P,  can  be  seen  which  is  moved  alter- 
nately up  and  down  by  the  pressure  of  the  steam  above  or  below  the 
piston.  By  the  piston  rod  A  this  motion  is  transmitted  to  a  huge  iron 
lever,  L,  called  the  beam^  which  is  supported  by  four  iron  columns.     The 


Fig.  327. 

beam  transmits  its  motion  to  a  connecting  rod,  I,  working  on  a  crank, 
K,  to  which  it  imparts  a  continuous  rotatory  motion.  The  crank  is  fixed 
to  a  horizontal  shaft,  which  turns  with  it,  and,  by  means  of  wheels  or 
endless  bands,  this  shaft  sets  in  motion  various  machines,  such  as 
spinning  frames,  saw  mills,  lathes,  etc. 

On  the  left  of  the  cylinder  is  a  valve  chest,  where,  by  a  mechanism 
which  will  presently  be  described,  the  steam  passes  alternately  above 
and  below  the  piston.  Now,  after  its  action  on  either  face  of  the  piston, 
it  must  disappear,  for  otherwise  a  pressure  would  be  exerted  in  two 
opposite  directions,  and  the  piston  would  remain  at  rest.  To  effect  this 
the  steam,  after  it  has  acted  on  one  side  of  the  piston,  passes  into  a  vessel, 
O,  called  the  condenser,  into  which  cold  water  is  injected.  It  is  almost 
completely  condensed  there,  and  consequently  the  pressure  ceases  in 


i 


-438]  Double-acting  Steam  Engine.  379 

that  part  of  the  cylinder  which  is  in  communication  with  the  condenser, 
and  as  there  is  now  pressure  on  only  one  face  of  the  piston,  it  either  rises 
or  sinks. 

The  use  of  the  condenser  depends  upon  Watt's  law  of  vapours  (337), 
that  when  two  vessels  communicating  with  each  other,  and  containing 
saturated  vapour,  are  at  different  temperatures,  the  tension  is  the  same 
in  both  vessels,  and  is  that  corresponding  to  the  temperature  of  the  colder 
vessel. 

The  injected  water  is  rapidly  heated  by  the  condensation  of  the  steam, 
and  must  be  constantly  renewed.  This  is  effected  by  means  of  two 
pumps  ;  one  M,  is  called  the  air  pump,  and  pumps,  from  the  condenser, 
the  heated  water  which  it  contains,  and  also  the  air  which  was  dis- 
solved in  the  water  of  the  boiler,  and  which  passes  with  the  steam  into 
the  cylinder  and  condenser  ;  the  other,  R,  is  called  the  cold  water 
pump,  and  forces  cold  water  from  a  well,  or  from  a  river,  into  the  con- 
denser. 

A  third  pump,  O,  which  is  called  the  feed  pump,  utilises  the  heated 
water  by  forcing  it  from  the  condenser  into  the  boiler. 

Double  acting  steam  engine. 

A.  Piston  rod  connected  with  a  parallel  motion,  and  serving  to  trans- 
mit to  the  beam  the  upward  and  downward  motion  of  the  piston. 

B.  Rod  fixed  to  the  cylinder,  or  elsewhere,  and  supporting  the  guiding 
arm  or  radius  rod,  C. 

C.  Double  guiding  arm  directing  the  parallel  motion. 

DDDE.  Rods  forming  at  the  end  of  the  beam  a  parallel  motion,  to 
which  is  fixed  the  piston  rod,  and  the  object  of  which  is  to  guide  the 
motion  of  this  rod  in  a  straight  line. 

F.  Rod  of  the  air  pump ^  which  removes  from  the  condenser  the  air  and 
heated  water  which  it  contains. 

G.  Rod  of  the  feed  pump,  which  forces  into  the  boiler  through  the 
tube  S  the  heated  water  pumped  from  the  condenser. 

H.  Rod  of  the  cold  water  pump,  which  supplies  the  cold  water  neces- 
sary for  condensation. 

I.  Cotmecting  rod,  which  transmits  the  motion  of  the  beam  to  the 
crank. 

K.  Crank,  which  imparts  the  motion  of  the  rod  to  the  horizontal 
shaft. 

L.  Beam,  which  moves  on  an  axle  in  its  middle,  and  transmits  the 
motion  of  the  piston  to  the  conneciing  rod  I. 

M.  Cylinder  of  the  air  pump,  in  connection  with  the  condenser  O. 

N.  Reservoir  for  the  heated  water  pumped  by  the  air  pump  from  the 
condenser. 

O.  Condenser  into  which  cold  water  is  injected  to  condense  the  steam 
after  it  has  acted  on  the  piston. 

P.  Metallic  piston,  moving  in  a  cast-iron  cylinder  ;  this  piston  receives 
the  direct  pressure  of  the  steam,  and  transmits  the  motion  to  all  parts  of 
the  machine^ 


38o  On  Heat.  [438- 

O.  Feeding  force  pump,  which  sends  the  water  into  the  boiler. 

R.  Cold  water  pump. 

S.  Pipe  by  which  the  hot  water  from  the  feed  pump  passes  into  the 
boiler. 

T.  Pipe  by  which  cold  water  from  the  reservoir  of  the  pump,  R,  passes 
into  the  condenser. 

U.  Pipe  by  which  the  steam  from  the  cylinder  passes  into  the  con- 
denser after  acting  on  the  piston. 

V.  Large  iron  wheel,  called  the  fly  wheels  which,  by  its  inertia,  serves 
to  regulate  the  motion,  especially  when  the  piston  is  at  the  top  or  bottom 
of  its  course,  and  the  crank  K  at  its  dead  points. 

Y.  Bent  lever  which  imparts  the  motion  of  the  eccentric  e  to  the  slide 
valve  b. 

Z.  Eccentric  rod. 

a.  Aperture  which  communicates  both  with  the  upper  and  lower  part 
•of  the  cylinder,  according  to  the  position  of  the  slide  valve,  and  by  which 
steam  passes  into  the  condenser  through  the  tube  U. 

b.  Rod  transmitting  motion  to  the  slide  valve.,  by  which  steam  is  alter- 
nately admitted  above  and  below  the  piston.  This  will  be  described  in 
greater  detail  in  the  next  article. 

c.  Aperture  by  which  steam  reaches  the  valve  chest. 

d.  Stuffing  box,  in  which  the  piston  rod  works  without  giving  exit  to 
the  steam. 

e.  Eccentric,  fixed  to  the  horizontal  shaft,  and  rotating  in  a  collar,  to 
which  the  rod  Z  is  attached. 

m.  Rod  which  connects  the  rod  of  the  slide  valve  b  to  the  bent  lever 
Y,  and  to  the  eccentric. 

The  lower  part  of  the  figure  does  not  exactly  represent  the  usual 
arrangement  of  the  pumps.  The  drawing  has  been  modified  in  order 
more  clearly  to  show  how  these  parts  work,  and  their  connection  with 
each  other. 

439.  Distribution  of  the  steam.  Eccentric.— Fig.  328  represents 
the  details  of  the  valve  chest  or  arrangement  for  the  distribiitioii  of 
steajn.  The  steam  from  the  boiler  passes  by  a  pipe,  c,  into  a  cast-iron 
box  on  the  side  of  the  cylinder.  In  the  sides  of  the  cylinder  there  are 
three  openings  or  ports,  11,  n,  and  a,  of  which  m  communicates  by  an 
internal  conduit  with  the  upper  part  of  the  cylinder,  and  n  with  the 
lower  part.  A  slide,  /,  works  over  these  three  orifices.  It  is  fixed  to  a 
vertical  rod,  b,  which  is  jointed  at  m  to  a  larger  rod,  d,  and  receives  an 
upward  and  downward  motion  from  the  bent  lever  yoS,  attached  to  the 
eccentric  rod.  When  the  slide  is  at  the  top  of  its  course,  as  shown  in 
the  figure,  the  steam  passes  through  n  into  the  lower  part  of  the  cylinder, 
while  the  steam  cannot  pass  through  the  orifice  n,  for  it  is  covered  by  the 
slide. 

But  the  vapour  which  is  above  the  piston  passes  through  //  and  through 
a  into  the  hole  r,  from  which  it  enters  the  condenser.  The, piston  is  then 
only  pressed  upwards,  and  therefore  ascends. 

When  the  slide  is  at  the  bottom  of  its  course,  the  steam  enters  the 


-440] 


Single  Acting  Steam  Engine. 


381 


cylinder  by  the  aperture  ii,  and  passes  from  the  lower  part  of  the  cylinder 
into  the  condenser  by  n  and  a.  The  piston  consequently  descends,  and 
this  motion  goes  on  for  each  displacement  of  the  slide. 

The  upward  and  downward  motion  of  the  slide  is  effected  by  means 
of  the  eccentric.     This  is  a  circular  piece,  E,  fixed  to  the  horizontal  shaft, 


Fig.  328. 


A,  but  in  such  a  manner  that  its  centre  does  not  coincide  with  the  axis 
of  this  shaft.     The  eccentric  works  with  gentle  friction  in  a  collar,  C,  to 
which  the   rod  ZZ   is   fixed.     The  collar,  without  rotating,  follows  the 
motion  of  the  eccentric,  and  receives  an  alternating  motion  in  a  horizontal 
direction,  which  it  communicates  to  the  lever  S^/,  and  from  thence  to  the 
slide. 
^      /■    440.  Singrle  acting:  engine. — In  a  single  acting  e7igine  the  steam  only 
\«^acts  on  the  upper  face  of  the  piston  ;  a  counterpoise  fixed  to  the  other 
/    end  of  the  beam  makes  the  piston  rise.     These  engines  were  first  con-. 
'        structed  by  Watt  for  pumping  water  from  mines,  and  are  still  used  for 
this  purpose  in  Cornwall,  and  also  for  the  supply  of  water  to  towns.     They 
are  preferred  for  these  purposes  from  their  simplicity,  but  for  other  pur- 
poses they  have  been  superseded  by  the  double  acting  engine. 

Fig.  329  represents  a  section.  The  beam  BB  is  of  wood,  with  wooden 
segments  at  each  end,  to  which  chains  are  attached.  One  of  these 
chains  is  connected  with  the  piston,  and  the  other  with  the  pump. 
On  the  right  of  the  cylinder  A  is  a  valve  chest,  C,  into  which  steam 
passes  from  the  boiler  by  the  tube  T.      There  are  three  valves,  ?w,  ft,  and 


382 


On  Heat. 


[440 


0,  on  a  vertical  rod.     The  valves  m  and  o  open  upwards,  the  valve  n 
downwards. 

When  m  and  o  are  open,  as  shown  in  the  drawing,  the  steam  passes 
through  the  tubs  T,  over  the  piston,  while  the  steam,  which  is  below,  is 
forced  into  the  condenser  through  the  tube  M.     The  piston  therefore 


/\ 


Fig.  329. 

descends.  The  rod,  on  which  are  the  valves,  ?;/,  n,  and  0^  is  connected 
with  a  bent  lever,  dck^  moving  on  a  joint  c.  This  bent  lever  closes  and 
opens  the  valves.  For  this  purpose  there  are  two  catches,  b  and  a,  on  a 
rod,  F,  connected  with  the  beam,  by  means  of  which  the  rod  works 
against  the  end  of  the  bent  lever.  From  the  arrangement  of  the  valves, 
as  represented  in  the  drawing,  the  piston  sinks  and  carries  with  it  the 
rod  F,  and,  consequently,  the  catch  strikes  against  the  lever,  and  makes 
it  sink  at  the  same  time  as  the  rod  dino  ;  the  valves  vt  and  o  then  close, 
while  n  opens. 

The  communication  with  the  boiler  as  well  as  with  the  condenser  is 
now  cut  off,  and  the  steam  which  has  made  the  piston  sink  passes  below 
by  the  pipe  C.  As  it  presses  equally  on  both  faces,  the  piston  would 
remain  at  rest,  but  it  rises  in  consequence  of  the  traction  of  the  weight  Q. 
Very  little  force  is  necessary  for  this;  for  the  pump,  the  rod  of  which 
is  fixed  to  the  weight  Q,  only  requires  power  when  its  piston  rises.  When 
the  piston  P  is  at  the  top  of  its  course,  the  catch  a  strikes  in  turn  against 


-441]  Locomotive  Engines.  383 

the  lever  k^  raises  the  rod  dmo^  the  steam  again  passes  to  the  top  of  the 
piston,  which  again  descends,  and  so  on. 

441.  locomotives. — Locomotive  engines,  or  simply  locomotives,  are 
steam  engines  which,  mounted  on  a  carriage,  propel  themselves  by 
transmitting  their  motion  to  wheels. 

The  parallel  motion,  the  beam,  and  the  fly  wheel  form  no  part  of  a 
locomotive  The  principal  parts  are  the  framework,  the  fire  box,  the 
casing  of  the  boiler,  the  smoke  box,  the  steam  cylinders,  with  their  valves, 
the  driving  wheels,  and  the  fi^ed pump. 

The  framework  is  of  oak,  and  rests  on  the  axles  of  the  wheels.  Fig. 
330  represents  the  driver  of  the  locomotive  in  the  act  of  opening  the 
regulator  valve  I,  placed  in  the  upper  part  of  the  steam  dome.  In  the 
lower  part  of  this  is  the  fire  box,  from  whence  the  flame  and  the  pro- 
ducts of  combustion  pass  into  the  smoke  box  Y,  and  then  into  the 
chimney  Q,  after  having  previously  traversed  125  brass  fire  tubes  which 
pass  through  the  boiler.  The  boiler,  which  connects  the  fire  box  with 
the  smoke  box,  is  made  of  iron,  and  is  cylindrical.  It  is  cased  with 
staves  of  mahogany,  which,  being  a  bad  conductor,  prevents  its  cooling 
too  rapidly.  The  steam  passes  from  the  boiler  into  two  cylinders  placed 
on  either  side  of  the  smoke  box.  There,  by  means  of  a  steam  chest 
similar  to  that  already  described,  it  acts  alternately  on  the  two  faces  of 
the  piston,  the  motion  of  which  is  transmitted  to  the  axle  of  the  large 
driving  wheels.  This  arrangement  of  the  slide  valve  is  not  seen  in 
tjie  drawing,  because  it  is  placed  under  the  frame  between  the  two 
cylinders.  After  having  acted  on  the  pistons,  the  steam  is  forced 
through  the  blast  pipe  E  into  the  chimney,  thus  increasing  the  draught. 

The  motion  of  the  pistons  is  transmitted  to  the  two  large  driving 
wheels  by  two  connecting  rods,  which,  by  means  of  cranks,  connect  the 
piston  rods  with  the  axles  of  the  wheels.  The  alternating  motion  of  the 
slide  valve  is  effected  by  means  of  eccentrics  placed  on  the  axles  of  the 
large  wheels. 

The  feeding  or  supply  of  water  to  the  boiler  is  obtained  by  means 
of  two  pumps,  placed  under  the  frame,  and  moved  by  eccentrics.  These 
pumps  suck  the  water  from  a  reservoir  placed  on  the  tender,  which  is 
a  carriage  attached  to  the  locomotive  for  carrying  the  necessary  water 
and  coal. 

Expla7iation  of  Figtire  330. 

A.  Copper  tube,  into  which  steam  passes  by  the  extremity  I,  and 
which,  dividing  at  the  other  end  into  two  branches,  conveys  the  steam  to 
the  two  cyhnders  which  contain  the  pistons. 

B.  Handle  of  the  lever,  by  which  the  motion  is  reversed.  It  imparts 
motion  to  a  rod,  C,  which  communicates  with  the  steam  chest. 

C.  Rod  by  which  the  motion  is  reversed. 

D.  Lower  part  of  the  fire  box  and  ash  pan. 

E.  Escape  pipe  for  the  steam  after  acting  on  the  pistons. 

F.  Iron  cyhnder  containing  a  piston,  P.   There  is  one  of  these  on  each 


384 


On  Heat. 


[441- 


side  of  the  engine,  and  the  one  in  front  is  represented  as  being  left  open 
in  order  that  the  piston  may  be  seen. 

G.  Rod  which  opens  the  regulator  valve  I,  in  order  to  allow  the  steam 
to  pass  into  the  tube  A.  In  the  drawing  the  driver  holds  in  his  hand  the 
lever  which  moves  this  rod. 


H.  Cock  for  blowing  off  water  from  the  boiler. 

I.  Regulator  valve,  which  is  opened  and  closed  by  hand,  so  as  to  regu- 
late the  quantity  of  steam  passing  into  the  cylinders. 


-442]  Locomotive  Engines.  385 

K.  Large  rod  connecting  the  head  of  the  piston  rod  with  the  crank  M 
of  the  driving  wheel. 

L.  Lamp  for  use  by  night. 

M.  Crank,  which  transmits  the  motion  of  the  piston  to  the  axle  of  the 
large  wheel. 

N.  Coupling  iron,  by  which  the  tender  is  attached. 

O.  Fire  door,  by  which  coke  is  introduced. 

P.  Metallic  piston,  the  rod  of  which  is  connected  with  the  rod  K. 

O.  Chimney,  by  which  both  steam  and  smoke  escape. 

R,  R.  Feed  pipes,  through  which  the  water  in  the  tender  passes  to  two 
force  pumps,  which  are  not  shown  in  the  drawing. 

S.  Guard  for  removing  obstructions  on  the  rails. 

T,  T.  Springs  on  which  the  engine  rests. 

U,  U.  Iron  rails  fixed  in  chairs  on  wooden  sleepers. 
•  V.  Frame  of  the  stuffing  box  of  the  cylinder. 

X,  X.  Cylindrical  boiler,  covered  with  mahogany  staves,  which,  from 
their  bad  conductivity,  hinder  the  loss  of  Keat.  The  level  of  the  water  is 
just  below  the  tube  A.  In  the  water  are  the  tubes  aa,  through  which  the 
smoke  and  flames  pass  into  the  smoke  box. 

Y.  Smoke  box,  in  which  the  fire  tubes  a  terminate. 

Z,  Z.  Fire  box,  covered  by  a  dome,  into  which  the  steam  passes. 

a.  Brass  tubes,  of  which  there  are  125,  open  at  both  ends,  and  termi- 
nating at  one  end  in  the  fire  box,  and  at  the  other  in  the  smoke  box. 
These  tubes  transmit  to  the  water  the  heat  of  the  fire. 

bb.  Toothed  segment,  placed  on  the  side  of  the  fire  box,  and  in  which 
the  arm  of  the  lever  B  works.  When  the  handle  is  pushed  forward  or 
pulled  back  as  far  as  it  can  go,  the  engine  is  in  full  forward  or  backward 
gear  respectively  ;  the  intermediate  teeth  give  various  rates  of  expansion 
in  backward  and  forward  motion,  the  middle  tooth  being  a  dead  point. 

e.  Cases  containing  springs  by  which  the  safety  valves  /  are  regulated. 

g.  Signal  whistle. 

/.  Safety  valves. 

;/z,  /«.  Steps. 

n.  Glass  tube,  showing  the  height  of  water  in  the  boiler. 

r,  r.  Guiding  rods,  for  keeping  the  motion  of  the  pistons  in  a  straight 
line. 

^,  /.  Blowing-off  taps,  for  use  when  the  pistons  are  in  motion. 

V.  Rod  by  which  motion  is  transmitted  to  these  taps. 

442.  Reaction  machines.  Eolipyle, — In  reaction  machines  steam 
acts  by  a  reactive  force  like  water  in  a  hydraulic  tourniquet  (205).  The 
idea  of  these  machines  is  by  no  means  new ;  Hero  of  Alexandria,  who 
invented  the  fountain  which  bears  his  name,  described  the  following 
apparatus,  which  is  known  as  the  reaction  machine. 

It  consists  of  a  hollow  metaUic  sphere  which  rotates  on  two  pivots 
(fig.  331).  At  the  ends  of  a  diameter  are  two  tubulures,  pierced  laterally 
in  opposite  directions  by  orifices  through  which  vapour  escapes.  Water 
is  introduced  into  this  apparatus  by  heating  it,  and  then  allowing  it  to 
cool  in  cold  water.     If  the  apparatus  be  then  heated  to  boihng,  the  vapour 

s 


386 


On  Heat. 


[442- 


disengaged  imparts  to  it  a  rotatory  motion,  which  is  due  to  the  pressure 
of  the  vapour  on  the  side  opposite  to  that  from  which  it  escapes. 

Numerous  attempts  have  been  made  to  use  this  reactive  force  of  the 
vapour  on  a  large  scale  as  a  motive  force,  and  endeavours  have  also  been 


Fig.  331- 

made  to  cause  steam  to  act  by  impulse  by  directing  a  jet  of  steam  on  the 
float  board  of  a  paddle  wheel  ;  but  in  both  cases  the  steam  exerts  by  no 
means  so  great  an  effect  as  is  obtained  when  it  acts  by  expansion  on  a 
piston. 

443.  Various  kinds  of  steam  engrines. — A  low  pressure  engine,  is  one 
in  which  the  pressure  of  the  vapour  does  not  much  exceed  an  atmosphere  : 
and  a  high  pressure  engine  is  one  in  which  the  pressure  of  the  steam 
usually  exceeds  this  amount  considerably.  Low  pressure  engines  are 
mostly  condensing  engi7ies  ;  in  other  words,  they  generally  have  a  con- 
denser where  the  steam  becomes  condensed  after  having  acted  on  the 
piston  :  on  the  other  hand,  high  pressure  engiries  are  frequently  without  a 
condenser  ;  the  locomotive  is  an  example. 

If  the  communication  between  the  cylinder  and  boiler  remains  open 
during  the  whole  motion  of  the  piston,  the  steam  retains  essentially  the 
same  elastic  force,  and  is  said  to  act  without  expatision  ;  but  if,  by  a 
suitable  arrangement  of  the  slide  valve,  the  steam  ceases  to  pass  into 
the  cylinder  when  the  piston  is  at  |  or  |  of  its  course,  then  the  vapour 
expands ;  that  is  to  say,  in  virtue  of  its  elastic  force,  which  is  due  to 
the  high  temperature,  it  still  acts  on  the  piston  and  causes  it  to  finish 
its  course.  Hence  a  distinction  is  made  between  expa?iding  and  710 n- 
expanding  engines. 

444.  "Work  of  an  engine.  Borse-power. — The  work  of  an  engine  is 
measured  by  the 

Mean  pressure  on  piston  x  area  of  piston  x  length  of  stroke. 
In  England  the  unit  of  work  is  the  foot-pou7td\  that  is,  the  work  per- 


I 


-446]  Woj'k  of  an  Engine.  387 

formed  in  raising  a  weight  of  one  pound  through  a  height  of  a  foot. 
Thus,  to  raise  a  weight  of  14  pounds  through  a  height  of  20  feet  would 
require  280  foot-pounds.  In  France  the  kilogrammetre  is  used;  that  is, 
the  work  performed  in  raising  a  kilogramme  through  a  metre.  This  unit 
corresponds  to  7*233  foot-pounds. 

The  rate  of  work  in  machines  is  the  amount  of  work  performed  in  a 
given  time;  a  second  or  an  hour,  for  example.  In  England  the  rates  of 
work  are  compared  by  means  of  horse-power,  which  is  a  conventional 
unit,  and  represents  550  foot-pounds  in  a  second.  In  France  a  similar 
unit  is  used,  called  the  chevalvapeur,  which  represents  the  work  performed 
in  raising  75  kilogrammes  through  one  metre  in  a  second.  It  is  equal  to 
about  542  foot-pounds  per  second. 

The  useful  effect  of  an  engine  is  only  about  0*5  to  07  of  the  calculated 
theoretical  effect;  the  unavoidable  resistance  and  the  motion  of  the 
various  parts  of  the  machine  consume  a  portion.  If  the  work  be  calcu- 
lated from  the  heat  known  to  be  produced  from  a  given  weight  of 
combustible,  the  discrepancy  is  far  greater.  The  best  Cornish  engines 
do  not  give  more  than  14  per  cent,  of  the  theoretical  yield  of  the  com- 
bustible. 

445.  Kirn's  experiments. — Hirn  made  an  important  series  of  experi- 
ments in  order  to  determine  by  means  of  the  steam  engine  the  mechani- 
cal equivalent  of  heat.  On  the  one  hand,  steam  of  known  temperature 
and  pressure  was  allowed  to  act  upon  the  steam  engine,  which  was 
one  of  100  horse-power.  The  amount  of  heat  contained  in  it  could  be 
readily  calculated.  The  amount  of  work  which  the  engine  performed 
was  also  determined  by  means  of  a  dynamometer.  The  steam  was 
ultimately  condensed  in  the  condenser,  and  the  amount  of  heat  could 
readily  be  measured  by  known  calorimetrical  methods.  It  was  found 
in  all  cases  less  than  that  which  originally  passed  into  the  engine,  and 
the  difference  represented  the  amount  of  heat  which  had  been  converted 
into  work  in  the  engine;  in  Hirn's  experiments,  for  every  unit  of  heat 
which  had  disappeared,  1354  units  of  work  had  been  performed ;  a  result, 
considering  the  difficulty  of  the  experiments,  closely  agreeing  with  the 
best  determinations  (467). 

446.  Gas  eng-ines. — Numerous  attempts  have  recently  been  made  to 
replace  the  expansive  force  of  steam  by  that  of  heated  air.  Yet  they 
have  hitherto  been  unsuccessful,  owing  to  practical  difficulties;  for  either 
the  temperature  had  to  be  so  high  that  it  was  impossible  to  keep  the 
valves  and  the  stuffing  boxes  tight,  or  else  it  was  necessary  greatly  to  in- 
crease the  dimensions  of  the  cylinder,  in  comparison  with  those  of  steam 
engines  of  the  same  power. 

In  gas  engines  a  mixture  of  coal  gas  and  of  atmospheric  air  contained 
in  a  cylinder  is  ignited  by  the  electrical  spark ;  and  the  expansive  force 
of  the  heated  gas  thus  produced  moves  the  piston.  As  the  combustion 
of  the  gaseous  mixture  takes  place  within  the  cylinder  itself,  the  loss  of 
heat  is  the  smallest.  They  have  moreover  the  advantage  of  requiring  no 
special  fire,  but  can  be  set  up  and  worked  in  any  space  provided  with 
gas.     Yet  hitherto  these  apparatus  have  only  succeeded  on  a  small  scale. 


388  On  Heat  [447- 


CHAPTER  XI. 

SOURCES   OF   HEAT  AND   COLD. 

447.  Bifferent  sources  of  heat. — The  following  different  sources  of 
heat  may  be  distinguished  :  i.  the  mechanical  sources^  comprising  friction, 
percussion,  and  pressure  ;  ii.  ^h^  physical  sources — that  is,  solar  radiation, 
terrestrial  heat,  molecular  actions,  changes  of  condition,  and  electricity  ; 
iii.  the  chernical  sou?'ces,  or  molecular  combinations,  and  more  especially 
combustion. 

In  what  follows  it  will  be  seen  that  heat  may  be  produced  by  reversing 
its  effects ;  as,  for  instance,  when  a  liquid  is  solidified  or  a  gas  compressed 
(44b) ;  though  it  does  not  necessarily  follow  that  in  all  cases  the  reversal 
of  its  effects  causes  heat  to  be  produced — instead  of  it,  an  equivalent  of 
some  other  form  of  energy  may  be  generated. 

In  like  manner  heat  may  be  caused  to  disappear,  or  cold  be  produced 
when  a  change  such  as  heat  can  produce  is  brought  about  by  other  means, 
as  when  a  liquid  is  vaporised  or  a  solid  liquefied  by  solution ;  though 
here  also  the  disappearance  of  heat  is  not  always  a  necessary  consequence 
of  the  production  by  other  means  of  changes  such  as  might  be  effected 
by  heat. 

MECHANICAL   SOURCES. 

448.  Beat  due  to  friction. — The  friction  of  two  bodies,  one  against  the 
other,  produces  heat,  which  is  greater  the  greater  the  pressure  and  the 
more  rapid  the  motion.  For  example,  the  axles  of  carriage  wheels,  by 
their  friction  against  the  boxes,  often  become  so  strongly  heated  as  to 
take  fire.  By  rubbing  together  two  pieces  of  ice  in  a  vacuum  below  zero. 
Sir  H.  Davy  partially  melted  them.  In  boring  a  brass  cannon  Rumford 
found  that  the  heat  developed  in  the  course  of  2^  hours  was  sufficient  to 
raise  26^  pounds  of  water  from  zero  to  100°,  which  represents  2650 
thermal  units  (418).  At  the  Paris  Exhibition,  in  1855,  MM.  Beaumont 
and  Mayer  exhibited  an  apparatus,  which  consisted  of  a  wooden  cone 
covered  with  hemp,  and  moving  with  a  velocity  of  400  revolutions  in  a 
minute,  in  a  hollow  copper  cone,  which  was  fixed  and  immersed  in  the 
water  of  an  hermetically-closed  boiler.  The  surfaces  were  kept  covered 
with  oil.  By  means  of  this  apparatus  88  gallons  of  water  were  raised 
from  10  to  130  degrees  in  the  course  of  a  few  hours. 

In  the  case  of  flint  and  steel,  the  friction  of  the  flint  against  the  steel 
raises  the  temperature  of  the  metallic  particles,  which  fly  off  heated  to 
such  an  extent  that  they  take  fire  in  the  air. 

The  luminosity  of  aerolites  is  considered  to  be  due  to  their  friction 
against  the  air,  and  by  their  condensation  of  the  air  in  front  of 
them  (449). 

Dr.  Tyndall  has  devised  an  experiment  by  which  the  great  heat  de- 
veloped by  friction  is  illustrated  in  a  striking  manner.  A  brass  tube 
(fig.  332),  about  4  inches  in  length  and  f  of  an  inch  in  diameter,  is  fixed 


-449] 


Mechanical  Sources  of  Heat. 


389 


on  a  small  wheel.  By  means  of  a  cord  passing  round  a  much  larger  one, 
this  tube  can  be  rotated  with  any  desired  velocity.  The  tube  is  three 
parts  full  of  water,  and  is  closed  by  a  cork.  In  making  the  experiment, 
the  tube  is  pressed  between  a  wooden  clamp,  while  the  wheel  is  rotated 


with  some  rapidity.  The  water  rapidly  becomes  heated  by  the  friction, 
and  its  temperature  soon  exceeding  the  boiling  point,  the  cork  is  pro- 
jected to  a  height  of  several  yards  by  the  elastic  force  of  the  steam. 

449.  Beat  due  to  pressure  and  percussion. — If  a  body  be  so  com- 
pressed that  its  density  is  increased,  its  temperature  rises  according  as 
the  volume  diminishes.  Joule  has  verified  this  in  the  case  of  water  and 
of  oil,  which  were  exposed  to  pressures  of  15  to  25  atmospheres.  In  the 
case  of  water  at  i'2°  C,  increase  of  pressure  caused  lowering  of  tempera- 
ture, a  result  which  agrees  with  the  fact  that  water  contracts  by  heat  at 
this  temperature.     Similarly,  when  weights  are  laid  on  metallic  pillars, 


Fig-  33?. 

heat  is  evolved,  and  absorbed  when  they  are  removed.  So  in  like  manner 
the  stretching  of  a  metallic  wire  is  attended  with,  a  diminution  of  tem- 
perature. 

The  production  of  heat  by  the  compression  of  gases  is  easily  shown 
by  means  of  the  pnejwiatic  syringe  (fig.  333).  This  consists  of  a  glass 
tube  with  thick  sides,  closed  hermetically  by  a  leather  piston.     At  the 


390  On  Heat.  [449- 

b  )ttom  of  this  there  is  a  cavity  in  which  a  small  piece  of  tinder  is  placed. 
The  tube  being  full  of  air,  the  piston  is  suddenly  plunged  downwards ; 
the  air  thus  compressed  disengages  so  much  heat  as  to  ignite  the  tinder, 
which  is  seen  to  burn  when  the  piston  is  rapidly  withdrawn.  The  in- 
flammation of  the  tinder  in  this  experiment  indicates  a  temperature  of  at 
least  300°.  At  the  moment  of  compression  a  bright  flash  is  observed, 
which  was  originally  attributed  to  the  high  temperature  of  the  air ;  but  it 
is  simply  due  to  the  combustion  of  the  oil  which  greases  the  piston. 
Instead  of  the  tinder,  cotton  very  shghtly  moistened  with  ether  or  bisul- 
|)hide  of  carbon  may  be  used. 

The  elevation  of  temperature  produced  by  the  pressure  in  the  above 
Experiment  is  sufficient  to  effect  the  combination,  and  therefore  the  deto- 
iiation,  of  a  mixture  of  hydrogen  and  oxygen. 

Percussion  is  also  a  source  of  heat.  In  firing  shot  at  an  iron  target,  a 
feheet  of  flame  is  frequently  seen  at  the  moment  of  impact ;  and  Mr. 
Whitworth  has  used  iron  shells  which  are  exploded  by  the  concussion  on 
striking  an  iron  target.  A  small  piece  of  iron  hammered  on  the  anvil 
becomes  very  hot.  The  heat  is  not  simply  due  to  an  approximation  of 
the  molecules — that  is,  to  an  increase  in  density — but  arises  from  a  vibra- 
tory motion  imparted  to  them;  for  lead,  which  does  not  increase  in 
density  by  percussion,  nevertheless  becomes  heated. 

The  heat  due  to  the  impact  of  bodies  is  not  difficult  to  calculate. 
Whenever  a  body  moving  with  a  velocity  v  is  suddenly  arrested  in  its 
motion,  by  whatever  cause,  its  vis  viva  is  converted  into  heat.  This  holds 
equally  whatever  be  the  cause  to  which  the  motion  is  due;  whether 
it  be  that  acquired  by  a  stone  falling  from  a  height ;  by  a  bullet 
fired   from   a  gun,   or  the  rotation   of  a   copper   disc  by  means  of  a 

turning  table.     The  vis  viva  of  any  moving  body  is  expressed  by      ' — ; 

or  in  foot-pounds  by  — ^ ,  where  w  is  the  weight  in  pounds,  v  the  velo- 
city  in  feet  per  second,  and  g  is  about  29 ;  and  if  the  whole  of  this  be 

converted  into  heat,  its  equivalent  in  thermal  units   will   be  

2^x  1390* 

Suppose,  for  instance,  a  lead  ball  weighing  a  pound  be  fired  from  a  gun, 

and  strike  against  a  target,  what  amount   of  heat  will  it  produce  ?     We 

may  assume  that  its  velocity  will  be  about  1,600  per  second;  then  its  vis 

viva  will  be  -^ =  40,000  foot-pounds,  the  equivalent  of  which  in 

2  X  32 

heat  is  — ' =  287  thermal  units.     If  we  assume  that  the  heat  is  equally 

1390 

distributed  between  the  ball  and  the  target,  then  the  share  of  the  former 

will  be  14-3  thermal  units;  and  if,  for  simpHcity's  sake,  we  assume  that 

its  temperature  is  originally  zero,  then,  taking  its  specific  heat  at  0-0314, 

we  shall  have 

I  X  0-0314  X  /=  14-3  or  /  =  457°, 

which  is  a  temperature  considerably  above  that  of  the  melting  point  of 
lead  (315). 


-450]  Physical  Sources  of  Heat.  391 

By  allowing  a  lead  ball  to  fall  from  various  heights  on  an  iron  plate, 
both  experience  an  increase  of  temperature  which  may  be  measured  by 
the  thermopile  ;  and  from  these  increases  it  may  be  easily  shown  that 
the  heat  is  directly  proportional  to  the  height  of  fall,  and  therefore  to  the 
square  of  the  velocity. 

By  similar  methods  Mayer  has  calculated  that  if  the  motion  of  the 
earth  were  suddenly  arrested  the  temperature  produced  would  be  sufficient 
to  melt  and  even  volatilise  it ;  while,  if  it  fell  into  the  sun,  as  much  heat 
would  be  produced  as  results  from  the  combustion  of  5,000  spheres  of 
carbon  the  size  of  our  globe. 

PHYSICAL   SOURCES. 

450.  Solar  radiation. — The  most  mtense  of  all  sources  of  heat  is  the 
sun.  The  cause  of  its  heat  is  unknown  ;  some  have  considered  it  to  be 
an  ignited  mass  experiencing  immense  eruptions,  while  ethers  have  re- 
garded it  as  composed  of  layers  acting  chemically  on  each  other  like  the 
couples  of  a  voltaic  battery,  and  giving  rise  to  electrical  currents,  which 
produce  light  and  solar  heat.  On  both  hypotheses  the  incandescence  ot 
the  sun  would  have  a  limit. 

Different  attempts  have  been  made  to  determine  the  quantity  of  heat 
annually  emitted  by  the  sun.  M.  Pouillet,  by  means  of  an  apparatus 
which  he  calls  a  pyrheliometer,  has  calculated  that  if  the  total  quantity 
of  heat  which  the  eartl\  receives  from  the  sun  in  the  course  of  a  year  were 
employed  to  melt  ice,  it  would  be  capable  of  melting  a  layer  of  ice  all 
round  the  earth  of  35  yards  in  thickness.  But  from  the  surface  which 
the  earth  exposes  to  the  solar  radiation,  and  from  the  distance  which 
separates  the  earth  from  the  sun,  the  quantity  of  heat  which  the  earth 
receives  can  only  be  a^ni^oooo  °^  ^^  ^^^^  emitted  by  the  sun. 

Faraday  has  calculated  that  the  average  amount  of  heat  radiated  in  a 
day  on  each  acre  of  ground  in  the  latitude  of  London  is  equal  to  that 
which  would  be  produced  by  the  combustion  of  sixty  sacks  of  coal. 

Various  hypotheses  have  been  propounded  to  account  for  the  in- 
variability in  the  amount  of  heat  emitted  by  the  sun.  The  most  probable 
supposition  is  that  originally  put  forth  by  Mayer,  but  which  has  been  de- 
veloped by  Waterston  and  Sir  W.  Thomson,  according  to  which  the  heat 
which  the  sun  loses  by  radiation  is  replaced  by  the  fall  of  meteoric  stones  or 
aerolites  against  its  surface.  These  are  what  we  know  as  shooting  stars, 
which  often  appear  in  the  heavens  with  great  brilliancy,  especially  on  the 
14th  August  and  15th  November.  These  fa'l  against  the  sun  with  a 
velocity  far  transcending  anything  met  with  on  the  surface  of  our  globe, 
and  by  their  impact  develop  an  amount  of  heat  which  more  than  com- 
pensates what  the  sun  loses  by  radiation.  It  has  been  calculated  that  an 
amount  falling  into  the  sun  every  year  which  would  not  increase  its 
thickness  by  more  than  21  yards  would  be  sufficient  for  this  purpose. 

According  to  Helmholtz  the  heat  of  the  sun  was  produced  originally 
by  the  condensation  of  a  nebulous  mass  and  is  maintained  by  a  continu- 
ance of  this  contraction.     A  sudden  contraction  of  the  primitive  nebular 


392  071  Heat.  [450- 

mass  of  the  sun  to  its  present  volume  would  produce  a  temperature  of 
28  millions  of  degrees  centigrade  ;  and  a  contraction  of  -^-^^-^  of  its  mass 
would  be  sufficient  to  supply  the  heat  radiated  by  the  sun  in  2000 
years. 

451.  Terrestrial  heat. — Our  globe  possesses  a  heat  peculiar  to  it, 
which  is  called  the  terrestrial  heat.  The  variations  of  temperature  which 
occur  at  the  surface  gradually  penetrate  to  a  certain  depth,  at  which  their 
influence  becomes  too  slight  to  be  sensible.  It  is  hence  concluded  that 
the  solar  heat  does  not  penetrate  below  a  certain  internal  layer,  which  is 
called  the  layer  of  constant  temperatiire  :  its  depth  below  the  earth's 
external  surface  varies,  of  course,  in  different  parts  of  the  globe  ;  at  Paris 
it  is  about  30  yards,  and  the  temperature  is  constant  at  1 1  -8°  C. 

Below  the  layer  of  constant  temperature,  the  temperature  is  observed 
to  increase,  on  the  average,  1°  C.  for  every  90  feet.  This  increase  has 
been  verified  in  mines  and  artesian  wells.  According  to  this,  at  a  depth 
of  3,000  yards,  the  temperature  of  a  corresponding  layer  would  be  100°, 
and  at  a  depth  of  20  to  30  miles  there  would  be  a  temperature  sufficient 
to  melt  all  substances  which  exist  on  the  surface.  Hot  springs  and 
volcanoes  confirm  the  existence  of  this  central  heat. 

Various  hypotheses  have  been  proposed  to  account  for  the  existence  of 
this  central  heat.  That  most  usually  admitted  by  physicists  is  that  the 
earth  was  originally  in  a  liquid  state  in  consequence  of  the  high  tempera- 
ture, and  that  by  radiation  the  surface  has  gradually  solidified,  so  as  to 
form  a  solid  crust.  The  thickness  of  this  crust  is  not  believed  to  be  more 
than  40.  to  50  miles,  and  the  interior  is  probably  still  in  a  liquid  state. 
The  cooling  must  be  very  slow,  in  consequence  oif  the  imperfect  conduc- 
tivity of  the  crust.  For  the  same  reason  the  central  heat  does  not  appear 
to  raise  the  temperature  of  the  surface  more 
than  3^  of  a  degree. 

452.  Heat  produced  by  absorption  and 
imbibition. — Molecular  phenomena,  such  as 
imbibition,  absorption,  capillary  actions,  are 
usually  accompanied  by  disengagement  of 
heat.  Pouillet  found  that  whenever  a  liquid  is 
poured  on  a  finely-divided  solid,  an  increase 
of  temperature  is  produced  which  varies 
with  the  nature  of  the  substances.  With  in- 
organic substances,  such  as  metals,  the  ox- 
ides, the  earths,  the  increase  is  ^^  of  a  degree; 
but  with  organic  substances,  such  as  sponge, 
flour,  starch,  roots,  dried  membranes,  the 
increase  varies  from  i  to  10  degrees. 

The  absorption  of  gases  by  solid  bodies 
presents  the  same  phenomena.  Dobereiner 
found  that  when  platinum,  in  the  fine  state 
of  division  known  as  platinum  black,  is 
placed  in  oxygen,  it  absorbs  many  hundred 
times  its  volume,  and  that  the  gas  is  then  in  such  a  state  of  density,  and 


Fig-  334- 


-553]  Chemical  Sources  of  Heat.  393 

the  temperature  so  high,  as  to  give  rise  to  intense  combustions.  Spongy 
platinum  produces  the  same  effect.  A  jet  of  hydrogen  directed  on  it 
takes  fire. 

The  apparatus  known  as  Dobereiner's  Lajnp  depends  on  this  property 
of  hnely-divided  platinum.  It  consists  of  two  glass  vessels  (fig.  334).  The 
first,  A,  fits  in  the  lower  vessels  by  means  of  a  tubulure  which  closes  it 
hermetically.  At  the  extremity  of  the  tubulure  there  is  a  mass  of  zinc, 
Z,  immersed  in  dilute  sulphuric  acid.  By  the  chemical  action  of  the 
zinc  on  the  dilute  acid  hydrogen  gas  is  generated,  which,  finding  no 
issue,  forces  the  liquid  out  of  the  vessel  B  into  the  vessel  A,  so  that  the 
zinc  is  not  in  contact  with  the  liquid.  The  stopper  of  the  upper  vessel 
is  raised  to  give  exit  to  the  air  in  proportion  as  the  water  rises.  On  a 
copper  tube,  H,  fixed  in  the  side  of  the  vessel  B,  there  is  a  small  cone,  E, 
perforated  by  an  orifice  ;  above  this  there  is  some  spongy  platinum  in 
the  capsule  D. 

As  soon  now  as  the  cock,  which  closes  the  tube  H,  is  opened,  the 
hydrogen  escapes,  and  coming  in  contact  with  the  spongy  platinum,  is 
ignited. 

M.  Favre  has  found  that  when  a  gas  is  absorbed  by  charcoal  the 
amount  of  heat  produced  by  the  absorption  of  a  given  weight  of  sulphurous 
acid,  or  of  protoxide  of  nitrogen,  greatly  exceeds  that  which  is  disengaged 
in  the  liquefaction  of  the  same  weight  of  gas  ;  for  carbonic  acid,  the 
heat  produced  by  absorption,  exceeds  even  the  heat  which  would  be 
disengaged  by  the  solidification  of  the  gas.  The  heat  produced  by  the 
absorption  of  these  gases  cannot,  therefore,  be  explained  by  assuming 
that  the  gas  is  liquefied,  or  even  solidified  in  the  pores  of  the  charcoal. 
It  is  probable  that  it  is  due  to  that  produced  by  the  liquefaction  of  the 
gas,  and  to  the  heat  due  to  the  imbibition  of  the  liquid  so  produced  in 
the  charcoal. 

The  heat  produced  by  the  changes  of  condition  has  been  already  treated 
of  in  the  articles  solidification  and  liquefaction  ;  the  heat  produced  by 
electrical  action  will  be  discussed  under  the  head  of  Electricity. 

CHEMICAL   SOURCES. 

453.  Chemical  combinations.  Combustion. — Chemical  combinations 
are  usually  accompanied  by  a  certain  elevation  of  temperature.  When 
these  combinations  take  place  slowly,  as  when  iron  oxidises  in  the  air,  the 
heat  produced  is  imperceptible  ;  but  if  they  take  place  rapidly,  the  dis- 
engagement of  heat  is  very  intense.  The  same  quantity  of  heat  is  produced 
in  both  cases,  but  when  evolved  slowly  it  is  dissipated  as  fast  as  formed. 

Combustion  is  chemical  combination  attended  with  the  evolution  of 
light  and  heat.  In  the  ordinary  combustion  in  lamps,  fires,  candles,  the 
carbon  and  hydrogen  of  the  coal,  or  of  the  oil,  etc.,  combine  with  the 
oxygen  of  the  air.  But  combustion  does  not  necessarily  involve  the  pre- 
sence of  oxygen.  If  either  powdered  antimony  or  a  fragment  of  phos- 
phorus be  placed  in  a  vessel  of  chlorine,  it  unites  with  chlorine,  producing 
thereby  heat  and  flame. 

S3 


394  On  Heat.  [453- 

Many  combustibles  burn  with  flame,  h.  flame  is  a  gas  or  vapour  raised 
to  a  high  temperature  by  combustion.  Its  ill jminating  power  varies  with 
the  nature  of  the  product  formed.  The  presence  of  a  solid  body  in  the 
flame  increases  the  illuminating  power.  The  flames  of  hydrogen,  carbonic 
oxide,  and  alcohol  are  pale,  because  they  only  contain  gaseous  products 
of  combustion.  But  the  flames  of  candles,  lamps,  coal  gas,  have  a  high 
illuminating  power.  They  owe  this  to  the  fact  that  the  high  temperature 
produced  decomposes  certain  of  the  gases  with  the  production  of  carbon, 
which,  not  being  perfectly  burned,  becomes  incandescent  in  the  flame. 
Coal  gas,  when  burnt  in  an  arrangement  by  which  it  obtains  an  adequate 
supply  of  air,  is  almost  entirely  devoid  of  luminosity.  A  non-luminous 
flame  may  be  made  kiminous  by  placing  in  it  platinum  wire,  or  asbestos. 
The  temperature  of  a  flame  does  not  depend  on  its  illuminating  power. 
A  hydrogen  flame,  which  is  the  palest  of  all  flames,  gives  the  greatest  heat. 

Chemical  decomposition  in  which  the  attraction  of  heterogeneous 
molecules  for  each  other  is  overcome,  and  they  are  moved  further  apart, 
is  an  operation  requiring  an  expenditure  of  work  or  an  equivalent  con- 
sumption of  heat ;  and  conversely,  in  chemical  combination,  motion  is 
transformed  into  heat.  When  bodies  attract  each  other  chemically  their 
molecules  move  towards  each  other  with  gradually  increasing  velocity, 
and  when  impact  has  taken  place  the  progressive  motion  of  the  molecules 
ceases,  and  is  converted  into  a  rotating,  vibrating,  or  progressive  motion 
of  the  molecules  of  the  new  body. 

The  heat  produced  by  chemical  combination  of  two  elements  may  be 
compared  to  that  due  to  the  impact  of  bodies  against  each  other.  Thus 
the  action  of  the  atoms  of  oxygen  which,  in  virtue  of  their  progressive 
motion,  -and  of  chemical  attraction,  rush  against  ignited  carbon,  has  been 
hkened  %y  Tyndall  to  the  action  of  meteorites  which  fall  into  the  sun. 

454.  Heat  disengragred  during-  combustion. — Many  physicists,  more 
especially  Lavoisier,  Rumford,  Dulong,  Despretz,  Hess,  Favre  and  Silber- 
mann,  and  Andrews,  have  investigated  the  quantity  of  heat  disengaged 
by  various  bodies  in  chemical  combinations. 

In  these  experiments  Lavoisier  used  the  ice  calorimeter  already  de- 
scribed. Rumford  used  a  calorimeter  known  by  his  name,  which  consists 
of  a  rectangular  copper  canister  filled  with  water.  In  this  canister  there 
is  a  worm  which  passes  through  the  bottom  of  the  box,  and  terminates 
below  in  an  inverted  funnel.  Under  this  funnel  is  burnt  the  substance 
experimented  upon.  The  products  of  combustion,  in  passing  through  the 
worm,  heat  the  water  of  the  canister,  and  from  the  increase  of  its  tem- 
perature the  quantity  of  heat  evolved  is  calculated.  MM.  Despretz  and 
Dulong  have  successively  modified  Rumford's  calorimeter  by  allowing 
the  combustion  to  take  place,  not  outside  the  canister,  but  in  a  chamber 
placed  in  the  liquid  itself ;  the  oxygen  necessary  for  the  combustion  en- 
tered by  a  tube  in  the  lower  part  of  the  chamber,  and  the  products  of 
combustion  escaped  by  another  tube  placed  at  the  upper  part  and  twisted 
in  a  serpentine  form  in  the  mass  of  the  liquid  to  be  heated.  MM.  Favre 
and  Silbermann  have  improved  this  calorimeter  very  greatly  (434),  not 
only  by  avoiding  or  taking  account  of  all  possible  sources  of  error,  but  by 


-455] 


Heating. 


395 


arranging  it  for  the  determination  of  the  heat  evolve  i  in  other  chemical 
actions  than  those  of  ordinary  combustion. 

The  experiments  of  MM.  Favre  and  Silbermann  are  the  most  trust- 
worthy, as  having  been  executed  with  the  greatest  care.  They  agree  very 
closely  with  those  of  Dulong.  Taking  as  thermal  unit  the  heat  necessary 
to  raise  the  temperature  of  a  pound  of  water  through  otie  degree  Centi- 
grade, the  following  table  gives  the  thermal  units  in  round  numbers  dis- 
engaged by  a  pound  of  each  of  the  substances  in  burning  in  oxygen  : — 


Hydrogen  . 

•     34462 

Sulphur 

.     2220 

Marsh  gas 

.     13063 

Anthracite    . 

..    8460 

defiant  gas 

.     11858 

Charcoal 

..   8080 

Oil  of  turpentine 

.     10852 

Coal      .         .         .         . 

.     Bqdo. 

Olive  oil    . 

.       9860 

Tallow .... 

.     8000 

Ether 

.       9030 

Diamond 

•     7770 

Coke 

7000 

Absolute  alcohol  . 

.     7180 

Wood,  dry 

■   .       4025 

Phosphorus  . 

•     5750 

Wood,  moist 

.       3100 

Bisulphide  of  carbon     . 

.     3401 

Carbonic  oxide 

2400 

Iron       .... 

.     1576 

The  experiments  of  Dulong,  of  Despretz,  and  of  Hess  prove  that  a 
body  in  burning  always  produces  the  same  quantity  of  heat  in  reaching 
the  same  degree  of  oxidation,  whether  it  attains  this  at  once  or  only 
reaches  it  after  passing  through  intermediate  stages.  Thus  a  given  weight 
of  carbon  gives  out  the  same  amount  of  heat  in  burning  directly  to  car- 
bonic acid  as  if  it  were  first  changed  into  carbonic  oxide,  and  then  this 
were  burnt  into  carbonic  acid. 

455.  Animal  beat. — In  all  organs  of  the  human  body,,  as  well  as  that 
of  all  animals,  processes  of  oxidation  are  continually  going  on.  Oxygen 
passes  through  the  lungs  into  the  blood,  and  so  into  all  parts  of  the  body. 
In  like  manner  the  oxidisable  bodies,  which  are  principally  hydrocarbons 
pass  by  the  process  of  digestion  into  the  blood,  and  likewise  into  all 
parts  of  the  body,  while  the  products  of  oxidation,  carbonic  acid  and 
water,  are  eliminated,  by  the  skin,  the  lungs,  etc.  Oxidation  in  the  muscle 
produces  motion  of  the  molecules,  which  are  changed  into  contraction  of 
the  muscular  fibres  ;  all  other  oxidations  produce  heat  directly.  When 
the  body  is  at  rest,  all  its  functions,  even  involuntary  motions,  are  trans- 
formed into  heat.  When  the  body  is  at  work,  the  more  vigorous  oxida- 
tions of  the  working  parts  are  transferred  to  the  others.  Moreover,  a 
great  part  of  the  muscular  work  is  changed  into  heat,  by  friction  of  the 
muscle  and  of  the  sinews  in  their  sheaths,  and  of  the  bones  in  their 
sockets.  Hence  the  heat  produced  by  the  body  when  at  work  is  greater 
than  when  at  rest.  The  blood  distributes  heat  uniformly  through  the 
body,  which  in  a  normal  condition  has  a  temperature  of  37'5°.  The  blood 
of  mammalia  has  the  same  temperature,  that  of  birds  is  somewhat  higher. 
In  fever  the  temperature  rises  to  42°-44°,  and  in  cholera,  or  when  near 
death,  sinks  to  35°. 

The  function  of  producing  work  in  the  animal  organism  was  formerly 
separated  from  that  of  the  production  of  heat.     The  latter  was  held  to  be 


396 


On  Heat. 


[455- 


due  to  the  oxidation  of  the  hydrocarbons  of  the  fat,  while  the  work  was 
ascribed  to  the  chemical  activity  of  the  nitrogenous  matter.  This  view 
has  now  been  generally  abandoned  ;  for  it  has  been  found  that  during 
work,  there  is  no  increase  in  the  secretion  of  urea,  which  is  the  result  of 
the  oxidation  of  nitrogenous  matter  ;  moreover,  the  organism  while  at 
rest  produces  less  carbonic  acid  and  requires  less  oxygen  than  when  it  is 
at  work  ;  and  the  muscle  itself,  both  in  the  living  organism  and  also  when 
removed  from  it  and  artificially  stimulated,  requires  more  oxygen  in  a 
state  of  activity  than  when  at  rest.  For  these  reasons  the  production  of 
work  is  also  ascribed  to  the  oxidation  of  organic  matter. 

The  process  of  vegetation  in  the  living  plant  is  not  in  general  con- 
nected with  any  oxidation.  On  the  contrary,  under  the  influence  of  the 
sun's  rays,  the  green  parts  of  plants  decompose  the  carbonic  acid,  of  the 
atmosphere  into  free  oxygen  gas  and  into  carbon,  which  uniting  with  the 
elements  of  water  form  cellulose,  starch,  sugar  and  so  forth.  In  order  to 
effect  this  an  expenditure  of  heat  is  required  which  is  stored  up  in  the 
plant  and  reappears  during  the  combustion  of  wood  or  of  the  coal  arising 
from  its  decomposition. 

At  the  time  of  blossoming  a  process  of  oxidation  goes  on,  which,  as  in 
the  case  of  the  blossoming  of  the  Victoria  regia,  is  attended  with  an 
appreciable  increase  of  temperature. 


HEATING. 

456.  Different  kinds  of  beating:. — Heating  is  the  art  of  utilising  for  do- 
mestic and  industrial  purposes  the  sources  of  heat  which  nature  offers  to  us. 
Our  principal  source  of  artificial  heat  is  the  combustion  of  coal,  coke, 
turf,  wood,  and  charcoal. 

We  may  distinguish  five  kinds  of  heating,  according  to  the  apparatus 
used  :  ist,  heating  with  an  open  fire  ;  2nd, 
heating  with  an  enclosed  fire,  as  with  a 
stove  ;  3rd,  heating  by  hot  air  ;  4th,  heat- 
ing by  steam  ;  5th,  heating  by  the  circula- 
tion of  hot  water. 

457.  Fire-places.  —  Fire-places  are 
open  hearths  built  against  a  wall  under  a 
chimney,  through  which  the  products  of 
combustion  escape. 

However  much  they  may  be  improved, 
fire-places  will  always  remain  the  most 
imperfect  and  costly  mode  of  heating,  for 
they  only  render  available  13  per  cent, 
of  the  total  heat  yielded  by  coal  or  coke, 
and  6  per  cent,  of  that  by  wood.  This 
enormous  loss  of  temperature  arises  from 
the  fact,  that  the  current  of  air  necessary 
'^'  ^^^'  for  combustion  always  carries  with  it  a 

large  quantity  of  the  heat  produced,  which  is  lost  in   the  atmosphere. 


-458]  Heating  by  Hot  A  ir.  397 

Hence  it  was  that  Franklin  said  fire-places  should  be  adopted  in  cases 
where  the  smallest  quantity  of  heat  was  to  be  obtained  from  a  given 
quantity  of  combustible.  Notwithstanding  their  want  of  economy,  how-" 
ever,  they  will  always  be  preferred  as  the  healthiest  and  pleasantest  mode 
of  heating,  on  account  of  the  cheerful  light  which  they  emit,  and  the  ven- 
tilation which  they  ensure. 

458.  Braugrht  of  fire-places. — Th.t  drattght  of  a  fire  is  the  upward 
current  in  the  chimney  caused  by  the  ascent  of  the  products  of  combus- 
tion ;  when  the  current  is  rapid  and  continuous,  the  chimney  is  said  to 
draw  well. 

The  draught  is  caused  by  the  difference  between  the  temperature  of  the 
inside  and  that  on  the  outside  of  the  chimney  ;  for,  in  consequence  of  this 
difference,  the  gaseous  substances  whidi  fill  the  chimney  are  lighter  than 
the  air  of  the  room,  and  consequently  equilibrium  is  impossible.  The 
weight  of  the  column  of  gas  CD,  fig.  335,  in  the  chimney  being  less  than 
that  of  the  external  column  of  air  AB  of  the  same  height,  there  is  a  pres- 
sure from  the  outside  to  the  inside  which  causes  the  products  of  combus- 
tion to  ascend  the  more  rapidly  in  proportion  as  the  difference  in  weight 
of  the  two  gaseous  masses  is  greater. 

The  velocity  of  the  draught  of  a  chimney  may  be  determined  theoreti- 
cally by  the  formula 

^  =  s/2ga{t'-t)h, 

in  which  g  is  the  acceleration  of  gravity,  n  the  coefficient  of  the  expansion 
of  air,  h  the  height  of  the  chimney,  f  the  mean  temperature  of  the  air 
inside  the  chimney,  and  t  the  temperature  of  the  surrounding  air. 

The  currents  caused  by  the  difference  in  temperature  of  two  communi- 
cating gaseous  masses  may  be  demonstrated  by  placing  a  candle  near  the 
top  and  near  the  bottom  of  the  partially-opened  door  of  a  warm  room. 
At  the  top,  the  flame  will  be  turned  from  the  room  towards  the  outside, 
while  the  contrary  effect  will  be  produced  when  the  candle  is  placed  on 
the  ground.  The  two  effects  are  caused  by  the  current  of  heated  air  which 
issues  by  the  top  of  the  door,  while  the  cold  air  which  replaces  it  enters  at 
the  bottom. 

In  order  to  have  a  good  draught  a  chimney  ought  to  satisfy  the  follow- 
ing conditions  : 

i.  The  section  of  the  chimney  ought  not  to  be  larger  than  is  necessary 
to  allow  an  exit  for  the  products  of  combustion,  otherwise  ascending  and 
descending  currents  are  produced  in  the  chimney,  which  cause  it  to  smoke. 
It  is  advantageous  to  place  on  the  top  of  the  chimney  a  conical  pot  nar- 
rower than  the  chimney,  so  that  the  smoke  may  escape  with  sufficient 
velocity  to  resist  the  action  of  the  wind. 

ii.  The  chimney  ought  to  be  sufficiently  high,  for,  as  the  draught  is 
caused  by  the  excess  of  the  external  over  the  internal  pressure,  this  ex- 
cess is  greater  in  proportion  as  the  column  of  heated  air  is  longer. 

iii.  The  external  air  ought  to  pass  into  the  chamber  with  sufficient 
rapidity  to  supply  the  wants  of  the  fire.  In  a  hermetically  closed  room 
the  combustibles  would  not  burn,  or  descending  currents  would  be  formed 


393 


On  Heat. 


[458 


which  would  drive  the  smoke  into  the  room.  Usually  air  enters  in  suffi- 
cient quantity  by  the  crevices  of  the  doors  and  windows. 

IV,  Two  chimneys  should  not  communicate,  for  if  one  draws  better  than 
the  other,  a  descending  current  of  air  is  produced  in  the  latter,  which  car- 
ries smoke  with  it. 

For  the  strong  fires  required  by  steam  boilers  and  the  like,  very  high 
chimneys  are  needed,  of  course  the  increase  in  height  would  lose  its 
effect  if  the  hot  column  above  became  cooled  down.  Hence  chimneys 
are  often  made  with  hollow  walls,  that  is  of  separate  concentric  layers  of 
masonry,  the  space  between  them  containing  air. 

459.  Stoves. — Stoves  are  apparatus  for  heating  with  a  detached  fire, 
placed  in  the  room  to  be  heated,  so  that  the  heat  radiates  in  all  directions 
round  the  stove.  At  the  lower  part  is  the  draught  hole  by  which  the  air 
necessary  for  combustion  enters.  The  products  of  combustion  escape  by 
means  of  iron  chimney  pipes.  This  mode  of  heating  is  one  of  the  most 
economical,  but  it  is  by  no  means  so  healthy  as  that  by  open  fire-places, 
for  the  ventilation  is  very  bad,  more  especially  where,  as  in  Sweden,  and 
in  Germany,  the  stoves  are  fed  from  the  outside  of  the  room.  These 
stoves  also  emit  a  bad  smell,  probably  arising  from  the  decomposition  of 
organic  substances  in  the  air  by  their  contact  with  the  heated  sides  of  the 
chimney  pipes  ;  or  possibly,  as  Deville  and  Troost's  recent  researches 
seem  to  show,  from  the  diffusion  of  gases  through  the  heated  sides  of  the 
stove. 

The  heating  is  very  rapid  with  blackened  metal  stoves,  but  they  also 


Fig.  336. 

cool  very  rapidly.  Stoves  constructed  of  polished  earthenware,  which  are 
common  on  the  Continent,  heat  more  slowly,  but  more  pleasantly,  and 
they  retain  the  heat  longer. 


-462] 


SoiLvces  of  Cold. 


399 


460.  Heating:  by  steam. — Steam,  in  condensing,  gives  up  its  latent 
heat  of  vaporisation,  and  this  property  has  been  used  in  heating  baths, 
workshops,  public  buildings,  hothouses,  etc.  For  this  purpose  steam  is 
generated  in  boilers  similar  to  those  used  for  steam-engines,  and  is  then 
made  to  circulate  in  pipes  placed  in  the  room  to  be  heated.  The  vapour 
condenses,  and  in  doing  so  imparts  to  the  pipes  the  latent  heat,  which  be- 
comes free,  and  thus  heats  the  surrounding  air. 

461.  Heatingr  by  hot  air.— Heating  by  hot  air  consists  in  heating  the 
air  in  the  lower  part  of  a  building,  from  whence  it  rises  to  the  higher  parts 
in  virtue  of  its  lessened  density.  The  apparatus  is  arranged  as  represented 
in  figure  336. 

A  series  of  bent  tubes,  AB,  only  one  of  which  is  shown  in  the  figure,  is 
placed  in  a  furnace,  F,  in  the  cellar.  The  air  passes  into  the  tubes  through 
the  lower  end  A,  where  it  becomes  heated,  and  rising  in  the  direction  of 
the  arrows,  reaches  the  room  M  by  a  higher  aperture  B.  The  various 
rooms  to  be  heated  are  provided  with  one  or  more  of  these  apertures, 
which  are  placed  as  low  in  the  room  as  possible.  The  conduit  O  is  an 
ordinary  chimney. 

These  apparatus  are  more  economical  than  open  fire-places,  but  they 
are  less  healthy,  owing  to  the  want  of  ventilation. 


b 


i-'ig  337- 

462.  Heating:  by  bot  water. — This  consists  of  a  continuous  circulation 
of  water,  which  having  been  heated  in  a  boiler,  rises  through  a  series  of 


400  On  Heat  [462- 

tubes,  and  then,  after  becoming  cool,  passes  into  the  boiler  again  by  a 
similar  series. 

Figure  337  represents  an  apparatus  for  heating  a  building  of  several 
stories.  The  heating  apparatus,  which  is  in  the  cellar,  consists  of  a  bell- 
shaped  boiler,  00^  with  an  internal  flue,  F.  A  long  pipe,  M,  fits  in  the 
upper  part  of  the  boiler,  and  also  in  the  reservoir  O,  placed  in  the  upper 
part  of  the  building  to  be  heated.  At  the  top  of  this  reservoir  there  is  a 
safety  valve,  j,  by  which  the  pressure  of  the  vapour  in  the  interior  can  be 
regulated. 

The  boiler,  the  pipe  M,  and  a  portion  of  the  reservoir,  Q,  being  filled 
with  water,  as  it  becomes  heated  in  the  boiler  an  ascending  current  of 
hot  water  rises  to  the  reservoir  Q,  while  at  the  same  time  descending 
currents  of  colder  and  denser  water  pass  from  the  lower  part  of  the 
reservoir  Qinto  receivers,  b,  d,f,  filled  with  water.  The  water  from  these 
passes  again  through  pipes  into  other  receivers,  a,  c,  e,  and  ultimately 
reaches  the  lower  part  of  the  boiler. 

During  this  circulation  the  hot  water  heats  the  pipes  and  the  receivers, 
which  thus  become  true  water  stoves.  The  number  and  the  dimensions 
of  these  parts  are  readily  determined  from  the  fact  that  a  cubic  footof 
water  is  theoretically  sufficient  to  communicate  the  necessary  heat  to 
3,200  cubic  feet  of  air.  In  the  interior  of  the  receivers  a,  b,  c,  d,  e,f,  there 
are  cast-iron  tubes  which  communicate  with  the  outside  by  pipes,  P, 
placed  underneath  the  flooring.  The  air  becomes  heated  in  these  tubes, 
and  emerges  at  the  upper  part  of  the  receivers. 

The  principal  advantage  of  this  mode  of  heating  is  that  of  giving  a 
temperature  which  is  constant  for  a  long  time  ;  for  the  mass  of  water  only 
cools  slowly.  It  is  much  used  in  hothouses,  baths,  artificial  incubation, 
drying  rooms,  and  generally  wherever  a  uniform  temperature  is  desired. 


SOURCES   OF   COLD, 

463.  Various  sources  of  cold. — Besides  the  cold  caused  by  the 
passage  of  a  body  from  a  solid  to  the  liquid  state,  of  which  we  have 
already  spoken,  cold  is  produced  by  the  expansion  of  gases,  by  radiation 
in  general,  and  more  especially  by  nocturnal  radiation. 

464  Cold  produced  by  the  expansion  of  grases.  Ice  macbines. — 
We  have  seen  that  when  a  gas  is  compressed,  the  temperature  rises.  The 
reverse  of  this  is  also  the  case  :  when  a  gas  is  rarefied  a  reduction  of 
temperature  ensues,  because  a  quantity  of  sensible  heat  disappears  when 
the  gas  becomes  increased  to  a  larger  volume.  This  may  be  shown  by 
placing  a  delicate  Breguet's  thermometer  under  the  receiver  of  an  air- 
pump,  and  exhausting  ;  at  each  stroke  of  the  piston  the  needle  moves  in 
the  direction  of  zero,  and  regains  its  original  temperature  when  air  is 
admitted.  Kirk  has  invented  a  machine  for  the  manufacture  of  ice, 
which  depends  on  this  property.  The  heat  developed  by  the  compression 
of  air  is  removed  by  a  current  of  cold  water  ;  the  vessel  containing  the 
compressed  air  being  placed  in  brine,  the  air  is  allowed  to  expand  ;  in  so 


1 


-467]  Mechanical  Eqtdvalents  of  Heat.  40 1 

doing  it  cools  the  brine  so  considerably  as  to  freeze  water  contained  in 
vessels  placed  in  the  brine.  It  is  stated  that  by  this  means  a  ton  of  coals 
(used  in  working  a  steam-engine  by  which  the  compression  is  effected) 
can  produce  a  ton  of  ice. 

465.  Cold  produced  liy  nocturnal  radiation. — During  the  day,  the 
ground  receives  from  the  sun  more  heat  than  radiates  into  space,  and  the 
temperature  rises.  The  reverse  is  the  case  during  night.  The  heat  which 
the  earth  loses  by  radiation  is  no  longer  compensated  for,  and  consequently 
a  fall  of  temperature  takes  place,  which  is  greater  according  as  the  sky  is 
clearer,  for  clouds  send  towards  the  earth  rays  of  greater  intensity  than 
those  which  come  from  the  celestial  spaces.  In  some  winters  it  has  been 
found  that  rivers  have  not  frozen,  the  sky  having  been  cloudy,  although 
the  thermometer  has  been  for  several  days  below  —4°;  while  in  other 
less  severe  winters  the  rivers  freeze  when  the  sky  is  clear.  The  emissive 
power  exercises  a  great  influence  on  the  cold  produced  by  radiation  ;  the 
greater  it  is  the  greater  is  the  cold. 

In  Bengal,  the  nocturnal  cooHng  is  used  in  manufacturing  ice.  Large 
flat  vessels  containing  water  are  placed  on  non-conducting  substances, 
such  as  straw  or  dry  leaves.  In  consequence  of  the  radiation  the  water 
freezes,  even  when  the  temperature  of  the  air  is  10°  C.  The  same  method 
can  be  applied  in  all  cases  with  a  clear  sky. 

It  is  said  that  the  Peruvians,  in  order  to  preserve  the  shoots  of  young 
plants  from  freezing,  light  great  fires  in  their  neighbourhood,  the  smoke 
of  which,  producing  an  artificial  cloud,  hinders  the  cooling  produced  by 
radiation. 

466.  Absolute  zero  of  temperature.— As  a  gas  is  increased  ^yi  of  its 
volume  for  each  degree  Centigrade,  it  follows  that  at  a  temperature  of 
273°  C.  the  volume  of  any  gas  measured  at  zero  is  doubled.  In  likfe 
manner,  if  the  temperature  of  a  given  volume  at  zero  were  lowered  through 
-  273°,  the  contraction  would  be  equal  to  the  volume  ;  that  is,  the  volume 
would  not  exist. 

At  this  temperature  the  motion  of  the  molecules  of  the  gas  would 
completely  cease,  and  the  pressure  thereby  occasioned.  In  all  probability, 
before  reaching  this  temperature,  gases  would  undergo  some  change. 

This  point  on  the  Centigrade  scale  is  called  the  absolute  zero  of  tem- 
perature ;  the  temperatures  reckoned  from  this  point  are  called  absolute- 
temperatures.  They  are  clearly  obtained  by  adding  273  to  the  tempera- 
ture on  the  Centigrade  scale. 


CHAPTER  XII. 

MECHANICAL  EQUIVALENT  OF   HEAT. 

467.  Mechanical  equivalent  of  beat. — If  the  various  instances  of  the 
production  of  heat  by  motion  be  examined,  it  will  be  found  that  in  all 
cases  mechanical  force  is  consumed.  Thus,  in  rubbing  two  bodies  against 
each  other,  motion  is  apparently  destroyed  by  friction  ;  it  is  not,  however, 


402  On  Heat.  •   [^67- 

lost,  but  appears  in  the  form  of  a  motion  of  the  particles  of  the  body  ; 
the  motion  of  the  mass  is  transformed  into  a  motion  of  the  molecules. 

Again,  if  a  body  be  allowed  to  fall  from  a  height,  it  strikes  against  the 
ground  with  a  certain  velocity.  According  to  older  views,  its  motion  is 
destroyed,  vis  viva  is  lost.  This,  however,  is  not  the  case ;  the  vis  viva 
of  the  body  appears  as  vis  viva  of  its  molecules. 

In  the  case,  too,  of  chemical  action,  the  most  productive  artihcial  source 
of  heat,  it  is  not  difficult  to  conceive  that  there  is  in  the  act  of  combining 
an  impact  of  the  dissimilar  molecules  against  each  other,  an  effect  an- 
alogous to  the  production  of  heat  by  the  impact  of  masses  of  matter 
against  each  other. 

In  Hke  manner,  heat  may  be  made  to  produce  motion,  as  in  the  case 
of  the  steam-engine,  the  propulsion  of  shot  from  a  gun. 

Traces  of  a  view  that  there  is  a  connection  between  heat  and  motion 
are  to  be  met  with  in  the  older  writers,  Bacon  for  example  ;  and  Locke 
says  :  '  Heat  is  a  very  brisk  agitation  of  the  insensible  parts  of  the  object, 
which  produces  in  us  that  sensation  from  whence  we  denominate  the 
object  hot  ;  so  that  what  in  our  sensation  is  heat,  in  the  object  is  nothing 
but  motion.'  Rumford,  in  explaining  his  great  experiment  of  the  pro- 
duction of  heat  by  friction,  was  unable  to  assign  any  other  cause  for  the 
heat  produced  than  motion  ;  and  Davy,  in  the  explanation  of  his  experi- 
ment of  melting  ice  by  friction  in  vaci/o,  expressed  similar  views.  Carnot, 
in  a  work  on  the  steam-engine,  published  in  1824,  also  indicated  a  con- 
nection between  heat  and  work. 

The  views,  however,  which  had  been  stated  by  isolated  writers  had 
little  or  no  influence  on  the  progress  of  scientific  investigation,  and  it  is  in 
the  year  1842  that  the  modern  theories  may  be  said  to  have  had  their 
origin.  In  that  year  Dr.  Mayer,  a  physician  in  Heilbronn,  formally  stated 
that  there  exists  a  connection  between  heat  and  work  ;  and  he  it  was  who 
first  introduced  into  science  the  expression'  ?nec/ianicai  equivalent  ofheat.^ 
Mayer  also  gave  a  method  by  which  this  equivalent  could  be  calculated ; 
the  particular  results,  however,  are  of  no  value,  as  the  method,  though 
correct  in  principle,  is  founded  on  incorrect  data. 

In  the  same  year,  too,  Colding  of  Copenhagen  published  experiments 
on  the  production  of  heat  by  friction,  from  which  he  concluded  that  the 
evolution  of  heat  was  proportional  to  the  mechanical  energy  expended. 

About  the  same  time  as  Mayer,  but  quite  independently  of  him,  Joule 
commenced  a  series  of  experimental  investigations  on  the  relation  between 
heat  and  work.  These  first  drew  the  attention  of  scientific  men  to  the 
subject,  and  were  admitted  as  a  proof  that  the  transformation  of  heat 
into  mechanical  energy,  or  of  mechanical  energy  into  heat,  always  takes 
place  in  a  definite  numerical  ratio. 

Subsequently  to  Mayer  and  Joule,  several  physicists  by  their  theoretical 
and  experimental  investigations  have  contributed  to  establish  the  mecha- 
nical theory  of  heat,  namely,  in  this  country,  Sir  W.  Thomson  and  Ran- 
kine  ;  in  Germany,  Helmholtz,  Clausius,  and  Holtzmann  ;  and  in  France, 
Clapeyron  and  Regnault. 


-467] 


Mechanical  Equivalents  of  Heat. 


403 


The  following  are  some  of  the  most  important  and  satisfactory  of 
Joule's  experiments. 

A  copper  vessel,  B  (fig.  338),  was  provided  with  a  brass  paddle-wheel 
(indicated  by  the  dotted  lines),  which  could  be  made  to  rotate  about  a 
vertical  axis.  Two  weights,  E  and  F,  were  attached  to  cords  which 
passed  over  the  pulleys  C  and  D,  and  were  connected  with  the  axis  A. 
These  weights  in  falling  caused  the  wheel  to  rotate.  The  height  of  the 
fall,  which  in  Joule's  experiments  was  about  63  feet,  was  indicated  on 
the  scales  G  and  H.  The  roller  A  was  so  constructed  that  by  detaching 
a  pin  the  weights  could  be  raised  without  moving  the  wheel.  The  vessel 
B  was  filled  with  water  and  placed  on  a  stand,  and  the  weights  allowed  to 


sink.  When  they  had  reached  the  ground,  the  roller  was  detached  from 
the  axis,  and  the  weights  again  raised,  the  same  operations  being  repeated 
20  times.  The  heat  produced  was  measured  by  ordinary  calorimetric 
methods. 

The  work  expended  is  measured  by  the  product  of  the  weight  into  the 
height  through  which  >it  falls,  or  wh,  less  the  labour  lost  by  the  friction  of 
the  apparatus.  This  is  diminished  as  far  as  possible  by  the  use  of  friction 
wheels,  and  its  amount  is  determined  by  connecting  C  and  D  without  caus- 
ing them  to  pass  over  A,  and  then  determining  the  weight  necessary  to 
communicate  to  them  a  uniform  motion. 

In  this  way  it  has  been  found  that  a  thermal  unit — that  is,  the  quantity 
of  heat  by  which  a  pound  of  water  is  raised  through  1°  C. — is  generated 
by  the  expenditure  of  the  same  amount  of  work  as  would  be  required  to 
raise  1392  pounds  through  i  foot,  or  i  pound  through  1392  feet.  This  is 
expressed  by  saying  that  the  mechanical  equivalent  of  the  thermal  unit  is 
1392  foot-pounds. 

The  friction  of  an  iron  paddle-wheel  in  mercury  gave  1397  foot-pounds, 
and  that  of  the  friction  of  two  iron  plates  gave  1395  foot-pounds,  as  the 
mechanical  equivalent  of  one  thermal  unit. 

In  another  series  of  experiments,  the  air  in  a  receiver  was  compressed. 


404 


On  Heat. 


[467- 


by  means  of  a  force  pump,  both  being  immersed  in  a  known  weight  of 
water  at  a  known  temperature.  After  300  strokes  of  the  piston,  the  heat, 
C,  was  measured  which  the  water  had  gained.  This  heat  was  due  to  the 
compression  of  the  air  and  to  the  friction  of  the  piston.  To  ehminate  the 
latter  influence,  the  experiment  was  made  under  the  same  conditions,  but 
leaving  the  receiver  open.  The  air  was  not  compressed,  and  300  strokes 
of  the  piston  developed  Q'  thermal  units.  Hence  C  —  C^  is  the  heat  pro- 
duced by  the  compression  of  the  gas.     Representing  the  foot-pounds  ex- 

W 
pended  in  producing  this  heat  by  W,  we  have  for  the  value  of  the 

mechanical  equivalent  E.  By  this  method  Joule  obtained  the  number 
1442. 

The  mean  number  which  Joule  adopted  for  the  mechanical  equivalent 
of  one  thermal  unit  on  the  Centigrade  scale  is  1390  foot-pounds  ;  on  the 
Fahrenheit  scale  it  is  772  foot-pounds.  The  number  is  called  Joule's 
equivalent. 

On  the  metrical  system  424  metres  is  taken  as  the  height  through 
which  a  kilogramme  of  water  must  fall  to  raise  its  temperature  i  degree 
Centigrade. 

M.  Hirn  has  made  the  following  determination  of  the  mechanical  equi- 
valent by  means  of  the  heat  produced  by  the  compression  of  lead.  A 
large  block  of  sandstone,  CD  (fig.  339),  is  suspended  vertically  by  cords  ; 


Fig.  339. 


its  weight  is  P.  E  is  a  piece  of  lead,  fashioned  so  that  its  temperature 
may  be  determined  by  the  introduction  of  a  thermometer.  The  weight  of 
this  is  n,  and  its  specific  heat  c.  AB  is  a  cylinder  of  cast  iron,  whose 
weight  is/.  If  this  be  raised  to  A^B^,  a  height  of  /z,  and  allowed  to  fall 
again,  it  compresses  the  lead,  E,  against  the  anvil,  CD.  It  remains  to 
measure  on  the  one  hand  the  work  lost,  and  on  the  other  the  heat 
gained. 

The  hammer  AB  being  raised  to  a  height  h,  the  work  of  its  fall  is//z, 
but  as,  by  its  elasticity,  it  rises  again  to  a  height  h^  the  work  is/  {h-h^. 
The  anvil,  CD,  on  the  other  hand,  has  been  raised  to  a  height  H,  and 
has  absorbed  in  so  doing  PH  units  of  work.     The  work,  W,  definitely  ab- 


*♦ 


-467]  Mechanical  Equivalent  of  Heat.  405 

sorbed  by  the  lead  is  p  {h-h)  -  PH.  On  the  other  hand,  the  lead  has  been 
heated  by  9,  it  has  gained  n^V  thermal  units,  c  being  the  specific  heat  of 
lead,  and  the  mechanical  equivalent   is  therefore  equal  to  the  quotient 

A  series  of  six  experiments  gave  1394  as  the  mechanical  equivalent. 

The  following  is  the  method  which  Mayer  employed  in  calculating  the 
mechanical  equivalent  of  heat.  It  is  taken,  with  slight  modifications, 
from  Prof  Tyndall's  work  on  'Heat,' who,  while  strictly  following  Mayer's 
reasoning,  has  corrected  his  data. 

Let  us  suppose  that  a  rectangular  vessel  with  a  section  of  a  square 
foot  contains  at  0°  a  cubic  foot  of  air  under  the  ordinary  atmospheric 
pressure;  and  let  us  suppose  that  it  is  enclosed  by  a  piston  without 
weight. 

Suppose  now  that  the  cubic  foot  of  air  is  heated  until  its  volume  is 
doubled  ;  from  the  coefficient  of  expansion  of  air  we  know  that  this  is  the 
case  at  273°  C.  The  gas  in  doubling  its  volume  will  have  raised  the 
piston  through  a  foot  in  height ;  it  will  have  lifted  the  atmospheric  pressure 
through  this  distance.  But  the  atmospheric  pressure  on  a  square  foot  is 
in  round  numbers  15  x  144  =  2160  pounds.  Hence  a  cubic  foot  of  air  in 
doubling  its  volume  has  lifted  a  weight  of  2160  pounds  through  a  height 
of  a  foot. 

Now  a  cubic  foot  of  air  at  zero  weighs  1-29  ounces,  and  the  specific 
heat  of  air  under  constant  pressure,  that  is,  when  it  can  expand  freely,  as 
compared  with  that  of  an  equal  weight  of  water,  is  0*24 ;  so  that  the 
quantity  of  heat  which  will  raise  1-29  ounce  of  air  through  273°  will  only 
raise  0*24  x  1-29  =  0*3 1  oz.  of  water  through  the  same  temperatue ;  but 
0-31  oz.  of  water  raised  through  273°  is  equal  to  5*29  pounds  of  water 
raised  through  1°  C. 

That  is,  the  quantity  of  heat  which  will  double  the  volume  of  a  cubic 
foot  of  air,  and  in  so  doing  will  lift  2160  pounds  through  a  height  of  a 
foot,  is  5-29  thermal  units. 

Now  in  the  above  case  the  gas  has  been  heated  under  constant  pres- 
sure, that  is,  when  it  could  expand  freely.  If,  however,  it  had  been 
heated  under  constant  volume,  its  specific  heat  would  have  been  less  in 
the  ratio  i  :  i'4i4  (423),  so  that  the  quantity  of  heat  required  under  these 
circumstances  to  raise  the  temperature  of  a  cubic  foot  of  air  would  be 

5-29  X =  374.     Deducting  this  from  5-29,  the  difference  1-55  repre- 

1-41 

sents  the  weight  of  water  which  would  have  been  raised  1°  C.  by  the  ex- 
cess of  heat  imparted  to  the  air  when  it  could  expand  freely.  But  this 
excess  has  been  consumed  in  the  work  of  raising  2160  pounds  through  a 
foot.  Dividing  this  by  1-55  we  have  1393.  Hence  the  heat  which  will 
raise  a  pound  of  water  through  1°  C.  wiH  raise  a  weight  of  1393  pounds 
through  a  height  of  a  foot;  a  numerical  value  of  the  mechanical  equiva- 
lent of  heat  agreeing  as  closely  as  can  be  expected  with  that  which  Joule 
adopted  as  the  most  certain  of  his  experimental  results.  ' 

The  law  of  the  relation  of  heat  to  mechanical  energy  may  thus  be  stated  : 
Heat  ami  inechanical  energy  are  mutually  convertible;  and  heat  requires 


4o6 


On  Heat. 


[467- 


for  its  production^  and  prodiises  by  its  disappearance,  mechanical  energy 
in  the  ratio  of  1390  foot-pounds  for  every  thermal  taiit. 

A  variety  of  experiments  may  in  like  manner  be  adduced  to  show  that 
whenever  heat  disappears  work  is  produced.  For  example,  if  in  a  reser- 
voir immersed  in  water  the  air  be  compressed  to  the  extent  of  10  atmo- 
spheres :  supposing  that  now,  when  the  compressed  air  has  acquired  the 
temperature  of  the  water,  it  be  allowed  to  act  upon  a  piston  loaded  by  a 
weight,  the  weight  is  raised.  At  the  same  time  the  water  becomes  cooler, 
showing  that  a  certain  quantity  of  heat  had  disappeared  in  producing  the 
mechanical  effort  of  raising  the  weight. 

This  may  also  be  illustrated  by  the  following  experiment,  due  to  Prof. 
Tyndall. 

A  strong  metal  box  is  taken,  provided  with  a  stopcock,  on  which  can 
be  screwed  a  small  condensing  pump.  Having  compressed  the  air  by  its 
means,  as  it  becomes  heated  by  this  process,  the  box  is  allowed  to  stand 
for  some  time,  until  it  has  acquired  the  temperature  of  the  surrounding 


Fig.  340. 

medium.  On  opening  the  stopcock,  the  air  rushes  out;  it  is  expelled  by 
the  expansive  force  of  the  internal  air ;  in  short,  the  air  drives  itself  out. 
Work  is  therefore  performed  by  the  gas,  and  there  should  be  a  disap- 
pearance of  heat ;  and  if  the  jet  of  gas  be  allowed  to  strike  against  the 
thermo-pile,  the  galvanometer  is  deflected,  and  the  direction  of  its  deflec- 
tion indicates  a  cooling  (fig.  340). 

If,  on  the  contrary,  the  experiment  is  made  with  an  ordinary  pair  of 
bellows,  and  the  current  of  air  is  allowed  to  strike  against  the  battery,  the 
deflection  of  the  galvanometer'is  in  the  opposite  direction,  indicating  an 
increase  of  temperature  (fig.  341).  In  this  case  the  hand  of  the  experi- 
menter performs  the  work,  which  is  converted  into  heat. 

Joule  placed  in  a  calorimeter  two  equal  copper  reservoirs,  which  could 
be  connected  5y  a  tube.     One  of  these  contained  air  at  22  atmospheres, 


-468] 


Mechanical  Equivalents  of  Heat. 


407 


the  other  was  exhausted.  When  they  were  connected,  they  came  into 
equihbrium  under  a  pressure  of  1 1  atmospheres  ;  but  as  the  gas  in  expand- 
ing had  done  no  work,  there  was  no  alteration  in  temperature.  When, 
however,  the  second  reservoir  was  full  of  water,  the  air  in  entering  was 


fig.  34 


obliged  to  expel  it  and  thus  perform  work,  and  the  temperature  sank, 
owing  to  an  absorption  of  heat. 

For  further  information  the  student  of  this  subject  is  referred  to  the 
following  works : — Tyndall  on  Heat  as  a  Mode  of  Motion,  Maxwell  on 
Heat  (Longmans),  Balfour  Stewart  on  Heat  (Macmillan),  and  Tait  on 
Thermodynamics  (Edmonston  and  Douglas).  A  condensed,  though 
complete  and  systematic,  account  of  the  dynamical  theory  of  heat  is  met 
with  in  Professor  Foster's  articles  on  '  Heat,'  in  Watts's  Dictionary  of 
Chemistry. 

468.  Dissipation  of  energry. — Rankine  has  the  following  interesting 
observations  on  a  remarkable  consequence  of  the  mutual  convertibility 
which  has  been  shown  to  exist  between  heat  and  other  forms  of  energy. 
Sir  W.  Thomson  has  pointed  out  the  fact,  that  there  exists  at  least  in 
the  present  state  of  the  known  world  a  predominating  tendency  to  the 
conversion  of  all  the  other  forms  of  physical  energy  into  heat,  and  to  the 
uniform  diffusion  of  all  heat  throughout  all  matter.  The  form  in  which 
we  generally  find  energy  originally  collected  is  that  of  a  store  of  chemical 
power  consisting  of  uncombined  elements.  The  combination  of  these 
elements  produces  energy  in  the  form  known  by  the  name  of  electrical 
currents,  part  only  of  which  can  be  employed  in  analysing  chemical 
compounds,  and  thus  reconverted  into  a  store  of  chemical  power ;  the 
remainder  is  necessarily  converted  into  heat;  apart  only  of  this  heat  can 
be  employed  in  analysing  compounds  or  in  reproducing  electric  currents. 
If  the  remainder  of  the  heat  be  employed  in  expanding  an  elastic  substance, 
it  may  be  converted  entirely  into  visible  motion,  or  into  a  store  of  visible 
mechanical  power,  (by  raising  weights,  for  example)  provided  the  elastic 


4o8 


On  Heat, 


[468 


substance  is  enabled  to  expand  until  its  temperature  falls  to  the  point 
which  corresponds  to  the  absolute  privation  of  heat;  but  unless  this 
condition  is  fulfilled,  a  certain  proportion  only  of  the  heat,  depending  on 
the  range  of  temperature  through  which  the  elastic  body  works,  can  be 
converted,  the  rest  remaining  in  the  state  of  heat.  On  the  other  hand, 
al]  visible  motion  is  of  necessity  ultimately  converted  into  heat  by  the 
agency  of  friction.  There  is  then  in  the  present  state  of  the  known  world, 
a  tendency  towards  the  conversion  of  all  physical  energy  into  the  sole 
form  of  heat. 

Heat,  moreover,  tends  to  diffuse  itself  uniformly  by  conduction  and 
radiation,  until  all  matter  shall  have  acquired  the  same  temperature. 
There  is,  consequently,  so  far  as  we  understand  the  present  condition  of 
the  universe,  a  tendency  towards  a  state  in  which  all  physical  energy  will 
be  in  the  state  of  heat,  and  that  heat  so  diffused,  that  all  matter  will  be 
at  the  same  temperature ;  so  that  there  will  be  an  end  of  all  physical 
phenomena. 

Vast  as  this  speculation  may  seem,  it  appears  to  be  soundly  based  on 
experimental  data,  and  to  truly  represent  the  present  condition  of  the 
universe  as  far  as  we  know  it. 


r-/ 


-469]       Transmission,  Velocity,  and  Intensity  of  Light.      409 


n 


BOOK  VII. 

ON   LIGHT. 


:    ,/    ./<^'/7t^   ^^(QHAPTE^   I.  /  ' 

TRANSMISSION,  VELOCITY,  AND   INTENSITY  OF   LIGHT. 

469.  Theories  of  lig-bt. — Light  is  the  agent  v/hich,  by  its  action  on 
the  retina,  excites  in  us  the  sensation  of  vision.  That  part  of  physics 
which  deals  with  the  properties  of  Hght  is  known  as  optics. 

In  order  to  explain  the  origin  of  light,  various  hypotheses  have  been 
made,  the  most  important  of  which  are  the  <?;«m/<7«  or  <r^r/«ja(!/rtr  theory, 
and  the  undidatory  theory. 

On  the  emission  theory  it  is  assumed  that  luminous  bodies  emit,  in  all 
directions,  an  imponderable  substance,  which  consists  of  molecules  of  an 
extreme  degree  of  tenuity  ;  these  are  propagated  in  right  lines  with  an 
almost  infinite  velocity.  Penetrating  into  the  eye  they  act  on  the  retina, 
and  determine  the  sensation  which  constitutes  vision. 

On  the  undulatory  theory,  all  bodies,  as  well  as  the  celestial  spaces, 
are  filled  by  an  extremely  subtle  elastic  medium,  which  is  called  the  liimi- 
niferoHs  ether.  The  luminosity  of  a  body  is  due  to  an  infinitely  rapid 
vibratory  motion  of  its  molecules,  which,  when  communicated  to  the 
ether  is  propagated  in  all  directions  in  the  form  of  spherical  waves,  and 
this  vibratory  motion,  being  thus  transmitted  to  the  retina,  calls  forth  the 
sensation  of  vision.  The  vibrations  of  the  ether  take  place  not  in  the 
direction  of  the  wave,  but  in  a  plane  at  right  angles  to  it.  The  latter  are 
called  the  transversal  vibrations.  An  idea  of  these  may  be  formed  by 
shaking  a  rope  at  one  end.  The  vibrations,  or  to  and  fro  movements,  of 
the  particles  of  the  rope,  are  at  right  angles  to  the  length  of  the  rope,  but 
the  onward  motion  of  the  wave's  form  is  in  the  direction  of  the  length. 

On  the  emission  theory  the  propagation  of  light  is  effected  by  a  motion 
of  translation  of  particles  of  light  thrown  out  from  the  luminous  body, 
as  a  bullet  is  discharged  from  a  gun  ;  on  the  undulatory  theory  there  is 
no  progressive  motion  of  the  particles  themselves,  but  only  of  the  state 
of  disturbance  which  was  communicated  by  the  luminous  body ;  it  is  a 
motion  of  osdllation,  and,  like  the  propagation  of  waves  in  water,  takes 
place  by  a  series  of  vibrations. 

The  luminiferous  ether  penetrates  all  bodies,  but  on  account  of  its 


410  On  Light:  [469- 

extreme  tenuity  it  is  uninfluenced  by  gravitation  ;  it  occupies  space,  and 
although  it  presents  no  appreciable  resistance  to  the  motion  of  the  denser 
bodies,  it  is  possible  that  it  hinders  the  motion  of  the  smaller  comets. 
It  has  been  found,  for  example,  that  Encke's  comet,  whose  period  of  revo- 
lution is  about  3^  years,  has  its  period  diminished  by  about  O'li  of  a  day 
at  each  successive  rotation,  and  this  -diminution  is  ascribed  by  some  to 
the  resistance  of  the  ether. 

The  fundamental  principles  of  the  undulatory  theory  were  enunciated 
by  Huyghens,  and  subsequently  by  Euler.  The  emission  theory  prin- 
cipally owing  to  Newton's  powerful  support,  was  for  long  the  prevalent 
scientific  creed.  The  undulatory  theory  was  adopted  and  advocated  by 
Young,  who  showed  hoM-  a  large  number  of  optical  phenomena,  particularly 
those  of  diffraction,  were  to  be  explained  by  that  theory.  Subsequently  to, 
though  independently  of,  Young,  Fresnel  showed  that  the  phenomena  of 
diffraction,  and  also  those  of  polarisation,  are  explicable  on  the  same 
theory,  which,  since  his  time,  has  been  generally  accepted. 

The  undulatory  theory  not  only  explains  the  phenomena  of  light,  but  it 
reveals  an  intimate  connection  between  these  phenomena  and  those  of  heat 
(402);  it  shows  also,  how  completely  analogous  the  phenomena  of  light 
are  to  those  of  sound,  regard  being  had  to  the  differences  of  the  media  in 
which  these  two  classes  of  phenomena  take  place. 

470.  Xiuxninous,  transparent,  translucent,  and  opaque  bodies. — 
Luminous  bodies  are  those  which  emit  light,  such  as  the  sun,  and  ignited 
bod.'es.  Transpareiit  ox  diaphanous  bodies  are  those  which  readily  trans- 
mit light,  and  through  which  objects  can  be  distinguished  ;  water,  gases, 
polished  glass,  are  of  this  kind.  Translucent  bodies  transmit  light,  but 
objects  cannot  be  distinguished  through  them  :  ground  glass,  oiled  paper, 
etc.,  belong  to  this  class.  Opaque  bodies  do  not  transmit  fight;  for  ex- 
ample, wood,  metals,  etc.  No  bodies  are  quite  opaque  ;  they  are  all 
more  or  less  translucent  when  cut  in  sufficiently  thin  leaves. 

Foucault  has  recently  shown  that  when  the  object  glass  of  a  telescope 
is  thinly  silvered,  the  layer  is  so  transparent,  that  the  sun  can  be  viewed 
through  it  without  danger  to  the  eyes,  since  the  metalhc  surface  reflects 
the  greater  part  of  the  heat  and  light. 

471.  Ziuminous  ray  and  pencil. — A  luminous  7'ay  is  the  direction  of 
the  line  in  which  light  is  propagated  ;  a  luminous pe7icil  is  a  collection 
of  rays  from  the  same  source  ;  it  is  said  to  h^  parallel  v^\itx\  it  is  composed 
of  parallel  rays,  divergeiit  when  the  rays  separate  from  each  other,  and 
convergent  when  they  tend  towards  the  same  point.  Every  luminous  body 
emits  divergent  rectilinear  rays  from  all  its  points,  and  in  all  directions. 

472.  Propag:ation  ofligrbt  in  a  bomog:eneous  medium. — A  medium 
is  any  space  or  substance  which  light  can  traverse,  such  as  a  vacuum,  air, 
water,  glass,  etc.  A  medium  is  said  to  be  homogeneous  when  its  chemical 
composition  and  density  are  the  same  in  all  parts. 

/;/  every  homogeneous  medium  light  is  propagated  in  a  right  line.  For, 
if  an  opaque  body  is  placed  in  the  right  fine  which  joins  the  eye  and  the 
luminous  body,  the  light  is  intercepted.  The  light  which  passes  into 
a  dark  room  by  a  small  aperture,  leaves  a  luminous  trace,  which  is 


473] 


Shadoiv,  Pemunbra. 


411 


visible  from  the  light  falling  on  the  particles  suspended  in  the  atmo- 
sphere. 

Light  changes  its  direction  on  meeting  an  object  which  it  cannot  pene- 
trate, or  when  it  passes  from  one  medium  to  another.  These  phenomena 
will  be  described  under  the  heads  re/lection  and  refraction. 

473.  Shadow,  penumbra. — When  light  falls  upon  an  opaque  body  it 
cannot  penetrate  into  the  space  immediately  behind  it,  and  this  space  is 
called  the  shadow. 

In  determining  the  extent  and  the  shape  of  a  shadow  projected  by  a 
body,  two    cases   are   to  be  distinguished  :    that  in   which    the    source 


Fig.  342. 

of  light  is  a  single  point,  and  that  in  which  it  is  a  body  of  any  given 
extent. 

In  the  first  case,  let  S  (fig.  342)  be  the  luminous  point, and  M  a  spherical 
body,  which  causes  the  shadow.  If  an  infinitely  long  straight  line,  SG, 
move  round  the  sphere  M  tangentially,  always  passing  through  the  point 
S,  this  line  will  produce  a  conical  surface,  which,  beyond  the  sphere,  sepa- 
rates that  portion  of  space  which  is  in  shadow  from  that  which  is  illuminated. 
In  the  present  case,  on  placing  behind  the  opaque  body  a  screen,  PO,  the 
limit  of  the  shadow  HG  will  be  sharply  defined.  This  is  not,  however, 
usually,  the  case,  for  luminous  bodies  have  always  a  certain  magnitude, 
and  are  not  merely  luminous  points. 


Fig-  343- 

Suppose  that  the  luminous  and  illuminated  bodies  are  two  spheres,  SL 
and  MN  (fig.  343).  If  an  infinite  straight  line,  AG,  moves  tangentially  to 
both  spheres,  always  cutting  the  line  of  the  centre  in  the  point  A,  it  will 
produce  a  conical  surface  with  this  .point  for  a  summit,  and  which  traces 
behind  the  sphere  MN  a  perfectly  dark  space,  MGHN.  If  a  second  right 
Ime,  LD,  which  cuts  the  fine  of  centre  in  B,  moves  tangentially  to  the  two 
spheres,  so  as  to  produce  a  new  conical  surface,  BDC,  it  will  be  seen  that 

T  2 


412 


On  Light. 


[473 


all  the  space  outside  this  surface  is  illuminated,  but  that  the  part  between 
the  two  conical  surfaces  is  neither  quite  dark  nor  quite  light.  So  that  if  a 
screen,  PO,  is  placed  behind  the  opaque  body,  the  portion  cOdYi  of  the 
screen  is  quite  in  the  shadow,  while  the  space  ab  receives  light  from  cer- 
tain parts  of  the  luminous  body,  and  not  from  others.  It  is  brighter  than 
the  true  shadow,  and  not  so  bright  as  the  rest  of  the  screen,  and  it  is  ac- 
cordingly called  the pe numb ?^a. 

Shadows  such  as  these  dse  geometrical  shadows ;  physical  shadows^  ox 
those  which  are  really  seen,  are  by  no  means  so  sharply  defined.  A  cer- 
tain quantity  of  light  passes  into  the  shadow,  even  when  the  source  of  light 
is  a  mere  point,  and  conversely  the  shadow  influences  the  illuminated  part. 
This  phenomenon,  which  will  be  afterwards  described,  is  known  by  the 
name  of  diffractio7i. 

474.  Xmag:es  produced  by  small  apertures. — When  luminous  rays, 
which  pass  into  a  dark  chamber  through  a  small  apert^ii^e,  are  received 
upon  a  screen,  they  form  images  of  external  objects.  These  images  are 
inverted  ;  their  shape  is  always  that  of  the  external  objects,  and  is  inde- 
pendent of  the  shape  of  the  aperture. 

The  inversion  of  the  images  arises  from  the  fact  that  the  luminous  rays 
proceeding  from  external  objects,  and  penetrating  into  the  chamber, 
cross  one  another  in  passing  the  aperture,  as  shown  in  fig.  344.     Con- 


Fig.  344- 


tinuing  in  a  straight  line,  the  rays  from  the  higher  parts  meet  the  screen 
at  the  lower  parts,  and  inversely,  those  which  come  from  the  lower  parts 
meet  the  higher  parts  of  the  screen.  Hence  the  inversion  of  the  image. 
In  the  article  Camera  obscura,  it  will  be  seen  how  the  brightness  and  pre- 
cision of  the  images  are  increased  by  means  of  lenses. 

In  order  to  show  that  the  shape  of  the  image  is  independent  of  that  of 
the  aperture,  when  the  latter  is  sufficiently  small,  and  the  screen  at  an 
adequate  distance,  imagine  a  triangular  aperture,  O  (fig.  345),  made  in  the 
door  of  a  dark  chamber,  and  let  ab  be  a  screen  on  which  is  received  the 
image  of  a  flame,  AB.  A  divergent  pencil  from  each  point  of  the  flame 
penetrates  through  the  aperture,  and  forms  on  the  screen  a  triangular 
image  resembling  the  aperture.  But  the  union  of  all  these  partial  images 
produces  a  total  image  of  the  same  form  as  the  luminous  object.  For  if 
we  conceive  that  an  infinite  straight  line  moves  round  the  aperture,  with 
the  condition  that  it  is  always  tangential  to  the  luminous  object  AB,  and 
that  the  aperture  is  very  small,  the  straight  line  describes  two  cones,  the 


-476] 


Velocity  of  Light. 


413 


apex  of  which  is  the  aperture,  while  one  of  the  bases  is  the  luminous  ob- 
ject, and  the  other  the  luminous  object  on  the  screen — that  is,  the  image. 
Hence,  if  the  screen  is  perpendicular  to  the  right  line  joining  the  centre  of 


Fig.  345. 

the  aperture  and  the  centre  of  the  luminous  body,  the  image  is  similar  to 
the  body  ;  but  if  the  screen  is  obhque,  the  image  is  elongated  in  the  direc- 
tion of  its  obliquity.  This  is  what  is  seen  in  the  shadow  produced  by 
foliage  ;  the  luminous  rays  passing  through  the  leaves  produce  images 
of  the  sun,  which  are  either  round  or  elliptical,  according  as  the  ground 
is  perpendicular  or  oblique  to  the  solar  rays,  and  this  is  the  case  whatever 
be  the  shape  of  the  aperture  through  which  the  light  passes. 

475.  Velocity  of  ligrlit. — Light  moves  with  such  a  velocity  that  at  the 
surface  of  the  earth  there  is,  to  ordinary  observation,  no  appreciable  in- 
terval between  the  occurrence  of  any  luminous  phenomenon  and  its  per- 
ception by  the  eye.  And  accordingly,  this  velocity  was  first  detehnined 
by  means  of  astronomical  observations.  Romer,  a  Danish  astronomer,  in 
1675,  first  deduced  the  velocity  of  light  from  an  observation  of  the 
eclipses  of  Jupiter's  first  satellite. 

Jupiter  is  a  planet,  round  which  four  satellites  revolve  as  the  moon  does 
round  the  earth.     This  first  satellite,  E  (fig.  346),  suffers  occultation — that 


Fijj.  346. 

is,  passes  into  Jupiter's  shadow — at  equal  intervals  of  time,  which  are 
42h.  28m.  36s.  While  the  earth  moves  in.that  part  of  its  orbit,  ab,  nearest 
Jupiter,  its  distance  from  that  planet  does  not  materially  alter,  and  the 
intervals  between  two  successive  occultations  of  the  satellite  are  approxi- 
mately the  same  ;  but  in  proportion  as  the  earth  moves  away  in  its  revo- 
lution round  the  sun,  S,  the  interval  between  two  occultations  increases, 
and  when,  at  the  end  of  six  months,  the  earth  has  passed  from  the  position 


414 


On  Light. 


[475- 


T  to  the  position  T',  a  /^/rt/ retardation  of  i6m.  36s.  is  observed  between 
the  time  at  which  the  phenomenon  is  seen  and  that  at  which  it  is  calcu- 
lated to  take  place.  But  when'  the  earth  was  in  the  position  T,  the  sun's 
light  reflected  from  the  satellite  E  had  to  traverse  the  distance  ET,  while 
in  the  second  position  the  light  had  to  traverse  the  distance  ET'.  This 
distance  exceeds  the  first  by  the  quantity  TT',  for  from  the  great  distance 
of  the  satellite  E,  the  rays  ET  and  ET'  may  be  considered  parallel.  Con- 
sequently, hght  requires  i6m.  36s.  to  travel  the  diameter  TT'  of  the  ter- 
restrial orbit,  or  twice  the  distance  of  the  earth  from  the  sun,  which  gives 
for  its  velocity  190,00x3  miles  in  a  second. 

The  stars  nearest  the  earth  are  separated  from  it  by  at  least  206,265 
times  the  distance  of  the  sun.  Consequently,  the  light  which  they  send 
requires  3^  years  to  reach  us.  Those  stars,  which  are  only  visible  by  means 
of  the  telescope,  are  possibly,  at  such  a  distance  that  thousands  of  years 
would  be  required  for  their  light  to  reach  our  planetary  system.  They 
might  have  been  extinguished  for  years  without  our  knowing  it. 

476.  Foucault's  apparatus  for  determiningr  tbe  velocity  of  lig-bt. — 
Notwithstanding  the  prodigious  velocity  of  light,  M.  Foucault  has  suc- 
ceeded in  determining  it  experimentally  by  the  aid  of  an  ingenious  appa- 
ratus, based  on  the  use  of  the  rotating  mirror,  which  was  adopted  by 
Mr.  Wheatstone  in  measuring  the  velocity  of  electricity. 

In  the  description  of  this  apparatus,  a  knowledge  of  the  principal  pro- 
perties of  mirrors  and  of  lenses  is  presupposed.  Figure  347  represents  the 


Fig.  347- 


Fig.  34S. 


principal  parts  of  M.  Foucault's  arrangement.  The  window  shutter,  K,  of 
a  dark  chamber  is  perforated  by  a  square  aperture,  behind  which  a  platinum 
w^ire,  0,  is  stretched  vertically.  A  beam  of  solar  light  reflected  from  the 
outside  upon  a  mirror  enters  the  darkroom  by  the  square  aperture, meets 
the  platinum  wire,  and  then  traverses  an  achromatic  lens,  L,  with  a  long 
focus,  placed  at  a  distance  from  the  platinum  wire  less  than  double  the 


-476]  Velocity  of  L  ight.  4 1 5 

principal  focal  distance.  The  image  of  the  platinum  wire,  more  or  less 
magnified,  would  thus  be  formed  on  the  axis  of  the  lens  ;  but  the  luminous 
pencil  having  traversed  the  lens,  impinges  on  a  plane  mirror,  ;;z,  rotating 
with  great  velocity  ;  it  is  reflected  from  this,  and  forms  in  space  an  image 
of  the  platinum  wire,  which  is  displaced  with  an  angular  velocity  double 
that  of  the  mirror  (489).  This  image  is  reflected  by  a  concave  mirror,  M, 
whose  centre  of  curvature  coincides  with  the  axis  of  rotation  of  the  mirror 
;;/,  and  with  its  centre  of  figure.  The  pencil  reflected  from  the  mirror  M 
returns  upon  itself,  is  again  reflected  from  the  mirror  in,  traverses  the 
lens  a  second  time,  and  forms  an  image  of  the  platinum  wire,  which 
appears  on  the  wire  itself  so  long  as  the  mirror  m  turns  slowly. 

In  order  to  see  this  image  without  hiding  the  pencil  which  enters  by 
the  aperture  K,  a  mirror  of  unsilvered  glass,  V,  with  parallel  faces,  is 
placed  between  the  lens  and  the  wire,  and  is  inclined  so  that  the  reflected 
rays  fall  upon  a  powerful  eyepiece,  P. 

The  apparatus  being  arranged,  if  the  mirror  m  is  at  rest,  the  ray  after 
meeting  M  is  reflected  to  ?;/,  and  from  thence  returns  along  its  former 
path,  till  it  meets  the  glass  plate  V  in  «,  and  being  partially  reflected, 
forms  at  d — the  distance  ad  being  equal  to  ao — an  image  of  the  wire, 
which  the  eye  is  enabled  to  observe  by  means  of  the  eyepiece  P.  If  the 
mirror,  instead  of  being  fixed,  is  moving  slowly  round — its  axis  being  at 
right  angles  to  the  plane  of  the  paper— there  will  be  no  sensible  change  in 
the  position  of  the  mirror  ni  during  the  brief  interval  elapsing  while  light 
travels  from  in  to  M  and  back  again,  but  the  image  will  alternately  disap- 
pear and  reappear.  If  now  the  velocity  of  m  is  increased  to  upwards  of 
30  turns  per  second,  the  interval  between  the  disappearance  and  reap- 
pearance is  so  short  that  the  impression  on  the  eye  is  persistent,  and  the 
image  appears  perfectly  steady. 

Lastly,  if  the  mirror  turns  with  sufficient  velocity,  there  is  an  appreci- 
able change  in  its  position  during  the  time  which  the  light  takes  in  making 
the  double  journey  from  in  to  M,  and  from  M  to  ;;/  ;  the  return  ray,  after 
its  reflection  from  the  mirror  ;«,  takes  the  direction  inb,  and  forms  its 
image  at  / ;  that  is,  the  image  has  undergone  a  total  deviation,  di. 
Speaking  precisely,  there  is  a  deviation  as  soon  as  the  mirror  turns,  even 
slowly,  but  it  is  only  appreciable  when  it  has  acquired  a  certain  magni- 
tude, which  is  the  case  when  the  velocity  of  rotation  is  sufficiently  rapid, 
or  the  distance  Mw  sufficiently  great,  for  the  deviation  necessarily  in- 
creases with  the  time  which  the  light  takes  in  returning  on  its  own  path. 

In  M.  Foucault's  experiment  the  distance  M;;/  was  only  13^  feet ;  when 
the  mirror  rotated  with  a  velocity  of  600  to  800  turns  in  a  second,  devia- 
tions of  ^-^  to  Yo  of  3-  millimetre  were  obtained 

If  yim  =  l,  Lm  =  /',  oL  =  r,  and  representing  by  n  the  number  of  turns 
in  a  second,  by  <'  the  absolute  deviation  di,  and  by  V  the  velocity  of  light, 
M.  Foucault  arrived  at  the  formula 

y_    SirPnr 

from   which   the   velocity  of  fight  is   calculated  at    185,157  miles  in  a 


41 6  On  Light.  [476- 

second  ;  this  number,  which  is  less  than  that  ordinarily  assumed,  agrees 
remarkably  well  with  the  value  deduced  from  the  new  determinations  of 
the  value  of  the  solar  parallax. 

In  this  apparatus  hquids  can  be  experimented  upon.  For  that  purpose 
a  tube,  AB,  lo  feet  long,  and  filled  with  distilled  water,  is  placed  between 
th2  turning  mirror  ;;z,  and  a  concave  mirror  M',  identical  with  the  mirror 
M.  The  luminous  rays  reflected  by  the  rotating  mirror,  in  the  direction 
wM',  traverse  the  column  of  water  AB  twice  before  returning  to  V.  But 
the  return  ray  then  becomes  reflected  at  c,  and  forms  its  image  at  h  ;  the 
deviation  is  consequently  greater  for  rays  which  have  traversed  water 
than  for  those  which  have  passed  through  air  alone  ;  hence  the  velocity 
of  light  is  less  in  water  than  in  air. 

This  is  the  most  important  part  of  these  experiments.  For  it  had  been 
shown  theoretically  that  on  the  undulatory  theory  the  velocity  of  light 
must  be  less  in  the  more  highly  refracting  medium,  while  the  very  oppo- 
site is  a  necessary  consequence  of  the  emission  theory.  Hence  Foucault's 
result  may  be  regarded  as  a  crucial  test  of  the  validity  of  the  undulatory 
theory. 

The  mechanism  which  M.  Foucault  uses  to  turn  the  mirror  with  great 
velocity  consists  of  a  small  steam  turbine,  bearing  a  sort  of  resemblance 
to  the  syren,  and,  like  that  instrument,  giving  a  higher  sound  as  the  ro- 
tation is  more  rapid  ;  in  fact,  it  is  by  the  pitch  of  the  note  that  the 
velocity  of  the  rotation  is  determined. 

477.  Experiments  of  WC.  Fizeau. — In  1849  M.  Fizeau  measured 
directly  the  velocity  of  light,  by  ascertaining  the  time  it  took  to  travel 
from  Suresnes  to  Montmartre  and  back  again.  The  apparatus  employed 
was  a  toothed  wheel,  capable  of  being  turned  more  or  less  quickly,  and 
with  a  velocity  that  could  be  exactly  ascertained.  The  teeth  were  made 
of  precisely  the  same  width  as  the  intervals  between  them.  The  appa- 
ratus being  placed  at  Suresnes,  a  pencil  of  parallel  rays  was  transmitted 
through  an  interval  between  two  teeth  to  a  mirror  placed  at  Montmartre. 
The  pencil,  directed  by  a  properly-arranged  system  of  tubes  and  lenses, 
returned  to  the  wheel.  As  long  as  the  apparatus  was  at  rest  the  pencil 
returned  exactly  through  the  same  interval  as  that  through  which  it  first 
set  out.  But  when  the  wheel  was  turned  sufficiently  fast,  a  tooth  was 
made  to  take  the  place  of  an  interval,  and  the  ray  was  intercepted.  By 
causing  the  wheel  to  turn  more  rapidly,  it  reappeared  when  the  interval 
between  the  next  two  testh  had  taken  the  place  of  the  former  tooth  at  the 
instant  of  the  return  of  the  pencil. 

The  distance  between  the  two  stations  was  28,334  ft.  By  means  of  the 
data  furnished  by  this  distance,  by  the  dimensions  of  the  wheel,  its 
velocity  of  rotation,  etc.,  M.  Fizeau  found  the  velocity  of  light  to  be 
196,000  miles  per  second,  a  result  agreeing  with  that  given  by  astronomi- 
cal observation  as  closely  as  can  be  expected  in  a  determination  of  this 
kind. 

M.  Comu  has  recently  investigated  the  velocity  of  light  by  M.  Fizeau's 
method,  and  has  obtained  the  number  185,420  miles.     The  two  stations, 


-478]  In  tensity  of  L  ight.  4 1 7 

which*  were  6-4  miles  apart,  were  a  pavilion  of  the  Ecole  Polytechnique 
and  a  room  in  the  barracks  of  Mont  Valerien. 

478.  laws  of  the  intensity  of  ligrht. — The  intensity  of  illumination 
is  the  quantity  of  light  received  on  the  unit  of  surface;  it  is  subject  to 
the  following  laws  : — 

I.  The  intensity  of  illumination  on  a  given  surface  is  inversely  as  the 
square  of  its  distance  from  the  source  of  light. 

II.  The  intensity  of  illumination  which  is  received  obliquely  is  propor- 
tional to  the  cosine  of  the  angle  which  the  luminous  rays  7nake  with  the 
normal  to  the  illuminated  surface. 

In  order  to  demonstrate  the  iirst  law,  let  there  be  two  circular  screens, 
CD  and  AB  (fig.  349),  one  placed  at  a  certain  distance  from  a  source  of 
light,  L,  and  the  other  at  double  this  distance,  and  let  j  and  S  be  the 


Fig-  349-    • 

areas  of  the  two  screens.  Ma  be  the  total  quantity  of  light  which  is 
emitted  by  the  source  in  the  direction  of  the  cone  ALB,  the  intensity  of 
the  light  on  the  screen  CD,  that  is,  the  quantity  which  falls  on  the  unit 

of  surface  is  -,  and  the  intensity  on  the  screen  AB  is  -.      Now,   as   the 
s  S 

triangles  ALB  and  CLD  are  similar,  the  diameter  of  AB  is  double  that  of 

CD  ;  and  as  the  surfaces  of  circles  are  as  the  squares  of  their  diameters, 

the  surface  S  is  four  times  s^  consequently  the  intensity  ^  is   one-fourth 

o 

Of^ 

s ' 

The  same  law  may  also  be  demonstrated  by  an  experiment  with  the 
apparatus  represented  in  fig.  351.  It  is  made  by  comparing  the  shadows 
of  an  opaque  rod  cast  upon  a  glass  plate,  in  one  case  by  the  fight  of  a 
single  candle,  and  in  another  by  that  of  four  candles,  placed  at  double 
the  distance  of  the  first.  In  both  cases  the  shadows  have  the  same 
intensity. 

Figure  349  shows  that  it  is  owing  to  the  divergence  of  the  luminous 
rays  emitted  from  the  same  source  that  the  intensity  of  light  is  inversely 
as  the  square  of  the  distance.  The  illumination  of  a  surface  placed  in  a 
beam  of  parallel  luminous  rays  is  the  same  at  all  distances,  at  any  rate  in 
a  vacuum,  for  in  air  and  in  other  transparent  media  the  intensity  of  light 
decreases  in  consequence  of  absorption,  but  far  more  slowly  than  the 
square  of  the  distance. 


On  Light. 


[478 


The  second  law  of  intensity  corresponds  to  the  law  which  we  have 
found  to  prevail  for  heat :  it  may  be  theoretically  deduced  as  follows  :  let 

DA,  EB  (fig.  350)  be  a  pencil 
of  parallel  rays  falling  obliquely 
on  a  surface,  AB,  and  let  om  be 
the  normal  to  this  surface.  If 
S  is  the  section  of  the  pencil, 
a  the  total  quantity  of  light, 
which  falls  on  the  surface  AB, 
and  I  that  which  falls  on  the  unit 
of  surface  (that  is,  the  intensity  of 


illumination),  we  have  I 


a 
AB' 


But  as  S  is  only  the  projection  of  AB  on 


a  plane  perpendicular  to  the  pencil,  we  know  from  trigonometry  that  S  ^ 
AB  cos  a,  from  which  AB 


S 
— ^ — -.     This  value,  substituted  in  the  above 
cos  a 


equation,  gives  1 


-  cos  (t^  a  formula  which  demonstrates  the  law  of  the 


cosine,  for  as  o  and  S  are  constant  quantities,  I  is  proportional  to  cos  a. 

The  law  of  the  cosine  applies  also  to  rays  emitted  obliquely  by  a  lumi- 
nous surface;  that  is,  the  rays  are  less  intense  in  proportion  as  they  are 
more  inclined  to  the  surface  which  emits  them.  In  this  respect  they  cor- 
respond to  the  third  law  of  the  intensity  of  radiant  heat. 

479.  Pbotoxneters. — A  photoneter  is  an  apparatus  for  measuring  the 
relative  intensities  of  light. 

Riunford's photoineter.  This  consists  of  a  ground  glass  screen,  in  front 
of  which  is  fixed  an  opaque  rod  (fig.  351);  the  lights  to  be  compared — for 


Fig.  351. 

instance,  a  lamp  and  a  candle — are  placed  at  a  certain  distance  in  such  a 
manner  that  each  projects  on  the  screen  a  shadow  of  the  rod.  The 
shadows  thus  projected  are  at  first  of  unequal  intensity,  but  by  altering 
the  position  of  the  lamp,  it  may  be  so  placed  that  the  intensity  of  the  two 
shadows  is  the  same.  Then,  since  the  shadow  thrown  by  the  lamp  is 
illuminated  by  the  candle,  and  that  thrown  by  the  candle  is  illuminated 
by  the  lamp,  the  illumination  of  the  screen  due  to  each  light  is  the  same. 


-479]  Photometers.  419 

The  intensities  of  the  two  lights,  that  is,  the  iUuminations  which  they 
would  give  at  equal  distances,  are  then  directly  proportional  to  the  squares 
of  their  distances  from  the  shadows  ;  that  is  to  say,  that  if  the  lamp  is 
three  times  the  distance  of  the  candle,  its  illuminating  power  is  nine 
times  as  great. 

For  if  /  and  i'  are  the  intensities  of  the  lamp  and  the  candle  at  the  unit 
of  distance,  and  d  and  d'  their  distances  from  the  shadows,  it  follows, 
from  the  first  law  of  the  intensity  of  light,  that  the  intensity  of  the  lamp 

at  the  distance  d  is   ^-,.  and  that  of  the  candle  ^,0  at  the  distance  d'.     On 
d-  d 

the  screen  these  two   intensities   are  equal;   hence-    ,  =   —or  -=       ' 

d'      d"^        i'      d"^ 

which' was  to  be  proved. 

Bunseu's photometer. — When  a  grease  spot  is  made  on  apiece  of  bibu- 
lous paper,  the  part  appears  translucent.  If  the  paper  be  illuminated  by 
a  light  placed  in  front,  the  spot  appears  darker  than  the  surrounding 
space;  if,  on  the  contrary,  it  be  illuminated  from  behind,  the  spot  appears 
light  on  a  dark  ground.  If  the  greased  part  and  the  rest  appear  un- 
changed, the  intensity  of  illumination  on  both  sides  is  the  same.  Bunsen's 
photometer  depends  on  an  application  of  this  principle.  A  circular  spot 
is  made  on  a  paper  screen  by  means  of  a  solution  of  spermaceti  in  naph- 
tha ;  behind  this  is  placed  a  light  of  a  certain  intensity,  which  serves  as  a 
standard ;  in  this  country  it  is  usually  a  wax  candle  of  known  dimensions. 
The  hght  to  be  tested  is  then  moved  in  a  right  line  to  such  a  distance  in 
front  of  the  diaphragm  that  there  is  no  difference  in  brightness  between 
the  greased  part  and  the  rest  of  the  screen.  By  measuring  the  distances 
of  the  lights  from  the  screen,  their  relative  illuminating  powers  are 
deduced  from  what  has  been  previously  said. 

By  this  kind  of  determination  great  accuracy  cannot  be  attained,  more 
especially  when  the  lights  to  be  compared  are  of  different  colours,  one, 
for  instance,  being  yellow,  and  the  other  of  a  bluish  tint.  In  this  case, 
the  determination  of  the  relative  brightness  is  quite  uncertain. 

Wheatstonis  photometer. — The  principal  part  of  this  instrument  is  a 
steel  bead,  P  (fig.  352),  fixed  on  the  edge  of  a  disc,  which  rotates  on  a 
pinion,  0,  working  in  a  larger  toothed  wheel.  The  wheel  fits  in  a  cylin- 
drical copper  box,  which  is  held  in  one  hand,  while  the  other  works  a 
P 


N 


Fig.  353- 

handle.  A,  which  turns  a  central  axis,  the  motion  of  which  is  transmitted 
by  a  spoke,  a,  to  the  pinion  0.  In  this  way  the  latter  turns  on  itself,  and 
at  the  same  time  revolves  round  the  circumference  of  the  box ;  the  bead 


420 


071  L  ighU 


[479- 


shares  the  double  motion,  and  consequently  describes  a  curve  in  the  iform 
of  a  rose  (fig.  353). 

Now,  let  M  and  N  be  the  two  lights  whose  intensities  are  to  be  com- 
pared ;  the  photometer  is  placed  between  them  and  rapidly  rotated.  The 
brilliant  points  produced  by  the  reflection  of  the  light  on  the  two  opposite 
sides  of  the  bead  give  rise  to  two  luminous  bands,  arranged  as  represented 
in  hg.  353.  If  one  of  them  is  more  brilliant  than  the  other — that  which 
proceeds  from  the  light  M,  for  instance — the  instrument  is  brought 
nearer  the  other  light  until  the  two  bands  exhibit  the  same  brightness. 
The  distance  of  the  photometer  from  each  of  the  two  lights  being 
then  measured,  their  intensities  are  proportioiial  to  the  squares  of  the 
distances. 


CHAPTER    11. 


REFLECTION   OF   LIGHT.      MIRRORS. 

480.  Xiaws  of  the  reflection  of  light. — When  a  luminous  ray  meets 
a  polished  surface,  it  is  reflected  according  to  the  following  two  laws, 
which,  as  we  have  seen,  also  prevail  for  heat : — 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

1 1 .  The  iticident  and  the  reflected 
ray  are  both  in  the  sa7ne  plane, 
which  is  perpendicular  to  the  reflec- 
ting surface. 

The  words  are  here  used  in  the 
same  sense  as  in  article  384,  and 
need  no  further  explanation. 

First  proof — The  two  laws  may 
be  demonstrated  by  the  apparatus 
represented  in  fig.  354.  It  consists 
of  a  graduated  circle  in  a  vertical 
plane.  Two  brass  slides  move 
round  the  circumference;  on  one 
of  them  there  is  a  piece  of  ground 
glass,  P,  and  on  the  other  an 
opaque  screen,  N,  in  the  centre  of 
which  is  a  small  aperture.  Fixed 
to  the  latter  slide  there  is  also  a 
mirror,  M,  which  can  be  more  or 
less  inclined,  but  always  remains  in 
a  plane  perpendicular  to  the  plane 
of  the  graduated  circle.  Lastly,  there  is  a  small  polished  metallic  mirror, 
;;z,  placed  horizontally  in  the  centre  of  the  circle. 

In  making  the  experiment,  a  pencil  of  solar  light,  S,  is  caused  to 
impinge  on  the  mirror  M,  which  is  so  inclined  that  the  reflected  light 
passes  through  the  aperture  in  N,  and  falls  on  the  centre  of  the  mirror  ;//. 


Fig-  354- 


-481]  Reflection  of  LigJ it.  421 

The  luminous  pencil  then  experiences  a  second  reflection  in  a  direction 
;«P,  which  is  ascertained  by  moving  P  until  an  image  of  the  aperture  is 
found  in  its  centre.  The  number  of  degrees  comprised  in  the  arc  AN  is 
then  read  off,  and  likewise  that  in  AP ;  these  being  equal,  it  follows  that 
the  angle  of  reflection  AwP  is  equal  to  the  angle  of  incidence  A?;?M. 

The  second  law  follows  from  the  arrangement  of  the  apparatus,  the 
plane  of  the  rays  Mw  and  mV  being  parallel  to  the  plane  of  the  graduated 
circle,  and,  consequently,  perpendicular  to  the  mirror  m. 

Second  Proof. — The  law  of  the  reflection  of  light  may  also  be  demon- 
strated by  the  following  experiment,  which  is  susceptible  of  greater  accu- 
racy than  that  just  described.  In  the  centre  of  a  graduated  circle,  M 
(fig.  355),  placed  in  a  vertical  position,  there  is  a  small  telescope  movable 
in  a  plane  parallel  to  the  limb  :  at  a  suitable  distance  there  is  a  vessel  full 
of  mercury,  which  forms  a  perfectly  horizontal  plane  mirror.  Some  par- 
ticular star  of  the  first  or  second  magnitude  is  viewed  through  the  tele- 
scope in  the  direction  AE,and  the  telescope  is  then  inclined  so  as  to  receive 
the  ray  AD  coming  from  the  star  after  being  reflected  from  the  brilliant 
surface  of  the  mercury.  In  this  way  the  two  angles  formed  by  the  rays 
EA  and  DA,  with  the  horizontal  AH,  are  found  to  be  equal,  from  which  it 


Fig-  355- 

may  easily  be  shown  that  the  angle  of  incidence  E'DE  is  equal  to  the 
angle  of  reflection  EDA.  For  if  DE  is  the  normal  to  the  surface  of  the 
mercury,  it  is  perpendicular  to  AH,  and  AED,  ADE  are  the  complements 
of  the  equal  angles  EAH,  DAH  ;  therefore  AED,  ADE  are  equal ;  but 
the  two  rays  AE  and  DE'  may  be  considered  parallel,  in  consequence  of 
the  great  distance  of  the  star,  and  therefore  the  angles  EDE'  and  DEA 
are  equal,  for  they  are  alternate  angles,  and,  consequently,  the  angle  EDE 
is  equal  to  the  angle  EDA. 

REFLECTION   OF   LIGHT   FROM    PLANE   SURFACES. 

481.  Mirrors.     Zmagres. — Mirrors  zx^  bodies  with  polished  surfaces 
which  shew  by  reflection  objects  presented  to  them.  The  place  at  which  ob- 


422 


On  Light. 


[481- 


jects  appear  is  their  image.  According  to  their  shape,  mirrors  are  divided 
into  plane,  concave,  convex,  spherical,  pai'aboUc,  conical,  etc. 

482.  Formation  of  imagres  by  plane  mirrors. — The  determination  of 
the  position  and  size  of  images  resolves  itself  into  investigating  the  images 
of  a  series  of  points.  And  first,  the  case  of  a  single  point,  A,  placed  be- 
fore a  plane  mirror,  MN  (fig.  356),  will  be  considered.  Any  ray,  AB,  in- 
cident from  this  point  on  the  mirror,  is  reflected  in  the  direction  BO, 
making  the  angle  of  reflection  DBO  equal  to  the  angle  of  incidence  DBA. 

If  now  a  perpendicular,  AN,  be  let  fall  from  the  point  A  on  the  mirror, 
and  if  the  ray  OB  be  prolonged  below  the  mirror  until  it  meets  this  per- 
pendicular on  the  point  a,  two  triangles  are  formed,  ABN  and  BNrt, 
which  are  equal,  for  they  have  the  side  BN  common  to  both,  and  the 
angles  ANB,  ABN,  equal  to  the  angles  ^NB,  rt;BN  ;  for  the  angles  ANB 
and  rtNB  are  right  angles,  and  the  angles  ABN  and  <t;BN  are  equal  to  the 
angle  OBM.  From  the  equality  of  these  triangles,  it  follows  that  «N  is 
equal  to  AN  ;  that  is,  that  any  ray,  AB,  takes  such  a  direction  after  being 
reflected,  that  its  prolongation  below  the  mirror  cuts  the  perpendicular  Ka 
in  the  point  a,  which  is  at  the  same  distance  from  the  mirror  as  the  point 


Fig-  356. 


Fig.  357- 


A.  This  applies  also  to  the  case  of  any  other  ray  from  the  point  A  -  AC, 
for  example.  From  this  the  important  consequence  follows,  that  all  rays 
from  the  point  A,  reflected  from  the  m\vYor,  follow  after  reflection,  the  same 
direction  as  if  they  had  all  proceeded  from  the  point  a.  The  eve  is  de- 
ceived, and  sees  the  point  A  at  a,  as  if  it  were  really  situated  at  a.  Hence 
in  plane  mirrors  the  image  of  a7iy  point  is  formed  behind  the  mirror  at  a 
distance  equal  to  that  of  the  given  point,  and  on  the  perpendicular  let  fall 
from  this  point  on  the  mirror. 

It  is  manifest  that  the  image  of  any  object  will  be  obtained  by  construct- 
ing according  to  this  rule  the  image  of  each  of  its  points,  or,  at  least,  of 
those  which  are  sufficient  to  determine  its  form.  Fig.  357  shows  how  the 
image  ab  of  any  object,  AB,  is  formed. 

It  follows  from  this  construction  that  in  plane  mirrors  the  image  is  of 
the  same  size  as  the  object  for  if  the  trapezium  ABCD  be  apphed  to  the 
trapezium  X^Zab,  they  are  seen  to  coincide,  and  the  object  AB  agrees 
with  its  image. 

A  further  consequence  from  the  above  construction  is,  that  in  plane 


-484]  Vertical  and  Real  Images.  42  3 

mirrors  the  image  is  symmetrical  in  reference  to  the  object,  and  not  in- 
verted. 

483.  Virtual  and  real  imagres. — There  are  two  cases  relative  to  the 
direction  of  rays  reflected  by  mirrors  according  as  the  rays  after  reflection 
are  convergent  or  divergent.  In  the  first  case  the  reflected  rays  do  not 
meet,  but  if  they  are  supposed  to  be  produced  on  the  other  side  of  the 
mirror,  their  prolongations  coincide  in  the  same  point,  as  shown  in  figs. 
356  and  357.  The  eye  is  then  affected,  just  as  if  the  rays  proceeded  from 
this  point,  and  it  sees  an  image.  But  the  image  has  no  real  existence,  the 
luminous  rays  do  not  come  from  the  other  side  of  the  mirror ;  this  appear- 
ance is  called  the  virtual  image.  The  images  of  real  objects  produced  by 
plane  mirrors  are  of  this  kind. 

In  the  second  case,  where  the  reflected  rays  converge,  of  which  we 
shall  soon  have  an  example  in  concave  mirrors,  the  rays  coincide  at  a 
point  in  front  of  the  mirror,  and  on  the  same  side  as  the  object.  They 
form  there  an  image  called  the  real  image,  for  it  can  be  received  on  a 
screen.  The  distinction  may  be  expressed  by  saying  that  realimages are 
those  formed  by  the  reflected  rays  themselves,  a?td  virttc^l  images  those 
formed  by  their  prolo7igations. 

484.  Multiple  imagres  formed  by  grlass  mirrors. — Metallic  mirrors 
which  have  but  one  reflecting  surface  only  give  one  image  ;  glass  mirrors 
give  rise  to  several  images,  which  are  readily  observed  when  the  image 
of  a  candle  is  looked  at  obliquely  in  a  looking- 
glass.  A  very  feeble  image  is  first  seen,  and  then 
a  very  distinct  one  ;  behind  this  there  are  several 
others,  whose  intensities  gradually  decrease 
until  they  disappear. 

This  phenomenon  arises  from  the  looking- 
glass  having  two  reflected  surfaces.  When  the 
rays  from  the  point  A  meet  the  first  surface,  a 
part  is  reflected  and  forms  an  image,  a,  of  the 
point  A,  on  the  prolongation  of  the  ray  <^E, 
reflected  by  this  surface  ;  the  other  part  passes  ^'^"  35^- 

into  the  glass,  and  is  reflected  at  <r,  from  the  layer  of  metal  which  covers 
the  hinder  surface  of  the  glass,  and  reaching  the  eye  in  the  direction  dW 
gives  the  image  a'.  This  image  is  distant  from  the  first  by  double  the 
thickness  of  the  glass.  It  is  more  intense,  because  metal  reflects  better 
than  glass. 

In  regard  to  the  other  images  it  will  be  remarked,  that  whenever  light 
is  transmitted  from  one  medium  to  another — for  instance,  from  glass  to 
air — only  some  of  the  rays  get  through,  the  remainder  are  reflected  at 
the  surface  which  bounds  the  two  media.  Consequently  when  the  pencil 
cd,  reflected  from  c,  attempts  to  leave  the  glass  at  d,  most  of  the  rays 
composing  it  pass  into  the  air,  but  some  are  reflected  at  d,  and  continue 
within  the  glass.  These  are  again  reflected  by  the  metallic  surface,  and 
form  a  third  image  of  A  ;  after  this  reflection  they  come  to  MN,  when 
many  emerge  and  render  the  third  image  visible,  but  some  are  again 
reflected  within  the  glass,  and  in  a  similar  manner  give  rise  to  a  fourth, 


424 


On  Light. 


[484- 


fifth,  etc.  image,  thereby  completing  the  series  above  described.  It  is 
manifest  from  the  above  explanation  that  each  image  must  be  much 
feebler  than  the  one  preceding  it,  and  consequently  not  more  than  a 
small  number  are  visible — ordinarily  not  more  than  eight  or  ten  in  all. 

This  multiplicity  of  images  is  objectionable  in  observations,  and,  ac- 
cordingly, metallic  mirrors  are  preferable  in  optical  instruments. 

485.  Multiple  imagres  from  two  plane  mirrors. — When  an  object 
is  placed  between  two  plane  mirrors,  which  form  an  angle  with  each 
other,  either  right  or  acute,  images  of  the  object  are  formed,  the  number 
of  which  increases  with  the  inclination  of  the  mirrors.  If  they  are  at 
right  angles  to  each  other,  three  images  are  seen,  arranged  as  repre- 
sented in  fig.  359.  The  rays  OC  and  OD  from  the  point  O,  after  a  single 
reflection,  give  the  one  an  image  O',  and  the  other  an  image  C,  while  the 
ray  OA,  which  has  undergone  two  reflections  at  A  and  B,  gives  the  third 
image,  O"'.  When  the  angle  of  the  mirrors  is  60°,  five  images  are  pro- 
duced, and  seven  if  it  is  45°.  The  number  of  images  continues  to  in- 
crease in  proportion  as  the  angle  diminishes,  and  when  it  is  zero — that  is, 

when  the  mirrors  are  parallel — the  number 
of  images  is  theoretically  infinite.  This 
multiplicity  arises  from  the  fact  that  the 
luminous  rays  undergo  an  increasing  num- 
ber of  reflections  from  one  mirror  to  the 
other. 

The  kaleidoscope^  invented  by  Sir  D. 
Brewster,  depends  on  this  property  of  in- 
clined mirrors.  It  consists  of  a  tube,  in 
which  are  three  mirrors  inclined  at  60°  ; 
one  end  of  the  tube  is  closed  by  a  piece  of 
ground  glass,  and  the  other  by  a  cap  pro- 
vided with  an  aperture.  Small  irregular 
pieces  of  coloured  glass  are  placed  at  one 
end  between  the  ground  glass  and  another  glass  disc,  and  on  looking 
through  the  aperture,  the  other  end  being  held  towards  the  light,  the  ob- 
jects and  their  images  are  seen  arranged  in  beautiful  symmetrical  forms  ; 
by  turning  the  tube  an  endless  variety  of  these  shapes  is  obtained. 

486.  Multiple  imagres  in  two  parallel  mirrors. —  In  this  case  the 
number  of  images  of  an  object  placed  between  them  is  theoretically  in- 
finite. Physically  the  number  is  limited,  for  as  the  incident  light  is  never 
totally  reflected,  the  images  gradually  become  fainter,  and  are  ultimately 
quite  extinguished. 

Fig.  360  shows  how  the  pencil  L^  reflected  once  from  M  gives  at  I 
the  image  of  the  object  L  at  a  distance  MI  =  ML  ;  then  the  pencil  \^b 
reflected  once  from  the  mirror  M,  and  once  froniN,  furnishes  the  image  V 
at  a  distance  nV  =  ti\  ;  in  like  manner  the  pencil  L<:  after  two  reflections 
on  M,  and  one  on  N  forms  the  image  \"  at  a  distance  mV'  =  mV,  and  so 
on  for  an  infinite  series.  The  images  /,  z^,  i" ,  are  formed  in  the  same 
manner  by  rays  of  light,  which  emitted  by  the  object  L  fall  first  on  the 
mirror  N. 


Fig.  359- 


-488]  Intensity  of  Reflected  Light.  425 

487.  Zrregrular  reflection. — The  reflection  from  the  surfaces  of  polished 
bodies,  the  laws  of  which  have  just  been  stated,  is  called  the  regular  or 
spsailar  reflection  ;  but  the  quantity  thus  reflected  is  less  than  the  incident 


Fig.  360. 

light.  The  light  incident  on  an  opaque  body  actually  separates  into  three 
parts  :  one  is  reflected  regularly,  another  irregularly,  that  is,  in  all  direc- 
tions ;  while  a  third  is  extinguished,  or  absorbed  by  the  reflecting  body. 
If  light  falls  on  a  transparent  body,  a  considerable  portion  is  transmitted 
with  regularity. 

The  irregularly  reflected  light  is  called  scattered  light :  it  is  that  which 
makes  bodies  visible.  The  light  which  is  reflected  regularly  does  not  give 
us  the  images  of  the  reflecting  surface,  but  that  of  the  body  from  which  the 
light  proceeds.  If,  for  example,  a  solar  beam  be  incident  on  a  well-polished 
mirror  in  a  dark  room,  the  more  perfectly  the  light  is  reflected  the  less 
visible  is  the  mirror  in  the  different  parts  of  the  room.  The  eye  does  not 
perceive  the  image  of  the  mirror,  but  that  of  the  sun.  If  the  reflecting 
power  of  the  mirror  be  diminished  by  sprinkling  on  it  a  light  powder,  the 
solar  image  becomes  feebler,  and  the  mirror  is  visible  from  all  parts  of  the 
room.  Perfectly  smooth,  polished  reflecting  surfaces,  if  such  there  were, 
would  be  invisible. 

488.  Intensity  of  reflected  ligrht. — The  intensity  of  the  reflecting 
power  of  a  body  increases  with  the  degree  of  polish  and  with  the 
obliquity  of  the  incident  ray.  For  instance,  if  a  sheet  of  white  paper  be 
placed  before  a  candle,  and  be  looked  at  very  obliquely,  an  image  of  the 
flame  is  seen  by  reflection,  which  is  not  the  case  if  the  eye  receives  less 
oblique  rays. 

The  intensity  of  the  reflection  varies  with  different  bodies,  even  when 
the  degree  of  polish  and  the  angle  of  incidence  are  the  same.  It  also 
varies  with  the  nature  of  the  medium  which  the  ray  is  traversing  before 
and  after  reflection.  Polished  glass  immersed  in  water  loses  a  great  part 
of  its  reflecting  power. 


426  On  Light.  [489- 

489.  Reflection  of  a  ray  of  ligrlit  in  a  rotating:  mirror. — When  a 
horizontal  ray  of  light  falls  on  a  plane  mirror  which  can  rotate  about  a 
vertical  axis,  if  the  mirror  is  turned  through  an  angle  a,  the  reflected  ray 
is  turned  through  double  the  angle. 

Let  mti  (fig.  361)  be  the  first  position  of  the  mirror,  m'n  its  position 
after  it  has  been  turned  through  the  angle  a  ;  and  let  OD  be  the  fixed 
incident  ray.  If  from  the  centre  of  rotation 
C,  with  any  radius  we  describe  the  circum- 
ference O  mn,  and  from  the  point  O,  where 
it  cuts  the  incident  ray,  chords  00'  and  OO'^ 
are  drawn  perpendicular  respectively  to  inn 
and  m'n  \  the  points  O'  and  O''  are  the 
images  of  the  point  O  in  the  two  positions  of 
the  mirror,  and  the  angles  CO'D  and  CO"D' 
are  each  equal  to  COD.  The  lines  O'D 
and  O'^D',  thus  making  equal  angles  with 
O'C  and  0"C,  the  angle  between  the  two 
former  lines  is  equal  to  that  betwesn  the  two 

rig.  ^61. 

latter,  that  is  it  will  be  equal  to  O'CO"  and 
will  be  measured  by  the  arc  O'O''.  The  rotations  of  the  reflected  ray, 
and  of  the  mirror  are  thus  measured  by  the  two  arcs  O'O'^  and  mm' 
respectively. 

Now  the  two  angles  O'  OO''  and  mZm'  are  equal,  for  they  have  their 
sides  perpendicular  each  to  each  ;  but  the  angle  O'OO''  which  is  an  angle 
at  the  circumference,  is  half  the  arc  00',  and  the  angle  mQm'  is  measured 
by  the  whole  arc  inm' ;  hence  OO'  is  the  double  of  mm\  which  shows  that 
when  the  mirror  has  turned  through  an  angle  a,  the  reflected  ray  has 
turned  through  2 or. 

490.  Hadley's  reflecting:  sextant. — The  principal  features  of  this 
instrument,  which  is  used  to  measure  the  angular  distance  of  any  two 
distant  objects,  are  represented  in  figure  362.  It  consists  of  a  me^al 
sector  the  arc  (f^  of  which  is  graduated.  About  the  centre  of  the  sector, 
an  index  arm,  ab,  turns  ;  this  is  provided  with  a  vernier  and  a  micrometer 
screw,  by  which  the  index  may  be  accurately  adjusted  and  also  clamped. 
A  mirror  at  a  is  fixed  at  right  angles  to  the  arm  ab,  and  therefore  moves 
with  it.  A  telescope  de  is  permanently  fixed  to  the  arm  ac  and  opposite 
to  it  is  a  second  mirror  m  also  permanently  fixed  ;  the  lower  half  of  this 
is  silvered,  and  the  axis  of  the  telescope  just  traverses  the  boundary  of 
the  silvered  and  unsilvered  part  of  the  mirror. 

In  making  an  observation  the  sextant  is  held  so  that  its  plane  may 
pass  through  both  the  objects  whose  angular  distance  is  to  be  measured. 
The  index  arm,  is  at  the  zero  of  the  graduation,  which  indicates  the 
parallelism  of  the  two  mirrors.  One  of  the  objects  is  then  viewed  in  the 
direction  om^  through  the  telescope  and  the  unsilvered  part  of  the  mirror 
m.  The  index  arm  is  then  moved  until  the  eye  sees  simultaneously  with 
this  the  image  of  another  object  g,  which  reaches  the  eye  after  successive 
reflections  from  the  mirror  «,  and  from  the  unsilvered  part  of  the  mirror  w  ; 
that  is  by  the  path  g^  a,  m,  e,  d,  0.   The  angle  mha  which  the  two  mirrors 


-491] 


Measurement  of  Small  Angles, 


427 


now  form  is  measured  by  the  graduation  of  the  sector  el,  and  is  half  the 
angle  gom.  For  when  the  two  mirrors  were  parallel,  the  angular  deflection 
of  the  ray  ^rt,  after  two  reflections  would  be  zero,  and  its  deflection  is  now 
the  angle  gem  ;  whence  by  the  last  article  the  mirror  a  must  have  turned 


''"-A 


through  half  that  angle,  the  mirror  m  having  been  fixed  in  position  through- 
out. 

491.  Measurement  of  small  angrles  by  reflection  from  a  mirror. — 

An  important  application  is  made  of  the  law  of  reflection  in  measuring 


i:^S 


-s|; 


-^ 


Fig.  363- 

small  angles  of  deflection  in  magnetic  and  other  observations.  The 
principle  of  this  method  will  be  understood  from  figure  363,  in  which  AG 
represents  a  telescope,  underneath  which,  and  at  right  angles  to  its  axis,  is 
fixed  a  graduated  scale  ss  ;  the  centre  of  which,  the  zero,  corresponds  to 
the  axis  of  the  telescope. 

Let  NS  be  the  object  whose  angular  deflection  is  to  be  measured,  a 


428  On  Light.  [491- 

magnet  for  instance,  and  let  7nm  represent  a  small  perfectly  plane  mirror 
fixed  rigidly  at  right  angles  to  the  axis  of  the  magnet.  If  now  at  the 
beginning  of  the  observation,  the  telescope  is  adjusted  so  that  the  image 
of  the  zero  appears  behind  the  cross  wires  its  axis  is  perpendicular  to  the 
mirror.  Now  when  the  mirror  is  turned  by  whatever  cause  through  an  angle 
a,  the  eye  will  see  through  the  telescope  the  image  of  another  division  of 
the  scale,  a  for  instance,  the  ray  proceeding  from  which  makes  with  the 
line  ^OA  the  angle  ia. 

From  the  distance  of  this  division  O^  from  the  zero  of  the  scale  and 

the  distance  Oc  from  the  mirror  we  have  tang  2a  =  — ?.      Thus  for  in- 

oc 

stance   if   Oa  is    I2    millimetres   and   oc  5,000  millimetres   then   tang 

I '' 
"2.1  =  — ^^  from  which  2a=8'  \^".     As  a  practised  eye  can  easily  read 

jjj  of  a  millimetre,  it  is  possible  by  such  an  arrangement  to  read  off  an 
angular  deflection  of  two  seconds. 


REFLECTION  OF  LIGHT  FROM  CURVED  SURFACES. 

492.  Spherical  mirrors. — It  has  been  already  stated  (481)  that  there 
are  several  kinds  of  curved  mirrors  ;  those  most  frequently  employed  are 
spherical  and  parabolic  mirrors. 

Spherical  mirrors  are  those  whose  curvature  is  that  of  a  sphere  ;  their 
surface  may  be  supposed  to  be  formed  by  the  revolution  of  an  arc  MN 
(fig.  364),  about  the  radius  CA,  which  unites  the  middle  of  the  arc  to  the 
centre  of  the  circle  of  which  it  is  a  part.  According  as  the  reflection  takes 
place  from  the  internal  or  the  external  face  of  the  mirror  it  is  said  to  be 
concave  or  convex.  C,  the  centre  of  the  hollow  sphere,  of  which  the  mirror 
forms  part,  is  called  the  cetitre  of  cii7'vatiire  or  geometrical  centre  :  the 
point  A  is  the  centre  of  the  figure.  The  infinite  right  line,  AL,  which 
passes  through  A  and  C,  is  the  principal  axis  of  the  mirror  :  any  right 
line  which  simply  passes  through  the  centre  C,  and  not  through  the  point 
A,  is  a  secondary  axis.  The  angle  MCN,  formed  by  joining  the  centre 
and  extremities  of  the  mirror,  is  the  aperture.  K  principal  or  meridional 
section  is  any  section  made  by  a  plane  through  its  principal  axis.  In 
speaking  of  mirrors  those  lines  alone  will  be  considered  which  lie  in  the 
same  principal  section. 

The  theory  of  the  reflection  of  light  from  curved  mirrors  is  easily 
deduced  from  the  laws  of  reflection  from  plane  mirrors,  by  considering 
the  surface  of  the  former  as  made  up  of  an  infinitude  of  extremely  small 
plane  surfaces,  which  are  its  elements.  The  normal  to  the  curved  surface 
at  a  given  point  is  the  perpendicular  to  the  corresponding  element,  or, 
what  is  the  same  thing,  to  its  corresponding  tangent  plane.  It  is  shown 
in  geometry  that  in  spheres  all  the  normals  pass  through  the  centre  of 
curvature,  so  that  the  normal  may  readily  be  drawn  to  any  point  of  a 
spherical  mirror. 

493.  Focus  of  a  spherical  concave  mirror. — In  a  curved  mirror  the 
focus  is  a  point  in  which  the  reflected  rays  meet  or  tend  to  meet  if  pro- 


<r 


-493]  Spherical  Mirrors.  429 

duced  either  backwards  or  forwards  ;  there  may  either  be  a  real  focus  or 
a  virtual  focus. 

Real  focus.-^\Ne  shall  first  consider  the  case  in  which  the  luminous 
rays  are  parallel  to  the  principal  axis,  which  presupposes  that  the  lumi- 
nous body  is  at  an  infinite  distance  ;  let  GD  (fig.  364)  be  such  a  ray. 

From  the  hypothesis  that  curved  mirrors  are  composed  of  a  number  of 
infinitely  small  plane  elements,  this  ray  would  be  reflected  from  the 
element  corresponding  to  the  point  D,  according  to  the  laws  of  the  reflec- 
tion from  plane  mirrors,  (480)  ;  that  is,  that  CD  being  the  normal  at  the 


Fig.  364. 

point  of  incidence  D,  the  angle  of  reflection  CDF  is  equal  at  the  angle  of 
incidence  GDC,  and  is  in  the  same  plane.  It  follows  from  this  that  the 
point  F,  where  the  reflected  ray  cuts  the  principal  axis,  divides  the  radius 
of  curvature  AC  very  nearly  into  two  equal  parts.  For  in  the  triangle 
DFC,  the  angle  DCF  is  equal  to  the  angle  CDG,  for  they  are  alternate 
and  opposite  angles ;  likewise  the  angle  CDF  is  equal  to  the  angle  CDG, 
from  the  laws  of  reflection  ;  therefore  the  angle  FDC  is  equal  to  the  angle 
FCD,  and  the  sides  FC  and  FD  are  equal  as  being  opposite  to  equal 
angles.  Now  the  smaller  the  arc,  AD,  the  more  nearly  does  DF  equal 
AF  ;  and  when  the  arc  is  only  a  small  number  of  degrees,  the  right  lines 
AF  and  FC  may  be  taken  as  approximately  equal,  and  the  point  F  may 
be  taken  as  the  middle  of  AC.  So  long  as  the  aperture  of  the  mirror  does 
not  exceed  8  to  10  degrees,  any  other  ray,  HB,  will  after  reflection  pass 
very  nearly  through  the  point  F.  Hence,  when  a  pencil  of  rays  parallel 
to  the  axis  falls  on  a  concave  mirror,  the  rays  intersect  after  reflection  in 
the  same  point,  which  is  at  an  equal  distance  from  the  centre  of  curvature 
and  from  the  mirror.  This  point  is  called  the  prmcipal  focus  of  the 
mirror,  and  the  distance  AF  is  ihe^  principal  focal  distaiice. 

All  rays  parallel  to  the  axis  meet  in  the  point  F-;  and,  conversely,  if  a 
luminous  object  be  placed  at  F,  the  rays  emitted  by  this  object  will  after 
refleccion  take  the  directions  DG,  BH,  parallel  to  the  principal  axis  ,  for 
in  this  case  the  angles  of  incidence  and  reflection  have  changed  places  ; 
but  these  angles  always  remain  equal. 

The  case  is  now  to  be  considered  in  which  the  rays  are  emitted  from  a 
luminous  point,  L  (fig.  365),  placed  on  the  principal  axis,  but  at  such  a 
distance  that  they  are  not  parallel,  but  divergent.  The  angle  LKC,  which 
the  incident  ray  LK  forms  with  the  normal  KC,  is  smaller  than  the  angle 
SKC,  which  the  ray  SK  parallel  to  the  axis  forms  with  the  same  normal, 
and,  consequently,  the  angle  of  reflection  corresponding  to  the  ray  LK 


430 


On  Light. 


[493- 


must  be  smaller  than  the  angle  CKF,  corresponding  to  the  ray  SK.  And, 
therefore,  the  ray  LK  will  meet  the  axis  after  reflection  at  a  point,  /,  be- 
tween the  centre  C  and  the  principal  focus  F.  So  long  as  the  aperture 
of  the  mirror  does  not  exceed  a  small  number  of  degrees,  all  the  rays 
from  the  point  L  will  intersect  after  reflection  in  the  point  /.  This  point 
is  called  the  conjugate  focus  ^  in  order  to  indicate  the  connection  between 
the  points  L  and  /.  These  points  are  reciprocal  to  each  other,  that  is,  if 
the  luminous  point  were  transferred  to  /,  its  conjugate  focus  would  be  at 
L,  /K  being  the  incident  and  KL  the  reflected  ray. 

On  considering  the  figure  365  it  will  be  seen  that  when  the  object  L  is 
brought  near  to  or  removed  from  the  centre  C,  its  conjugate  focus  ap- 


Fig.  365- 

preaches  or  recedes  in  a  corresponding  manner,  for  the  angles  of  inci- 
dence and  reflection  increase  or  decrease  together. 

If  the  object  L  coincide  with  the  centre  C,  the  angle  of  incidence  is 
null,  and  as  the  angle  of  reflection  must  be  the  same,  the  ray  is  reflected 
on  itself,  and  the  focus  coincides  with  the  object.  When  the  luminous 
object  is  between  the  centre  C  and  the  principal  focus,  the  conjugate 
focus  in  turn  is  on  the  other  side  of  the  centre,  and  is  further  from  the 
centre  according  as  the  luminous  point  is  nearer  the  principal  focus.  If 
the  luminous  point  coincides  with  the  principal  focus,  the  reflected  rays, 
being  parallel  to  the  axis,  will  not  meet,  and  there  is,  consequently,  no 
focus. 

Virtual  focus. — There  is,  lastly,  the  case  in  which  the  object  is  placed 
at  L,  between  the  principal  focus  and  the  mirror  (fig.  366).  Any  ray, 
LM,  emitted  from  the  point  L,  makes  with  the  normal  CM  an  angle  of 
incidence,   LMC,  greater  than  FMC  ;   the  angle  of  reflection  must  be 


Fig.  366. 


Fig.  367. 


greater  than  CMS,  and  therefore  the  reflected  ray  ME  diverges  from  the 
axis  AK.     This  is  also  the  case  with  all  rays  from  the  point  L,  and  hence 


-495]  Convex  Mirrors.  43 1 

these  rays  do  not  intersect,  and,  consequently,  form  no  conjugate  focus  ; 
but  if  they  are  conceived  to  be  prolonged  on  the  other  side  of  the  mirror, 
their  prolongations  will  intersect  in  the  same  point,  /,  on  the  axis,  and  the 
eye  experiences  the  same  impression  as  if  the  rays  Avere  emitted  from  the 
point  /.  Hence  a  virtual  focus  is  formed  quite  analogous  to  those  formed 
by  plane  mirrors  (483). 

In  all  these  cases  it  is  seen  that  the  position  of  the  principal  focus  is 
constant,  while  that  of  the  conjugate  foci  and  of  the  virtual  foci  vary. 
The  pri7icipal  and  the  conjugate  foci  are  always  on  the  same  side  of  the 
mirror  as  the  object,  while  the  vii'tual  focus  is  always  on  the  other  side  of 
the  mirror. 

Hitherto  the  luminous  point  has  always  been  supposed  to  be  placed 
on  the  principal  axis  itself,  and  then  the  focus  is  formed  on  this  axis.  In 
the  case  in  which  the  luminous  point  is  situate  on  a  secondary  axis,  LB 
(fig.  367),  by  applying  to  this  axis  the  same  reasoning  as  in  the  preceding 
case,  it  will  be  seen  that  the  focus  of  the  point  L  is  formed  at  a  point  /, 
on  the  secondary  axis,  and  that,  according  to  the  distance  of  the  point  L, 
the  focus  may  be  either  principal,  conjugate,  or  virtual. 

494.  Poci  of  convex  mirrors. —  In  convex  mirrors  there  are  only  virtual 
foci.  Let  SI,  TK  .  .  .  (fig.  368)  be  rays  parallel  to  the  principal  axis  of 
a  convex  mirror.  'These  rays,  after  reflection,  take  the  diverging  direc- 
tions IM,  KH,  which,  when  continued,  meet  in  a  point,  F,  which  is  the 


principal  virtual  focus  of  the  mirror.  By  means  of  the  triangle  CKF,  it 
may  be  shown,  in  the  same  manner  as  with  concave  mirrors,  that  the 
point  F  is  approximately  the  middle  of  the  radius  of  cury^ture,  CA. 

If  the  incident  luminous  rays,  instead  of  being  parallel  to  the  axis, 
proceed  from  a  point.  L,  situated  on  the  axis  at  a  finite  distance,  it  is  at 
once  seen  that  a  virtual  focus  will  be  formed  between  the  principal  focus 
F  and  the  mirror. 

495.  Determination  of  the  principal  focus. —  In  the  applications  of 
concave  and  convex  mirrors,  it  is  often  necessary  to  know  the  radius  of 
curvature.  This  is  tantamount  to  finding  the  principal  focus  ;  for  being 
situated  at  the  middle  of  the  radius,  it  is  simply  necessary  to  double  the 
focal  distance. 

To  find  this  focus  with  a  concave  mirror,  it  is  exposed  to  the  sun's  rays, 
so  that  its  principal  axis  is  parallel  to  them,  and  then  with  a  small  screen 


432  On  Light.  [495- 

of  ground  glass  the  point  is  sought  at  which  the  image  is  formed  with  the 
greatest  intensity  :  this  is  the  principal  focus.  The  radius  of  the  mirror 
is  double  this  distance. 

If  the  mirror  is  convex  it  is  covered  with  paper,  but  two  small  portions, 
H  and  I,  are  left  exposed  at  equal  distances  from  the  centre  of  the  figure 
A,  and  on  the  same  principal  section  (fig.  369).  A  screen,  MN,  in  the 
centre  of  which  is  aft  opening  larger  than  the  distance  HI,  is  placed 
before  the  mirror.  If  a  pencil  of  solar  rays,  SH,  S'l,  parallel  to  the  axis 
fall  on  the  mirror,  the  light  is  reflected  at  H  and  I,  on  the  parts  where  the 
mirror  is  left  exposed,  and  forms  on  the  screen  two  brilliant  images  at  h 
and  i.     By  moving  the  screen  MN  nearer  to  or  farther  from  the  mirror,  a 


Fig.  369. 

position  is  found  at  which  the  distance  hi  is  double  that  of  HI.  The  dis- 
tance AD  from  the  screen  to  the  mirror  then  equals  the  principal  focal 
distance.     For  the  arc   HAI  does  not  sensibly  differ  from  its  chord,  and 

HI      FA 
because  the  triangles  FHI  and  F/z/ are  similar,  -_^  =  _-  ;  but  HI  is  half 

ht      FD 

oihi,  and  therefore  also  FA  is  the  half  of  F'D,  and  therefore  AD  is  equal 

to  AF.     Further,  FA  is  the  principal  focal  distance  ;  for  the  rays  SH  and 

S'l  are  parallel  to  the  axis  :  consequently  also  twice  the  distance  AD 

equals  the  radius  of  curvature  of  the  mirror. 

496.  Formation  of  imag-es  in  concave  mirrors. — Hitherto  it  has 
been  supposed  that  the  luminous  or  illuminated  object  placed  in  front  of 
the  mirror  was  simply  a  point  ;  but  if  this  object  has  a  certain  magnitude, 
we  can  conceive  a  secondary  axis  drawn  through  each  of  its  points,  and 
thus  a  series  of  real  or  virtual  foci  could  be  determined,  the  collection  of 
which  composes  the  image  of  the  object.  By  the  aid  of  the  construc- 
tions which  have  served  for  determining  the  foci,  we  shall  investigate 
the  position  and  magnitude  of  these  images  in  concave  and  in  convex 
mirrors. 

Real  image. — We  shall  first  take  the  case  in  which  the  mirror  is  con- 
cave, and  the  object  AB  (fig.  370)  is  on  the  other  side  of  the  centre.  To 
obtain  the  image  or  the  focus  of  any  point.  A,  a  secondary  axis,  AE,  is 
drawn  from  this  point,  and  then  drawing  from  the  point  A  an  incident 
ray,  AD,  the  normal  to  this  point,  CD,  is  taken,  and  the  angle  of  reflec- 
tion CDrt  is  made  equal  to  the  angle  of  incidence  ADC.  The  point  a, 
where  the  reflected  ray  cuts  the  secondary  axis  AE,  is  the  conjugate  focus 
of  the  point  A,  because  every  other  ray  drawn  from  this  point  passes 
through  with  a.     Similarly  if  a  secondary  axis,  BI,  be  drawn  from  the 


-496] 


Concave  Mirrors. 


433 


point  B,  the  rays  from  this  point  meet  after  reflection  in  ^,  and  form  the 
conjugate  focus  of  B.  And  as  the  images  of  all  the  points  of  the  object 
are  formed  between  a  and  b^  ab  is  the  complete  image  of  AB.  From 
what  has  been  said  about  foci  (493),  it  appears  that  this  image  is  real, 
i?tveried,  smaller  than  the  object,  and  placed  between  the  cent7'e  of  ctirvatnre 
and  the  principal  focns.     This  image  may  be  seen  in  two  ways  ;  by  placing 


Fig.  370. 

the  eye  in  the  continuation  of  the  reflected  rays,  and  then  it  is  an  aerial 
image  which  is  seen  ;  or  the  rays  are  collected  on  a  screen,  on  which  the 
image  appears  to  be  depicted. 

If  the  luminous  or  illuminated  object  is  placed  at  ab,  between -the 
principal  focus  and  the  centre,  its  image  is  formed  at  AB.  It  is  then  a 
real  but  inverted  image ;  it  is  larger  than  the  object,  and  the  larger  as 
the  object,  ab,  is  nearer  the  focus. 

If  the  object  is  placed  in  the  principal  focus  itself,  no  image  is  pro- 
duced ;  for  then  the  rays  emitted  from  each  point  form,  after  reflection, 
as   many  pencils  respectively  parallel  to  the  secondary  axis,  which    is 


Fig.  371- 


drawn  through  the  point  from  which  they  are  emitted  (493),  and  hence 
neither  foci  nor  images  are  formed. 

When  all  points  of  the  object  AB  are  above  the  principal  axis  (fig.  371) 
by  repeating  the  preceding  construction,  it  is  readily  seen  that  the  image 
of  the  object  is  formed  at  ab. 

Virtual  image. — The  case  remains  in  which  the  object  is  placed  be- 
tween the  principal  focus  and  the  mirror.  Let  AB  be  this  object  (fig. 
372);  the  incident  rays  after  reflection  take  the  directions  DI  and  KH, 
and  their  prolongations  form  a  virtual  image,  a,  of  the  point  A,  on  the 
secondary  axis.  Similarly,  an  image  of  B  is  formed  at  b,  consequently 
the  eye  sees  at  ab  the  image  of  AB.  This  image  is  virtual,  erect,  and 
larger  than  the  object. 

U 


434 


On  Li^ht. 


[496 


Yxovci  what  has  teen  stated,  it  is  seen  that,  according  to  the  distance  of 
the  object,  concave  mirrors  produce  two  kinds  of  images,  or  none  at  all  ; 
a  person  notices  this  by  placing  himself  before  a  concave  mirror.     At  a 


Fig.  372.  _    ■ 

certain  distance  he  sees  an  image  of  himself  inverted  and  smaller  ;  this  • 
is  the  real  image  :  at  a  less  distance  the  image  becomes  confused,  and 
disappears  when  he  is  at  the  focus  ;  still  nearer  the  image  appears  erect, 
but  larger— it  is  then  a  virtual  image. 

497.  Formation  of  iznag-es  in  convex  mirrors. — Let  AB  (fig.  373) 
be  an  object  placed  before  a  mirror  at  any  given  distance.  AC  and  BC 
are  secondary  axes,  and  it  follows  from  what  has  been  already  stated, 
that  all  the  rays   from  A  are  divergent  after  reflection,  and  that  their 


Fig.  373- 

prolongations  pass  through  a  point,  a,  which  is  the  virtual  image  of  the 
point  A.  Similarly  the  rays  from  B  form  a  virtual  image  ^of  it  in  the 
point  b.  The  eye  which  receives  the  divergent  rays  DE,  KA,  .  .  .  sees  in 
ab  an  image  of  AB.  Hence,  whatever  the  position  of  an  object  before  a 
convex  mirror,  the  image  is  always  virtual^  erect,  a?ui  smaller  than  the 
object. 

498.  Formulae  for  spherical  mirrors. — The    relation  between  the 
position  of  an  object  and  that  of  its  image  in  spherical  mirrors  may  be 


-^ 


Fig.  374- 

expressed  by  a  very  simple  formula.     In  the  case  of  ccncave  mirrors,  let 
R  be  its  radius  of  curvature,  /  the  distance  LA  of  the  object,  L  (fig.  374) 


-499]  Forinulce  for  Mirrors.  435 

and /' the  distance /A  of  the  image  from  the  mirror.  In  the  triangle 
LM/,  the  noimal  MC  divides  the  angle  LM/  in  two  equal  parts,  and 
from  geometry  it   follows  that  the  two  segments   LC,   C/  are  to  each 

other  as  the  two  sides  containing  the  angle  ;  that  is,  — —  =  ^--.  :    therefore 

C/xLM  =  CLx/M. 

If  the  arc  AM  does  not  exceed  5  or  6  degrees,  the  lines  ML  and  M/ 
are  approximately  equal  to  AL  and  A/  ;  that  is,  to/  and/'. 

Further,  C/=  CA- A/=  R-/', 

and  also  CL  =  AL-AC  =/-R. 

These  values  substituted  in  the  preceding  equations  give 

From  which  transposing  and  reducing  we  have 

Rp  +  Kf  =  2pp'        .         .         .         .         (i) 
If  the  terms  of  this  equation  be  all  divided  by//'R,  we  obtain 

y^^"R (^' 

which  is  the  usual  form  of  the  equation. 
From  the  equation  (i)  we  get 

f=j:^ (3) 

which  gives  the  distance  of  the  image  from  the  mirror,  in  terms  of  the 
distance  of  the  object,  and  of  the  radius  of  curvature. 

499.  Discussion  cf  the  formulae  for  mirrors. — We  shall  now  in- 
vestigate the  different  values  of/',  according  to  the  values  of  /  in  the 
formula  (3). 

i.  Let  the  object  be  placed  at  an  infinite  distance  on  the  axis,  in  which 
case  the  incident  rays  are  parallel.  To  obtain  the  value  of/',  both  terms 
cf  the  fraction  (3)  must  be  divided  by/,  which  gives 

^       ^_K         .  .  .  .  (4) 

P 

R  R 

as  p  is  infinite,  -  is  zero,  and  we  have  /'  =  —  ;    that   is,    the    image   is 
/  2 

formed  in  the  principal  focus,  as  ought  to  be  the  case,  for  the  incident 
rays  are  parallel  to  the  axis. 

ii.  If  the  object  approaches  nearer  the  mirror,  /  decreases,  and  as  the 
denominator  of  the  formula  (4)  diminishes,  the  value  of/'  increases  ;  con- 
sequently the  image  approaches  the  centre  at  the  same  time  as  the  object, 
but  it  is  always  between  the  principal  focus  and  the  centre,  for  so  long  as 

R  R 

/is  > R,  we  have >—  and  < R. 

P 

u  2 


436  On  Light.  [499- 

iii.  When  the  object  coincides  with  the  centre,  /  =  R,  and,  consequently, 
/'  =  R  ;  that  is,  the  image  coincides  with  the  object. 

iv.  When  the  luminous  object  is  between  the  centre  and  the  principal 
focus, ^<R,  and  hence  from  the  formula  (4),^'>R  ;  that  is,  the  image  is 
formed  on  the  other  side  of  the  centre.     When  the  object  is  in  the  focus, 

R  R 

/  =  -  ,  which  gives  ^'  =  _-  =-  00  ;  that  is,  the  image  is  at  an  infinite  dis- 
tance, for  the  reflected  rays  are  parallel  to  the  axis. 

V.  Lastly,  if  the  object  is  between  the  principal  focus  and  the  mirror, 

we  get  p< —  ;  p'  is  then  negative,  because  the  denominator  of  the  for- 
mula (4)  is  negative.  Therefore,  the  distance/'  of  the  mirror  from  the 
image  must  be  calculated  on  the  axis  in  a  direction  opposite  to  p.  The 
image  is  then  virtual,  and  is  on  the  other  side  of  the  mirror. 

Making/'  negative  in  the  formula  (2),  it  become?  -—  -  =  y.-;  in  this 

p    p'     K 

form  it  comprehends  all  cases  of  virtual  images  in  concave  mirrors. 

In  the  case  of  convex  mirrors,  the  image  is  always  virtual  (497)  ;  P'  and 
R  are  of  the  same  sign,  since  the  image  and  the  centre  are  on  the  same 
side  of  the  mirror,  while  the  object  being  on  the  opposite  side,  p  is  of  the 
contrary  sign  ;  hence  in  the  formula  (2)  we  get 

1-^=1 (5) 

.    -j  P'    P     V.  .       ^^' 

as  the  formula  for  convex  mirrors.  It  may  also  be  found  directly  by  the 
same  geometrical  considerations  as  those  which  have  led  to  the  formula 
(2)  for  concave  mirrors. 

It  must  be  observed  that  the  preceding  formulae  are  not  rigorously  true, 
inasmuch  as  they  depend  upon  the  hypothesis  that  the  lines  LM  and  /M 
(fig.  374)  are  equal  to  LA  and  A/  ;  although  this  is  not  true,  the  error 
diminishes  without  limit  with  the  angle  MCA  :  and  when  this  angle  does 
not  exceed  a  few  degrees,  the  error  is  so  small  that  it  may,  in  practice,  be 
neglected. 

500.  Calculation  of  the  mag^nitude  of  imagoes. — By  means  of  the 
above  formulas  the  magnitude  of  an  image  may  be  calculated,  when  the 


distance  of  the  object,  its  magnitude,  and  the  radius  of  the  mirror  are 
given.     For  if  BD  be  the  object  (fig.  375),  bd  its  image,  and  if  the  distance 


-502] 


Spherical  A  berration. 


437 


A  and  the  radius  AC  be  known,  Ko  can  be  calculated  by  means  of  for- 
mula (3)  of  article  498.  Ko  known,  oC  can  be  calculated.  But  as  the  tri- 
angles BCD  and  dCb  are  similar,  their  bases  and  heights  are  in  the  pro- 
portion ^.^  :  BD  =  C^  :  CK,  or 

Length  of  the  image  :  length  of  the  object 

=  distance  from  image  to  centre  :  distance  from  the  object  to  centre. 

501.  Spberical  aberration.  Caustics. — In  the  foregoing  theory  of 
the  foci  and  images  of  spherical  mirrors,  it  has  already  been  observed 
that  the  reflected  rays  only  pass  through  a  single  point  when  the  aperture 
of  the  mirror  does  not  exceed  8  or  10  degrees  (493).  With  a  larger  aper- 
ture, the  rays  reflected  near  the  edges  meet  the  axis  nearer  the  mirror 
than  those  that  are  reflected  at  a  small  distance  from  the  neighbourhood 
of  the  centre  of  the  mirror.  Hence  arises  a  want  of  precision  in  these 
images,  which  is  called  spherical  aberration  by  reflection,  to  distinguish 
it  from  the  spherical  aberration  by  refraction,  which  occurs  in  the  case  of 
lenses. 

Every  reflected  ray  cuts  the  one  next  to  it  (fig.  376),  and  their  points  of 
intersection  forrn  in  space  a  curved  surface,  which  is  called  the  caustic  by 


Fig.  376. 

reflection.  The  curve  FM  represents  one  of  the  branches  of  a  section  of 
this  surface  made  by  the  plane  of  the  paper.  When  the  light  of  a  candle 
is  reflected  from  the  inside  of  a  cup  or  tumbler,  a  section  of  the  caustic 
surface  can  be  seen  by  partly  filling  the  cup  or  tumbler  with  milk.  , 

502.  Applications  of  mirrors.  Heliostat. — The  apphcations  of  plane  Y  ^ 
mirrors  in  domestic  economy  are  well  known.  Mirrors  are  also  frequently^  y  ts.*: 
used  in  physical  apparatus  for  sending  light  in  a  certain  direction.  The 
solar  light  can  only  be  sent  in  a  constant  direction  by  making  the  mirror 
movable.  It  must  have  a  motion  which  compensates  for  the  continual 
change  in  the  direction  of  the  sun's  rays  produced  by  the  apparent  diurnal 
motion  of  the  sun.  This  result  is  obtained  by  means  of  a  clockwork 
motion,  to  which  the  mirror  is  fixed,  and  which  causes  it  to  follow  the 
course  of  the  sun.  This  apparatus  is  called  the  heliostat.  The  reflection 
of  light  is  also  used  to  measure  the  angles  of  crystals  by  means  of  the 
instruments  known  as  7'eflecting  goniometers. 

Concave  spherical  mirrors  are  also  often  used.  They  are  applied  for 
magnifying  mirrors^  as  in  a  shaving  mirror.  They  have  been  employed 
for  burning  mirrors,  and  are  still  used  in  telescopes.  They  also  serve  as 
reflectors,  for  conveying  light  to  great  distances,  by  placing  a  luminous 
object  in  their  principal  focus.  For  this  purpose,  however,  parabohc 
mirrors  are  preferable. 


438 


On  Light. 


[503- 


Fig.  377- 


503,  Parabolic  mirrors. — Parabolic  mirrors  are  concave  mirrors, 
whose  surface  is  generated  by  the  revolution  of  the  arc  of  a  parabola,  AM, 
about  its  axis,  AX  (fig.  377). 

It  has  been  already  stated  that  in  spherical  mirrors  the  rays  parallel  to 
the  axis  converge  only  approximately  to  the  principal  focus,  and  reciprocally 

when  a  source  of  light  is  placed  in 
the  principal  focus  of  these  mirrors, 
the  reflected  rays  are  not  exactly 
parallel   to    the    axis.       Parabolic 
mirrors  are  free  from  this  defect  ; 
they  are  more  difficult  to  construct, 
but  are  far  better  for  reflectors.     It 
is  a  well-known  property  of  a  para- 
bola that  the  right  line  FM,  drawn 
from  the  focus  F,  to  any  point,  M, 
of  the  curve,  and  the  line  ML,  pa- 
rallel to  the  axis  AF,  make  equal 
angles  with  the  tangent  TT'  at  this 
point.     Consequently,  all  rays  parallel  to  the  axis  after  reflection  meet  in 
the  focus  of  the  mirror  F,  and,   conversely,  when  a  source  of  light  is 
placed  in  the  focus,  the  rays  incident  on  the 
mirror  are  reflected  exactly  parallel  to  the 
axis.    The  light  thus  reflected  tends  to  main- 
tain its  intensity  even  at  a  great  distance,  for 
it  has  been  seen   (478)  that  it  is  the  diver- 
gence of  the  luminous  rays  which  principally 
weakens  the  intensity  of  light. 

It  is  from  this  property  that  parabolic 
mirrors  are  used  in  carriage  lamps,  and  in 
the  lamps  placed  in  front  of  and  behind 
railway  trains.  These  reflectors  were  for- 
merly used  for  lighthouses,  but  have  been 
replaced  by  lenticular  glasses. 

When  two  equal  parabolic  mirrors  are  cut 
by  a  plane  perpendicular  to  the  axis  passing 
through  the  focus,  and  are  then  united  at 
their  intersections^  as  shown  in  the  figure 
378,  so  that  their  foci  coincide,  a  system  of 
reflectors  is  obtained  with  which  a  single  lamp  illuminates  in  two  direc- 
tions at  once.     This  arrangement  is  used  in  lighting  staircases. 


-505]  Refraction.  439 

CHAPTER    III. 

SINGLE   REFRACTION.      LENSES. 

504.  Phenomenon  of  refraction. — Refraction  is  the  deflection  or 
bending  which  luminous  rays  experience  in  passing  obhquely  from  one 
medium  to  another  ;  for  instance,  from  air  into  water.  We  say  obliquely, 
because  if  the  incident  ray  is  perpendicular  to  the  surface  separating  the 
two  media,  it  is  not  deflected,  and  continues  its  course  in  a  right  line. 

The  incident  ray  being  represented  by  SO  (fig.  379),  the  refracted  ray 
is  the  direction  OH  which  hght  takes  in  the  second  medium  ;  and  of  the 
angles  SO  A  and  HOB,  which  these  rays  form 
with  the  line  AB,  at  right  angles  to  the  surface 
which  separates  the  two  media,  the  first  is  the 
atigle  of  incidence,  and  the  other  the  angle  of 
refraction.  According  as  the  refracted  ray  ap- 
proaches or  deviates  from  the  normal,  the  second 
medium  is  said  to  be  more  or  less  refringent  or 
refracting  than  the  first. 

All  the  light  which  falls  on  a  refracting  surface  Fig-  379- 

does  not  completely  pass  into  it  ;  one  part  is  reflected  and  scattered, 
while  another  penetrates  into  the  medium. 

Analysis  shows  that  the  direction  of  refraction  depends  on  the  relative 
velocity  of  light  in  the  two  media.  On  the  undulatory  theory  the  more 
highly  refracting  medium  is  that  in  which  the  velocity  of  propagation  is 
least. 

Inuncrystallised  media,  such  as  air,  Hquids,  ordinary  glass,  the  luminous 
ray  is  singly  refracted  ;  but  in  certain  crystallised  bodies,  such  as  Iceland 
spar,  Selenite,  etc.,  the  incident  ray  gives  rise  to  two  refracted  rays.  The 
latter  phenomenon  is  called  double  refraction,  and  will  be  discussed  in 
another  part  of  the  book.  We  shall  here  deal  exclusively  with  single  re- 
fraction. 

505.  Iiaws  of  singrle  refraction. — When  a  luminous  ray  is  refracted  in 
passing  from  one  medium  into  another  of  a  different  refractive  power,  the 
following  laws  prevail  :— 

I.  Whatever  the  obliquity  of  the  incident  ray,  the  ratio  which  the  sine 
of  the  incident  angle  bears  to  the  sine  of  the  angle  of  refraction  is  constant 

for  the  same  two  media,  but  varies  with  different  media. 

II.  The  incident  and  the  refracted  ray  are  in  the  same  plane  which  is 
perpendicular  to  the  surface  separating  the  two  media. 

These  have  been  known  as  Descartes'  laws ;  they  are,  however,  really 
due  to  Willibrod  Snell  who  discovered  them  in  1620,  and  are  demonstrated 
by  the  same  apparatus  as  that  used  for  the  laws  of  reflection  (456).  The 
plane  mirror  in  the  centre  of  the  graduated  circle  is  replaced  by  a  semi- 
cylindrical  glass  vessel,  filled  with  water  to  such  a  height  that  its  level  is 
exactly  the  height  of  the  centre  (fig.  3^0).  If  the  mirror,  M,  be  then  so 
inclined  that  a  reflected  ray,  MO,  is  directed  towards  the  centre,  it  is 
refracted  on  passing  into  the  water,  but  it  passes  out  without  refraction 


440 


On  Light 


[505 


because  then  its  direction  is  at  right  angles  to  the  curved  sides  of  the 
vessel.  In  order  to  observe  the  course  of  the  refracted  ray,  it  is  re- 
ceived on  a  screen,  P,  which  is 
moved  until  the  image  of  the  aper- 
ture in  the  screen  N  is  formed  in 
its  centre.  In  all  positions  of  the 
screens  N  and  P,  the  sines  of  the 
angles  of  incidence  and  refraction 
are  measured  by  means  of  two 
graduated  rules,  movable  so  as  to 
be  always  horizontal,  and  hence 
perpendicular  to  the  diameter  AD. 
On  reading  off  the  lengths  of  the 
sines  of  the  angles  MOA  and  DOP 
in  the  scales  I  and  R,  the  numbers 
are  found  to  vary  with  the  position 
of  the  screens,  but  their  ratio  is 
constant  ;  that  is,  if  the  sine  of 
incidence  becomes  twice  or  three 
times  as  large,  the  sine  of  refrac- 
tion increases  in  the  same  ratio, 
Fig-  380.  which  demonstrates  the  first  law. 

The  second  law  follows  from  the  arrangement  of  the  apparatus,  for  the 
plane  of  the  graduated  limb  is  perpendicular  to  the  surface  of  the  liquid 
in  the  semi-cylindrical  vessel. 

506.  Index  of  refraction. — The  ratio  between  the  sines  of  the  in- 
cident and  refracted  angle  is  0.2^^^  index  of  refraction  ox  refractive  index. 
It  varies  with  the  media  ;  for  example,  from  air  to  water  it  is  |,  and  from 
air  to  glass  it  is  |. 

If  the  media  are  considered  in  an  inverse  order — that  is,  if  light  passes 
from  water  to  air,  or  from  glass  to  air— it  follows  the  same  course,  but  in 
a  contrary  direction,  PO  becoming  the  incident  and  OM  the  refracted 
ray.  Consequently,  the  index  of  refraction  is  reversed  ;  from  water  to 
air  it  is  then  |,  and  from  glass  to  air  f . 

507.  Effects  produced  by  refraction. — In  consequence  of  refraction, 
bodies  immersed  in  a  medium  more  highly  refracting  than  air  appear 
nearer  the  surface  of  this  medium,  but  they  appear  to  be  more  distant  if 
immersed  in  a  less  refracting  medium.  Let  L  (fig.  381)  be  an  object  im- 
mersed in  a  mass  of  water.  In  passing  thence  into  air,  the  rays  LA,  LB 
.  .  .  diverge  from  the  normal  to  the  point  of  incidence,  and  assume  the 
direction  AC,  BD  .  .  .  ,  the  prolongations  of  which  intersect  approximately 
in  the  point  L',  placed  on  the  perpendicular  L'K.  The  eye  receiving 
these  rays  sees  the  object  L  at  L'.  The  greater  the  obliquity  of  the  rays 
LA,  LB  .  .  .  the  higher  the  object  appears. 

It  is  for  the  same  reason  that  a  stick  plunged  obliquely  into  water 
appears  bent  (fig.  382),  the  immersed  part  appearing  raised. 

Owing  to  an  effect  of  refraction,  stars  are  visible  to  us  even  when  they 
are  below  the  horizon.     For  as  the  layers  of  the  atmosphere  are  denser 


-508] 


Total  Reflection, 


441 


in  proportion  as  they  are  nearer  the  earth,  and  as  the  refractive  power  of 
a  gas  increases  with  its  density  (518),  it  follows   that  on  entering  the 


Fig.  382. 


Fig.  383. 


atmosphere  the  luminous  rays  become  bent,  as  seen  in  the  fig.  383, 
describing  a  curve  before  reaching  the  eye,  so  that  we  see  the  star  at  S' 
along  the  tangent  of  this  curve  instead  of  at  S.  In  our  climate  the 
atmospheric  refraction  does  not  raise  the  stars  when  on  the  horizon  more 
than  half  a  degree.  Another  experimental  illustration  of  the  effect  of  re- 
fraction is  the  following  : — A  coin  is  placed  in  an  empty  porcelain  basin 
and  the  position  of  the  eye  is  so  adjusted  that  it  is  just  not  visible.  If 
now,  the  position  of  the  eye  remaining  unaltered,  water  be  poured  into 
the  basin  the  coin  becomes  visible.  A  consideration  of  fig.  381,  will 
suggest  the  explanation  of  this  phenomenon. 

508.  Total  reflection.  Critical  angrle. — When  a  luminous  ray 
passes  from  one  medium  into  another  which  is  less  refracting,  as  from 
water  into  air,  it  has  been  seen  that  the  angle  of  incidence  is  less  than 
the  angle  of  refraction.  Hence,  when  light  is  propagated  in  a  mass  of 
water  from  S  to  O  (fig.  384),  there  is  always  a  value  of  the  angle  of  inci- 
dence SOB,  such  that  the  angle  of  refraction,  AOR,  is  a  right  angle,  in 
which  case  the  refracted  ray  emerges  parallel  to  the  surface  of  the  water. 

This  angle,  SOB,  is  called  the  critical  angle ^  since  for  any  greater 
angle,  FOB,  the  incident  ray  cannot  emerge,  but  undergoes  an  internal 
reflection,  which  is  called  total  reflection^  because  the  incident  light  is 
entirely  reflected.  From  water  to  air  the  critical  angle  is  48°  35'  ;  from 
glass  to  air,  41°  48'. 


Fig.  384.  Fig.  3S5. 

The  occurrence  of  this  internal  reflection  may  be  observed  by  the 
following  experiment.     An  object  A,  is  placed  before  a  glass  vessel  filled 

U3 


442  On  Light  [608- 

with  water  (fig.  385)  ;  the  surface  of  the  liquid  is  then  looked  at  as 
shown  in  the  figure,  and  an  image  of  the  object  A  is  seen  at  a^  formed  by 
the  rays  reflected  at  w,  in  the  ordinary  manner  of  a  mirror. 

Similar  effects  of  the  total  reflection  of  the  images  of  objects  contained 
in  aquaria  are  frequently  observed,  and  add  much  to  the  interest  of  their 
appearance. 

509.  IVEiragre. — The  mirage  is  an  optical  illusion  by  which  inverted 
images  of  distant  objects  are  seen  as  if  below  the  ground  or  in  the 
atmosphere.  This  phenomenon  is  of  most  frequent  occurrence  in  hot 
climates,  and  more  especially  on  the  sandy  plains  of  Egypt.     The  ground 


Fig.  3S6. 

there  has  often  the  aspect  of  a  tranquil  lake,  on  which  are  reflected  trees 
and  the  surrounding  villages.  The  phenomenon  has  long  been  known, 
but  Monge,  who  accompanied  Napoleon's  expedition  to  Egypt,  was  the 
first  to  give  an  explanation  of  it. 

It  is  a  phenomenon  of  refraction,  which  results  from  the  unequal 
density  of  the  different  layers  of  the  air  when  they  are  expanded  by 
contact  with  the  heated  soil.  The  least  dense  layers  are  then  the  lowest, 
and  a  luminous  ray  from  an  elevated  object,  A  (fig.  386),  traverses  layers 
which  are  gradually  less  refracting ;  for,  as  will  be  shown  presently 
(518),  the  refracting  power  of  a  gas  diminishes  with  lessened  density. 
The  angle  of  incidence  accordingly  increases  from  one  layer  to  the  other, 
and  ultimately  reaches  the  critical  angle,  beyond  which  internal  reflec- 
tion succeeds  to  refraction  (508).  The  ray  then  rises,  as  seen  in  the 
figure,  and  undergoes  a  series  of  successive  refractions,  but  in  a  direction 
contrary  to  the  first,  for  it  now  passes  through  layers  which  are  gradually 
more  refracting.  The  luminous  ray  then  reaches  the  eye  with  the  same 
direction  as  if  it  had  proceeded  from  a  point  below  the  ground,  and  hence 
it  gives  ah  inverted  image  of  the  object,  just  as  if  it  had  been  reflected  at 
the  point  O,  from  the  surface  of  a  tranquillake.  ^ 

Mariners  sometimes  see  images  in  the  air  of  the  shores  or  of  distant 
vessels.     This  is  due  to  the  same  cause  as  the  mirage,  but  in  a  contrary 


-511] 


Prisms. 


443 


direction,  only  occurring  when  the  temperature  of  the  air  is  above  that 
of  the  sea,  for  then  the  inferior  layers  of  the  atmosphere  are  denser,  owing 
to  their  contact  with  the  surface  of  the  water. 


TRANSMISSION   OF   LIGHT  THROUGH   TRANSPARENT   MEDIA. 

510.  iw alia  wl til  parallel  faces. — When  light  traverses  a  medium 
with  parallel  faces  the  emergent  rays  are  parallel  to  the  incident  rays. 

Let  MN  (fig.  387)  be  a  glass  plate  with  parallel  faces,  let  SA  be  the 
incident  and  DB  the  emergent  ray,  /and  r  the  angles  of  incidence  and 
of  refraction  at  the  entrance  of  the  ray, 
and,  lastly,  i'  and  r'  the  same  angles  at 
'its  emergence.  At  A  the  light  undergoes 
a  first  refraction,  the  index  of  which  is 

^JJLf  (482).  At  D  it  is  refracted  a  second 
sm  r 

time,  and  the  index  is  then  ^ —  .     But 

sm  r' 

we  have  seen  that  the  index  of  refraction 
of  glass  to  air  is  the  reciprocal  of  its  re- 
fraction from  air  to  glass ;  hence 


Fig-  387- 


sm  r       sm  i 
But  as  the  two  normals  AG  and  DE  are  parallel,  the  angles  r  and  i'  are 
equal,  as  being  alternate  interior  angles.    As  the  numerators  in  the  above 
equation  are  equal,  the  denominators  must  be  also  equal ;  the  angles  r' 
and  i  are  therefore  equal,  and  hence  DB  is  parallel  to  SA. 

511.  Prism. — Inoptics  a/r/Vw  is  any  transparent  medium  comprised 
between  two  plane  faces  inclined  to  each  other.  The  intersection  of 
these  two  faces  is  the  edge  of  the  prism,  and  their  inclination  is  its 
refracting  angle.  Every  section  perpendicular  to  the  edge  is  called  a 
principal  sectioti. 

The  prisms  used  for  experiments  are  generally  right  triangular  prisms 
of  glass,  as  shown  in  fig.  388,  and  their  principal  section  is  a  triangle 


Fig. 


Fig.  389- 


(fig.  389).  In  this  section  the  point  A  is  called  the  summit  of  the  prism, 
and  the  right  line  BC  is  called  the  base;  these  expressions  have  reference 
to  the  triangle  ABC,  and  not  to  the  prism. 


444 


On  Light. 


[512 


512.  Patb  of  rays  in  prisms.  Angle  of  deviation. — When  the  laws 
of  refraction  are  known,  the  path  of  the  rays  in  a  prism  is  readily  deter- 
mined. Let  O  be  a  luminous  point  (fig.  389)  in  the  same  plane  as  the 
principal  section  ABC  of  a  prism,  and  let  OD  be  an  incident  ray.  This 
ray  is  refracted  at  D,  and  approaches  the  normal,  because  it  passes  into 
a  more  highly  refracting  medium.  At  K  it  experiences  a  second  refrac- 
tion, but  it  then  deviates  from  the  normal,  for  it  passes  into  air,  which  is 
less  refractive  than  glass.  The  light  is  thus  refracted  twice  in  the  same 
directio.i,  so  that  the  ray  is  deflected  towards  the  base,  and  consequently 
the  eye  which  receives  the  emergent  ray  KH  sees  the  object  O  at  O'; 
that  is,  objects  seen  through  a  prism  appear  deflected  towards  its  summit. 
The  angle  OEO',  which  the  incident  and  emergent  rays  form  with  each 
other,  expresses  the  deviation  of  light  caused  by  the  prism,  and  is  called 
the  angle  of  deviation. 

Besides  this,  objects  seen  through  a  prism  appear  in  all  the  colours 
of  the  rainbow ;  this  phenomenon  will  be  described  under  the  name  of 
dispersion. 

This  angle  increases  with  the  refractive  index  of  the  material  of  the 
prism,  and  also  witli  its  refracting  angle.     It  also  varies  with  the  angle 


Fig.  390. 


Fig.  391. 


under  which  the  luminous  ray  enters  the  prism.  The  angle  of  deviation 
increases  up  to  a  certain  limit,  which  is  determined  by  calculation,  know- 
ing the  angles  of  incidence  of  the  ray,  and  the  refracting  angle  of  the 
prism. 

That  the  angle  of  deviation  increases  with  the  refractive  index  may  be 
shown  by  means  of  the  polyprism.  This  name  is  given  to  a  prism 
formed  of  several  prisms  of  the  same  angle  connected  at  their  ends 
(fig.  390).  These  prisms  are  made  of  substances  unequally  refringent, 
such  as  flint  glass,  rock  crystal,  or  crown  glass.     If  any  object — a  line, 


-514] 


Prisms. 


445 


for  instance — be  looked  at  through  the  polyprism,  its  different  parts  are 
seen  at  unequal  heights.  The  highest  portion  is  that  seen  through  the 
flint  glass,  the  refractive  index  of  which  is  greatest ;  then  the  rock 
crystal  ;  and  so  on  in  the  order  of  the  decreasing  refractive  indices. 

The  prism  with  variable  angle,  fig.  391,  is  used  for  showing  that 
the  angle  of  deviation  increases  with  the  refraciing  angle  of  the  prism. 
It  consists  of  two  parallel  brass  plates,  BC  and  C,  fixed  on  a  support. 
Between  these  are  two  glass  plates  moving,  on  a  hinge,  with  some  friction 
against  the  plates,  so  as  to  close  it.  When  water  is  poured  into  the 
vessel  the  angle  may  be  varied  at  will.  If  a  ray  of  light,  S,  be  allowed 
to  fall  upon  one  of  them,  by  inclining  the  other  more,  the  angle  of  the 
prism  increases,  and  the  deviation  of  the  ray  is  seen  to  increase. 

513.  Application  of  rlgrht  angled  prisms  in  reflectors. — Prisms 
whose  principal  section  is  an  isosceles  right-angled  triangle  afford  an 
important  application  of  total  reflection  (508).  For  let  ABC  (fig.  392) 
be  the  principal  section  of  such  a  prism, 
O  a  luminous  point,  and  OH  a  ray  at 
right  angles  to  the  face  BC.  This  ray 
enters  the  glass  without  being  refracted, 
and  makes  with  the  face  AB  an  angle 
equal  to  B,  that  is  to  45  degrees,  and  there- 
fore greater  than  the  limiting  angle  of 
glass,  which  is  41°  48'  (508).  The  ray 
OH  undergoes  therefore  at   H  total  re-  ^''*-  39-- 

flection,  which  imparts  to  it  a  direction  HI  perpendicular  to  the  second 
face  AC.  Thus  the  hypothenuse  surface  of  this  prism  produces  the  effect  of 
the  most  perfect  plane  mirror,  and  an  eye  placed  at  I  sees  at  O'  the 
image  of  the  point  O.  This  property  of  right-angled  prisms  is  frequently 
used  in  optical  instruments. 

514.  Conditions  of  emergence  in  prisms. — In  order  that  any 
luminous  rays  refracted  at  the  first  face  of  a  prism  may  emerge  from  the 
second,  it  is  necessary  that  the  refractive  angle  of  the  prism  be  less  than 
twice  the  critical  angle  of  the  substance  of  which  the  prism  is  composed. 
P'or  if  LI  (fig.  393)  be  the  ray  in- 
cident on  the  first  face,  IE  the 
refracted  ray,  PI  and  PE  the 
normals,  the  ray  IE  can  only 
emerge  from  the  second  face  when 
the  incident  angle  lEP  is  less  than 
the  critical  angle  (508).  But  as 
the  incident  angle  LIN  increases, 
the  angle  EIP  also  increases, 
while  lEP  diminishes.  Hence, 
according  as  the  direction  of  the 
ray  LI  tends  to  become  parallel 
with  the  face  AB,  does  this  ray 
tend  to  emerge  at  the  second  face. 

Let  LI  be  now  parallel  to  AB,  the  angle  r  is  then  equal  to  the  critical 


Fig.  393- 


446 


On  Light. 


[514- 


angle  /  of  the  prism,  because  it  has  its  maximum  value.  Further, 
the  angle  EPK,  the  exterior  angle  of  the  triangle  IPE,  is  equal  to  r  +  z'; 
but  the  angles  EPK  and  A  are  equal,  because  their  sides  are  perpen- 
dicular, and  therefore  A  =  r  +  i'  \  therefore  also  A  =  /-i-  i\  for  in  this  case 
r  =  L  Hence,  if  A  =  2/ or  is  >2/,  we  shall  have  i'  =  1  ox  >/,  and  there- 
fore the  ray  would  not  emerge  at  the  second  face,  but  would  undergo 
internal  reflection,  and  would  emerge  at  a  third  face,  BC.  This  would 
be  much  more  the  case  with  rays  whose  incide.it  angle  is  less  than  BIN, 
because  we  have  already  seen  that  i'  continually  incrjases.  Thus,  in  the 
case  in  which  the  refracting  angle  of  a  prism  is  equal  to  2/  or  is  greater, 
no  luminous  ray  could  pass  through  the  faces  of  the  refracting  angle. 

As  the  critical  angle  of  glass  is  41°  48',  twice  this  angle  is  less  than 
90°,  and  accordingly,  objects  cannot  be  seen  through  a  glass  prism  whose 
refracting  angle  is  a  right  angle.  As  the  critical  angle  of  water  is  48°  35' 
light  could  pass  through  a  hollow  rectangular  prism  formed  of  three  glass 
plates  and  filled  with  water. 

If  we  suppose  A  to  be  greater  than  /  and  less  then  2/,  then  of  rays  in- 
cident at  I  some  within  the  angle  NIB  will  emerge  from  AC,  others  will 
not  emerge,  nor  will  any  emerge  that  are  incident  within  the  angle  NIA. 
If  we  suppose  A  to  have  any  magnitude  less  than  /,  all  rays  incident  at  I 
within  the  angle  NIB  will  emerge  .from  AC,  as  also  will  some  of  those 
incident  within  the  angle  NIA. 

515.  IVXiniinum  deviation. — When  a  pencil  of  solar  light  passes 
through  an  aperture,  A,  in  the  side  of  a  dark  chamber  (fig.  394),  the 
pencil  is  projected  in  a  straight  line,  AC,  on  a  distant  screen.  But  if 
a  vertical  prism  be  interposed  between  the  aperture  and  the  screen,  the 
pencil  is  deviated  towards  the  base  of  the  prism,  and  the  image  is  pro- 
jected at  D,  at  some  distance  from  the  point  C.  If  the  prism  be  turned, 
so  that  the  incident  angle  decreases,  the  luminous  disc  approaches  the 
point  C,  up  to  a  certain  position,  E,  from  which  it  reverts  to  its  original 
position  even  when  the  prism  is  rotated  in  the  same  direction.  Hence 
there  is  a  deviation,  EBC,  less  than  any  other.     It  may  be  demonstrated 


[^                          ^ 

is 

^^^^'fsmmsm.^ 

1 

^^^^t 

-^  ^  X   /     ■'     1     \   \  V-^.;^^-:^- 

Fig.  394- 

mathematically  that  this  ininiinian  deviation  takes  place  when  the  angles 
of  incidence  and  of  emergence  are  equal. 

The  angle  of  minimum  deviation  may  be  calculated  when  the  incident 
angle  and  the  refracting  angle  of  the  prism  are  known.     P'or,  when  the 


-516] 


Index  of  Refraction. 


447 


deviation  is  least,  as  the  angle  of  emergence  r'  is  equal  to  the  incident 
angle  i  (fig.  393),  r  must  =  i'.  But  it  has  been  shown  above  (514)  that 
A  =  r+/';  consequently, 

A  =  2r (I) 

If  the  minimum  angle  of  deviation  LDL  be  called  d,  this  angle  being 
exterior  to  the  triangle  DIE,  we  readily  obtain  the  equation 

d=i-  7' '  r'  —  i'  =  2i—2r, 

whence  d  =  2i~A (2) 

which  gives  the  angle  d,  when  z  and  A  are  known. 

From  the  formula  (i)  and  (2)  a  third  may  be  obtained,  which  serves 
to  calculate  the  index  of  refraction  of  a  prism,  when  its  refracting  angle 
and  the  minimum  deviation  are  known.  The  index  of  refraction  it  is  the 
ratio   of  the   sines   of  the   angles  of  incidence  and  refraction  ;    hence 

ft  =  -^, —  ;  replacing  /  and  r  from  their  values  in  the  above  equations  (i) 
sm  r  ^  \  / 

and  (2),  we  get 


<^) 


(3) 


516.  IMCeasurement  of  the  index  of  refraction  in  solids. — By  means 
of  the  preceding  formula  (3)  the  refractive  index  of  a  solid  may  be  calcu- 
lated when  the  angles  A  and  d  are  known. 

In  order  to  determine  the  angle  A,  the  substance  is  cut  in  the  form 
of  a  triangular  prism,  and  the  angle  measured  by  means  of  a  goniometer 
(502). 

The  angle  ^is  measured  in  the  following  manner  :  a  ray,  LI,  emitted 
from  a  distant  object  (fig.  393),  is  received  on  the  prism,  which  is  turned 


Fig-  395. 

in  order  to  obtain  the  minimum  deviation  EDU.  By  means  of  a  tele- 
scope with  a  graduated  circle,  the  angle  EDL'  is  read  off,  which  the 
refracted  ray  DE  makes  with  the  ray  DU,  coming  directly  from  the 
object ;  now  this  is.  the  angle  of  minimum  deviation,  assuming  that  the 
object  is  so  distant  that  the  two  rays  LI  and  L'D  are  approximately 
parallel.  These  values  then  only  need  to  be  substituted  in  the  equation 
(3)  to  give  the  value  of  n. 

This  method  is  due  to  Newton.  Under  many  circumstances  it  cannot 
be  employed  ;  for  instance,  when  the  refractive  index  of  a  mere  drop  of 
fluid  is  required.     In  this  case,  use  may  be  made  of  a  method  due  to 


448 


On  LigJit. 


[516- 


WoUaston,  which  depends  on  the  determination  of  the  critical  angle  of 
the  substance. 

517.  Measurement  of  the  index  of  refraction  of  liquids. — M.  Biot 
has   applied    Newton's    method  to  determining  the  refractive  index    of 

liquids.  For  this  purpose  a  cylindrical 
cavity  O,  of  about  075  in.  in  diameter,  is 
perforated  in  a  glass  prism,  PQ  (fig.  396), 
from  the  incident  face  to  the  face  of  emer- 
gence. This  cavity  is  closed  by  two  plates 
of  glass  which  are  cemented  on  the  sides  of 
this  prism.  Liquids  are  introduced  through 
a  small  stoppered  aperture,  B.  The  refract- 
ing angle  and  the  minimum  deviation  of  the 
F'S-  396.  liquid  prism  in  the  cavity  O  having  been 

determined,  their  values  are  introduced  into  the  formula  (3),  which  gives 

the  index. 

518.  IMCeasurement  of  the  index  of  refraction  of  grases, — A  method 
for  this  purpose  founded  on  that  of  Newton  has  been  devised  by  MM. 
Biot  and  Arago.  The  apparatus  which  they  use  consists  of  a  glass 
tube  (fig.  397),  bevelled  at  its  twc  ends,  and  closed  by  glass  plates,  which 
are  at  an  angle  of  143°  This  tube  is  connected  with  a  bell-jar,  H, 
in  which  there  is  a  siphon  barometer,  and  with  a  stopcock  by  means  of 

which  the  apparatus  can  be  exhausted, 
and  different  gases  introduced.  After 
having  exhausted  the  tube  AB,  a  ray  of 
light,  SA  is  transmitted,  which  is  bent 
away  from  the  normal  through  an  angle 
r  —  i  at  the  first  incidence,  and  towards 
it  through  an  angle  /'  —  r'  at  the  second. 
These  two  deviations  being  added,  the 
total  deviation  d  \s-  r-i^i' -r'.  In 
the  case  of  a  minimum  deviation,  /  =  ;-^ 
and  r  =  i\  whence  d=A~2i,  since  r  +  t' 
=  A  (514)-  The  index  from  vacuum  to 
air,  which  is  evidently  ^!^  ^,  has  therefore 


r\ 


sm  t 


the  value 


sm 


•r^ 


(4) 


Fig.  397. 


{^) 


Hence,  in  order  to  deduce  the  refrac- 
tive index  from  vacuum  into  air,  which  is  the  absolute  index  or  principal 
index,  it  is  simply  necessary  to  know  the  refracting  angle  A,  and  the 
angle  of  minimum  deviation  d. 

To  obtain  the  absolute  index  of  any  other  gas,  after  having  produced 
a  vacuum,  this  gas  is  introduced ;  the  angles  A  and  a  having  been  mea- 


-519] 


Lenses. 


449 


sured,  the  above  formula  gives  the  index  of  refraction  from  gas  to  air. 
Dividing  the  index  of  refraction  from  vacuum  to  air  by  the  index  of  re- 
fraction from  the  gas  to  air,  we  obtain  the  index  of  refraction  from  vacuum 
to  the  gas,  that  is,  its  absolute  index. 

By  means  of  this  apparatus  Biot  and  Arago  have  found  that  the  refrac- 
tive indices  of  gases  are  very  small  as  compared  with  those  of  solids  and 
liquids,  and  that  for  the  same  gas  the  7'efractive  power  is  proportional  to 
the  density  ;  meaning  by  the  refractive  action  of  a  substance  the  square 
of  its  refractive  index  less  unity ;  that  is,  n'^—i.  The  refractive  action 
divided  by  the  density,  or 


is  called  the  absolute  7'efractive  power. 


Table  of  the  absolute  indices  of  refraction. 


Diamond    . 

. 

2-47  to  275 

Plate  glass,  St.  Gobin 

1-543 

Phosphorus 

.     2-224 

Crown  glass 

I -600 

Sulphur 

.      2-II5 

Turpentine  . 

1-470 

Ruby 

, 

•    1779 

Alcohol 

1-374 

Bisulphide  of  carbon . 

.    1-678 

Albumen 

1-360 

Iceland  spar, 

ordinary  ray  .      1*654 

Ether    . 

1-358 

Iceland  spar. 

extraord 

nary 

Crystalline  lens 

1-384 

ray . 

. 

•     1-483 

Vitreous      ., 

1-339 

Flint  glass  . 

•     ^SIS 

Aqueous     ,. 

1-337 

Rock  salt    . 

. 

•     I-550 

Water  . 

1-336 

.,      crystal 

• 

.     1-548 

Ice       .         .         . 

1-310 

Refractive  indices  of  gases. 

Vacuum 

I  -oooooo 

Carbonic  acid         .         .     1-000449 

Hydrogen 

.     1-000138 

Hydrochloric  acid  .         .     1-000449 

Oxygen 

.     1000272 

Nitrous  oxide          .         .     1-000503 

Air  '      . 

I  -000294 

Sulphurous  acid      .         .     1-000665 

Nitrogen 

.     I  -000300 

Olefiant  gas    .         .         .1  -000678 

Ammonia 

.     I  -000385 

Chlorine 

.     I 

-000772 

LEx^JSES.      THEIR   EFFECTS. 

519.  Dififerent  kinds  of  lenses. — Lenses  are  transparent  media,  which, 
from  the  curvature  of  their  surfaces,  have  the  property  of  causing  the 
k  luminous  rays  which  traverse  them  either  to  converge  or  to  diverge. 
According  to  their  curvature  they  are  either  spherical,  cylindrical,  ellipti- 
cal, or  parabolic.  Those  used  in  optics  are  always  spherical.  They  are 
commonly  made  either  of  crown  glass,  which  is  free  from  lead,  or  of 
fli?it  glass,  which  contains  lead,  and  is  more  refractive  than  crown 
glass. 

The  combination  of  spherical  surfaces,  either  with  each  other  or  with 
plane  surfaces,  gives  rise  to  six  kinds  of  lenses,  sections  of  which  are 


450 


On  Light. 


[519- 


represented  in  fig.  398  ;  four  are  formed  by  two  spherical  surfaces,  and 
two  by  a  plane  and  a  spherical  surface. 

A  is  a  double  convex,  B  is  a  plano-convex,  C  is  a  converging  concavo- 
convex,  D  is  a  double  concave,  E  is  a  plano-concave,  and  F  is  a  diverging 
concavo-convex.  The  lens  C  is  also  called  the  converging  meniscus,  and 
the  lens  F  the  diverging  meniscus. 

v>        c  1) 


Fig.  398. 

The  first  three,  which  are  thicker  at  the  centre  than  at  the  borders,  are 
converging  ;  the  others,  which  are  thinner  in  the  centre,  are  diverging. 
In  the  first  group,  the  double  convex  lens  only  need  be  considered,  and 
in  the  second  the  double  concave,  as  the  properties  of  each  of  these  lenses 
apply  to  all  those  of  the  same  group. 
^^  I  n  lenses  whose  two  surfaces  are  spherical,  the  centres  for  these  surfaces 
are  caWedr  cenlres  of  curvature,  and  the  right  line  which  passes  through 
these  two  centres  is  the  'principal  axis.  In  a  plano-concave  or  plano- 
convex lens,  the  principal  axis  is  the  perpendicular  let  fall  from  the  centre 
of  the  spherical  face  on  the  plane  face. 

In  order  to  compare  the  path  of  a  luminous  ray  in  a  lens  with  that  in 
a  prism,  the  same  hypothesis  is  made  as  for  curved  mirrors  (492),  that  is, 
the  surfaces  of  these  lenses  are  supposed  to  be  formed  of  an  infinity  of 
small  plane  surfaces  or  elements  ;  the  normal  at  any  point  is  then  the 
perpendicular  to  the  plane  of  the  corresponding  element.  It  is  a  geo- 
metrical principle  that  all  the  normals  to  the  same  spherical  surface  pass 
through  its  centre.  On  the  above  hypothesis  we  can  always  conceive  two 
plane  surfaces  at  the  points  of  incidence  and  convergence,  which  are  in- 
clined to  each  other,  and  thus  produce  the  effect  of  a  prism.  Pursuing 
this  comparison,  the  three  lenses  A,  B,  and  C  may  be  compared  to  a 
succession  of  prisms  having  their  summits  outwards,  and  the  lenses  D, 
E,  and  F  to  a  series  having  their  summits  inwards  ;  from  this  we  see 
that  the  first  ought  to  condense  the  rays,  and  the  latter  to  disperse  them, 
for  we  have  already  seen  that  when  a  luminous  ray  traverses  a  prism  it 
is  deflected  towards  the  base  (512). 

520.  Foci  in  double  convex  lenses. — The  focus  of  a  lens  is  the  point 

where  the  refracted  rays,  or  their  prolongations,  meet.     Double  convex 

lenses  have  the  same  kind  of  foci  as  concave  mirrors  ;  that  is,  real  foci 

and  virtuaFfoci.  ~  ' 

Kealjoci.  We  shall  first  consider  the  case  in  which  the  luminous  rays 
which  fall  on  the  lens  are  parallel  to  its  principal  axis,  as  shown  in  the 
fig.  399.  In  this  case,  any  incident  ray,  LB,  in  approaching  the  normal 
of  the  point  of  incidence  B,  and  in  diverging  from  it  at  the  point  of  emer- 


-520] 


Convex  Lenses. 


451 


gence  D,  is  twice  refracted  towards  the  axis,  which  it  cuts  at  F.  As  all 
rays  parallel  to  the  axis  are  refracted  in  the  same  manner,  it  can  be  shown 
by  calculation  that  they  all  pass  very  nearly  through  the  point  F,  so  long 
as  the  arc  DE  does  not  exceed  10°  to  12°.  This  point  is  called  the 
pruicipal  focus,  and  the  distance  FA  is  the  principal  focal  distance.  It  is 
constant  in  the  same  lens,  but  varies  with  the  radii  of  curvature  and  the 


Fig.  399- 

index  of  refraction.  In  ordinary  lenses,  which  are  of  crown  glass,  and  in 
which  the  radii  of  the  two  surfaces  are  nearly  equal,  the  principal  focus 
coincides  very  closely  with  the  centre  of  curvature. 

/  We  shall  now  consider  the  case  in  which  the  luminous  object  is  outside 
the  principal  focus,  but  so  near  that  all  incident  rays  form  a  divergent 
pencil,  as  shown  in  fig.  400.    The  luminous  point  being  at  L,  by  comparing 


V 


Fig.  400. 

the  path  of  a  diver^^ing  ray,  LB,  with  that  of  a  ray,  SB,  parallel  to  the 
axis,  the  former  is  found  to  make  with  the  normal  an  angle,  LB«,  greater 
than  the  angle  SB;^  :  consequently,  after  traversing  the  lens,  the  ray  cuts 
the  axis  at  a  point,  /,  which  is  more  distant  than  the  principal  focus  F. 
As  all  rays  from  the  point  L  intersect  approximately  in  the  same  point  /, 
this  latter  is  the  conjugate  focics  of  the  point  L  ;  this  term  has  the  same 
meaning  here  as  in  the  cases  of  mirrors,  and  expresses  the  relation 
existing  between  the  two  points  L  and  /,  which  is  of  such  a  nature,  that  if 
the  luminous  point  is  moved  to  /,  the  focus  passes  to  L. 

According  as  the  object  comes  nearer  the  lens,  the  convergence  of  the 
emergent  rays  decreases,  and  the  focus  /  becomes  more  distant ;  when  the 
object  L  coincides  with  the  principal  focus,  the  emergent  rays  on  the  other 
side  are  parallel  to  the  axis,  and  there  is  no  focus,  or,  what  is  the  same 
thing,  it  is  infinitely  distant.    ^As  the  refracted  rays  are  parallel  in  this 


452 


On  LiorJit. 


[520 


case,  the  intensity  of  light  only  decreases  slowly,  and  a  simple  lamp  can 
illuminate  great  distances.  It  is  merely  necessary  to  place  it  in  the  focus 
of  a  double  concave  lens,  as  shown  in  fig.  401. 


Fig.  401. 

N^  Virtual  foci.  A  double  convex  lens  has  a  virtual  focus  when  the 
luminous  object  is  placed  between  the  lens  and  the  principal  focus,  as 
shown  in  fig.  402.     In  this  case  the  incident  rays  make  with  the  normal 


greater  angles  than  those  made  by  the  rays  FI  from  the  principal  focus  ; 
hence,  when  the  former  rays  emerge,  they  move  farther  from  the  axis 
than  the  latter,  and  form  a  diverging  pencil,  HK,  GM.  These  rays 
cannot  produce  a  real  focus,  but  their  prolongations  intersect  in  some' 
point,  /,  on  the  axis,  and  this  point  is  the  virtual  focus  of  the  pomt   L 

(483)- 

521.  Foci  in  double  concave  lenses. — In  double  concave  lenses  there 
are  only  virtual  foci,  whatever  the  distance  of  the  object.  Let  S'  be  any 
pencil  of  rays  parallel  to  the  axis  (fig.  403),  any  ray,  SI,  is  refracted  at  the 


Fig-  403-  t^ig-  404- 

point  of  incidence  I,  and  approaches  the  normal  CI.  At  the  point  of  emer- 
gence it  is  also  refracted,  but  diverges  from  the  normal  GC,  so  that  it  is 


-523] 


Focus  of  Lenses. 


453 


twice  refracted  in  a  direction  which  moves  it  from  the  axis  CC  As  the  same 
thing  takes  place  for  every  other  ray,  S'KMN,  it  follows  that  the  rays,  aftei^ 
traversing  the  lens,  form  a  diverging  pencil,  GH.  MN.  Hence  there  is  no 
real  focus,  but  the  prolongations  of  these  rays  cut  one  another  in  a  point, 
F,  which  is  the  principal  virtual  focus. 

In  the  case  in  which  the  rays  proceed  from  a  point,  L  (fig.  404),  on  the 
axis,  it  is  found  by  the  same  construction  that  a  virtual  focus  is  formed  at 
/,  which  is  between  the  principal  focus  and  the  lens. 

522.  Experimental  determination  of  the  principal  focus  of  lenses.— 
To  determine  the  principal  focus  of  a  double  convex  lens,  it  may  be  exposed 
to  the  sun's  rays  so  that  they  are  parallel  to  its  axis.  The  emergent  pen- 
cil being  received  on  a  ground  glass  screen,  the  point  to  which  the  rays 
converge  is  readily  seen  ;  it  is  the  principal  focus. 

With  a  double  concave  lens,  the  face  ab  (tig.  405)  is  covered  with  an 


Fig-  405- 

opaque  substance,  such  as  lampblack,  two  small  apertures,  a  and^,  being 
left  in  the  same  principal  section,  and  at  an  equal  distance  from  the  axis  ; 
a  pencil  of  solar  light  is  then  received  on  the  other  face,  and  the  screen  P, 
which  receives  the  emergent  rays,  is  moved  nearer  to  or  farther  from  the 
lens,  until  A  and  B,  the  spots  of  light  from  the  small  apertures  a  and  b^ 
are  distant  from  each  other  by  twice  ab.  The  distance  DI  is  then  equal 
to  the  focal  distance  FD,  because  the  triangles  Yab  and  FAB  are  similar, 
'rrr-523.  Optical  centre,  secondary  axis. — In  every  lens  there  is  a  point 
called  the  optical  ccnfre,  which  is  situated  on  the  axis,  and  which  has  the 


Fig.  406. 


Fig  407. 


property  that  any  luminous  ray  passing  through  it  experiences  no  angular 
deviation  ;  th&t  is,  that  the  emergent  ray  is  parallel  to  the  incident  ray. 
The  existence  of  this  point  may  be  demonstrated  in  the  following  manner : 
Let  two  parallel  radii  of  curvature,  CA  and  C'A'  (fig!  406)  be  drawn  to 


454  On  Light.  [523- 

the  two  surfaces  of  a  double  convex  lens.  Since  the  two  plane  elements 
of  the  lens  A  and  A'  are  parallel,  as  being  perpendicular  to  two  parallel 
right  lines,  it  will  be  granted  that  the  refracted  ray  KA,  A'K'  is  pro- 
pagated in  a  medium  with  parallel  faces.  Hence,  a  ray  which  reaches  A 
at  such  an  incHnation,  that  after  refraction  it  takes  the  direction  AA' 
will  emerge  parallel  to  its  first  direction  (521) ;  the  point  O,  at  which  the 
right  line  cuts  the  axis,  is  therefore  the  optical  centre.  The  position  of 
this  point  may  be  determined  for  the  case  in  which  the  curvature  of  the 
two  faces  is  the  same,  which  is  the  usual  condition,  by  observing  that  the 
triangles  COA  and  C'OA^  are  equal,  and  therefore  that  OC  =  OC,  which 
gives  the  point  O.  If  the  curvatures  are  unequal,  the  triangles  COA  and 
Q'OPJ  are  similar,  and  either  CO  or  CO  may  be  found,  and  therefore  also 
the  point  O. 

In  double  concave  or  concavo-convex  lenses  the  optical  centre  may  be 
determined  by  the  same  construction.  In  lenses  with  a  plane  face  this 
point  is  at  the  intersection  of  the  axis  by  the  curved  face. 
__ — Every  right  line,  PP'  (fig.  407),  which  passes  through  the  optical  centre 
-wTthout  passing  through  the  centres  of  curvature,  is  a  secondaiy  axis. 
From  the  property  of  the  optical  centre,  every  secondary  axis  represents  " 
a  luminous  rectilinear  ray  passing  through  this  point,  for  from  the  slight 
thickness  of  the  lenses,  it  may  be  assumed  that  rays  passing  through  the 
optical  centre  are  in  a  right  line ;  that  is,  that  the  small  deviation  may  be 
neglected  which  rays  experience  in  tra\ersing  a  medium  with  parallel 
faces  (fig.  387). 

So  long  as  the  secondary  axes  only  make  a  small  angle  with  the  prin- 
cipal axis,  all  that  has  hitherto  been  said  about  the  principal  axis  is  ap- 
plicable to  them ;  that  is,  that  rays  emitted  from  a  point,  P  (fig.  407),  on 
the  secondary  axis  PP',  nearly  converge  to  a  certain  point  of  t,his  axis,  P', 
and  according  as  the  distance  from  the  point  P  to  the  lens  is  greater  or 
less  than  the  principal  focal  distance,  the  focus  thus  formed  will  be  con- 
jugate or  virtual.  This  principle  is  the  foundation  of  what  follows  as  to 
the  formation  of  images. 

524.  Formation  of  imagoes  in  double  convex  lenses. —  In  lenses 
as  well  as  in  mirrors  the  image  of  an  object  is  the  collection  of  the  foci 
of  its  several  points ;  hence  the  images  furnished  by  lenses  are  real  or 
virtual  in  the  same  case  as  the  foci,  and  their  construction  resolves  itself 
into,  determining  a  series  of  points,  as  was  the  case  with  mirrors  (496). 
— i— ■  i-  -/^^«/  image.  Let  AB  ^fig.  408)  be  placed  beyond  the  principal  focus. 
If  a  secondary  axis,  Ka,  be  drawn  from  the  outside  point  A,  any  ray,  AC, 
from  this  point,  will  be  twice  refracted  at  C  and  D,  and  both  times  in  the 
same  direction,  approaching  the  secondary  axis,  which  it  cuts  at  a.  From 
what  has  been  said  in  the  last  paragraph,  the  other  rays  from  the  point  A 
will  intersect  in  the  point  rt,  which  is  accordingly  the  conjugate  focus  of 
the  point  A.  If  the  secondary  axis  be  drawn  from  the  point  B,  it  will  be 
seen,  in  like  manner,  that  the  rays  from  this  point  intersect  in  the  point  b^ 
and  as  the  points  between  A  and  B  have  their  foci  between  a  and  b,  a  real 
but  inverted  image  of  AB  will  be  formed  at  ab. 

In  order  to  see  this  image,  it  may  be  received  on  a  white  screen,  on 


-  524]  Double  Convex  L  enses,  555 

which  it  will  be  depicted,  or  the  eye  may  be  placed  in  the  path  of  the  rays 
emerging  from  it. 

Conversely,  if  ab   were   the  luminous   or   illuminated   object  which 


Fig.  408. 

emitted  rays,  its  image  would  be  formed  at  AB.  Tvvo  consequences 
important  for  the  theoiy  of  optical  instruments  follow  from  this :  that 
1st,  If  a?t  object  J  even  a  very  large  o?ie,  is  at  a  sufficient  distance  frotn  a 
double  convex  lens,  the  real  and  inverted  image  which  is  obtained  of  it  is 
very  small,  it  is  near  the  prijicipal  focjis,  but  somewhat  farther  from  the 
lens  than  this  is  ;  2nd,  If  a  very  small  object  be  placed  near  the  principal 
focus,  but  a  little  before  it,  the  image  which  is  formed  is  at  a  great  distance, 
it  is  much  larger,  and  that  in  proportion  as  the  object  is  7iear  the  prin- 
cipal focus.  In  all  cases  the  object  and  the  image  have  the  same  propor- 
tion as  their  distances  from  the  lens. 

These  two  principles  are  experimentally  confirmed  by  receiving  on  a 
screen  the  image  of  a  lighted  candle,  placed  successively  at  various  dis- 
tances from  a  double  convex  lens. 

ii.  Virtual ii?iage.  There  is  another  case  in  which  the  object  AB  (fig.  409) 
is  placed  between  the  lens  and  its  principal  focus.    If  a  secondary  axis,  Oa 


Fig.  409. 

be  drawn  from  the  point  A,  every  ray,  AC,  after  having  been  twice  refracted 
on  emerging,  diverges  from  this  axis,  since  the  point  A  is  at  a  less  dis- 
tance than  the  principal  focal  distance  (520).  This  ray,  continued  in  an 
opposite  direction,  will  cut  the  axis  Oa  in  the  point  a,  which  is  the  virtual 
focus  of  the  point  A.  Tracing  the  secondary  axis  of  the  point  B,  it  will 
be  found,  in  the  same  manner,  that  the  virtual  focus  of  this  point  is  formed 
at  b.  There  is,  therefore,  an  image  of  AB  at  ab.  This  is  a  virtual  image, 
it  is  erect,  and  larger  than  the  object. 


456 


On  Light. 


[524- 


The  magnifying  power  is  greater  in  proportion  as  the  lens  is  more  con- 
vex, and  the  object  nearer  the  principal  focus.  We  shall  presently  show 
how  the  magnifying  power  may  be  calculated  by  means  of  the  formulae 
relating  to  lenses  (527).  Double  convex  lenses,  used  in  this  manner  as 
magnifying  glasses,  are  called  simple  microscopes. 

525.  Formation  of  imagres  In  double  concave  lenses. — Double  con- 
cave lenses,  like  convex  mirrors,  only  give  virtual  images,  whatever  the 
distance  of  the  object. 

Let  AB  (fig.  410)  be  an  object  placed  in  front  of  such  a  lens.     If  the 

secondary  axis  be  drawn  from  the 
point  A,  all  rays,  AC,  AI,  from  this 
point  are  twice  refracted  in  the 
same  direction,  diverging  from  the 
axis  AO ;  so  that  the  eye,  receiv- 
ing the  emergent  rays  DE  and 
GH,  supposes  them  to  proceed 
from  the  point  where  their  pro- 
longations cut  the  secondary  axis 
AO  in  the  point  a.  In  like  manner. 
Fig.  410.  drawing   a    secondary    axis    from 

the  point  B,  the  rays  from  this 
point  form  a  pencil  of  divergent  rays,  the  direction  of  which,  prolonged, 
intersect  in  b.  Hence  the  eye  sees  at  ab  a  virtual  image  of  AB,  which  is 
always  erect ^  and  smaller  than  the  object. 

526.  Spberical  aberration.  Caustics. — In  the  theory  of  the  foci, 
and  of  the  images  formed  by  different  kinds  of  spherical  lenses,  it  has 
been  hitherto  assumed,  that  the  rays  emitted  from  a  single  point  intersect 
also  after  refraction  in  a  single  point.  This  is  virtually  the  case  with  a 
lens  whose  aperture — that  is,  the  angle  obtained  by  joining  the  edges  to 
the  principal  focus — does  not  exceed  10°  or  12°. 

Where,  however,  the  aperture  is  larger,  the  rays  which  traverse  the 
lens  near  the  edge  are  refracted  to  a  point  nearer  the  lens  than  the  rays 
which  pass  near  the  axis.  The  phenomenon  thus  produced  is  named 
spherical  abe?^ration  by  refraction  ;  it  is  analogous  to  the  spherical  aberra- 
tion produced  by  reflection.  The  luminous  surfaces  formed  by  the  inter- 
section of  the  refracted  rays  are  termed  caustics  by  i^efraction. 

Spherical  aberration  is  prejudicial  to  the  sharpness  and  definition  of  an 
image.  If  a  ground  glass  screen  be  placed  exactly  in  the  focus  of  a  lens, 
the  image  of  an  object  will  be  sharply  defined  m-the  centre,  but  indistinct 
at  the  edges  ;  and,  vice  versa,  if  the  image  is  sharp  at  the  edges,  it  will  be 
indistinct  in  the  centre.  This  defect  is  very  objectionable,  more  especially 
in  lenses  used  for  photography.  It  is  partially  obviated  by  placing  before 
the  lenses  diaphragms  provided  with  a  central  aperture  called  stops,  which 
admit  the  rays  passing  near  the  centre,  but  cut  off  those  which  pass  near 
the  edges. 

Mathematical  investigation  shows  that  convex  lenses,  whose  radii  of 
curvature  stand  in  the;  ratio  expressed  by  the  formula 
r   _  4  —  211^  +  n 
r  171^  -^  211   ^ 


-527] 


Lenses. 


457 


are  free  from  spherical  aberration ;  in  which  r  is  the  radius  of  curvature 
of  the  foci  turned  to  the  parallel  rays,  and  r  that  of  the  other  face,  while 
n  is  the  refractive  index.  Spherical  aberration  is  also  destroyed  by  com- 
bining different  lenses  of  suitable  curvature. 

Lenses  which  are  free  from  spherical  aberration  are  called  aplanatic. 

527.  Formulae  relating-  to  lenses. —  In  all  lenses,  the  relation  between 
the  distances  of  the  image  and  object,  the  radii  of  curvature,  and  the  re- 
fractive index,  may  be  expressed  by  a  formula.  In  the  case  of  a  double 
convex  lens,  let  P  be  a  luminous  point,  situate  on  the  axis,  fig.  411,  let  PI 


Fig.  4 


be  an  incident  ray,  IE  its  direction  within  the  lens,  EP'  the  emergent 
ray,  so  that  P'  is  the  conjugate  focus  of  P.  Further,  let  CI  and  CE  be 
the  normals  to  the  points  of  incidence  and  emergence,  and  I  PA  be  put 
equal  to  u,  EP'A'-/3,  ECA'  =  ;,  ICA  =  o,  NIP  =  /,  EIO  =  r,  IEO=/', 
N'EP'  =  r'. 

Because  the  angle  i  is  the  exterior  angle  of  the  triangle  PIC^,  and  the 
angle  r'  the  exterior  angle  of  the  triangle  CEP',  therefore,  i  =  a-vl,  and 
^  =  7  +  i^j  whence 

2+r'  =  a  +  /3-ry-h5  .  .  .  .  (l) 

But  at  the  point  I,  sin  i=^n  sin  r,  and  at  the  point  E,  sin  r'  =  «  sin  i  (506), 
n  being  the  refractive  index  of  the  lens.  Now  if  the  arc  AI  is  only  a 
small  number  of  degrees,  these  sines  may  be  considered  as  proportional 
to  the  angles  i,  r,  /',  and  y',  whence,  in  the  above  formula,  we  may  replace 
the  sines  by  their  angles,  which  gives  i=nr  and  r'=^ni\  from  which 
i^rv'  =  11  (r  +  i').  Further,  because  the  two  triangles  I OE  and  COC  have 
a  common  equal  angle,-  O,  therefore  ^+2'  =  )'  +  ^,  from  which  i-\-r'  =  7i 
(y  +  h).     Introducing  this  value  into  the  equation  (i)  we  obtain, 

n  (y  +  ^)  =  a  -f  /3  +  y  +  ^,  from  which  («  ~  i) -(y  +  ^)  =  a  1-  /3  .         .      (2) 

Let  CA'  be  denoted  by  R,  C'A  by  R',  PA  by/,  and  P^A'  hy  Z""-  Then 
with  centre  P  and  radius  PA  describe  the  arc  hd,  and  with  centre  P'  and 
radius  P^'A'  describe  the  arc  Aw.  Now  when  an  angle  at  the  centre  of  a 
circle  subtends  a  certain  arc  of  the  circumference^  the  quotient  of  the  arc 
divided  by  the  radius  measures  the  angle ;  consequently, 


Kd       Kd    ,. 


h'n 


A'E 
R 


y  and  0 


AI 
R'" 


Therefore  by  substitution  in  (2) 


4S8  ^      •  On  Light.  [527- 

Now  since  the  thickness  of  the  lens  is  very  small,  and  the  angles  are 
also  small,  and  Art',  AI,  A'E,  K'n  differ  but  little  from  coincident  straight 
lines,  and  are  therefore  virtually  equal ;  hence  the  above  equation  be- 
comes 

(«-)  r4')=^> (3) 

This  is  the  formula  for  double  convex  lenses  ;  \i p  be  =  oo,  we  have 

p  being  the  principal  focal  distance.     If  this  be  represented  by/,  we  get 

from  which  the  value  of/ is  easily  deduced.  Considered  in  reference  to 
formula  (4),  the  formula  (3)  assumes  the  form 

p'rr ^=' 

which  is  that  in  which  it  is  usually  employed.  When  the  image  is  virtual 
p  changes  its  sign,  and  formula  (5)  takes  the  form 

Tp'  f- ^'^ 

In  double  concave  lenses,^'  and/retain  the  same  sign,  but  that  of/ 
changes  ;  the  formula  (5)  becomes  then 

p  p      f 

The  formula  (7)  may  be  obtained  by  the  same  reasonings  as  the  other. 

528.  Relative  xuagrnitudes  of  imag-e  and  object. — From  the  equality 
of  the  triangles  AOB,  aOb  (fig.  408)  we  get  for  the  relative  magnitudes  of 

image  and  object  the   proportion  -_:=^;  whence^  ^-^  where  AB  =  o 

is  the  magnitude  of  the  object  and  ab^\  that  of  the  image ;  while  p  and 
p^  are  their  respective  distances  from  the  lens.      Replacing  p^  by  its 

value  from  the  equation  —  +  _  =  _,,  where  the  image  is  real,  or  from  the 
_      ^P    Pi    J 

equation  -——»=_,  where  it  is  virtual,  we  shall  obtain  the  different  values 
P    Px      f 

of  the  ratio  -  for  various  positions  of  the  object.     In  the  first  case  we 

have  I  / 

O  *  p~/ 
Thus  if  p>2f^l>o 

/  =  2/     1=0 

p<2/    I>o. 


530] 


Dispersion  of  Light. 


459 


In  the  second  case  when  the  image  is  virtual  we  shall  have 

I       f 
—  =  / — ,  so  that  in  all  cases  I  >0. 

o  f-f 
529.  ]baryng:o scope. — As  an  application  of  lenses  may  be  adduced  the 
laryngoscope^  which  is  an  instrument  recently  invented  to  facilitate  the 
investigation  of  the  larynx  and  the  other  cavities  of  the  mouth.  It  con- 
sists of  a  plane  convex  lens  L,  and  a  concave  reflector  M,  both  fixed  to  a 
ring  which  can  be  adjusted  to  any  convenient  lamp.  The  flame  of  the 
lamp  is  in  the  principal  focus  of  the  lens,  and  at  the  same  time  is  at  the 


Fig.  412. 

centre  of  curvature  of  the  reflector.  Hence  the  divergent  pencil  proceeding 
from  the  lamp  to  the  lens  is  changed  after  emerging  into  a  parallel 
pencil.  Moreover,  the  pencil  from  the  lamp  impinging  upon  the  mirror, 
is  reflected  to  the  focus  of  the  lens,  and  traverses  the  lens  forming  a 
second  parallel  pencil  which  is  supported  on  the  first.  This  being  directed 
into  the  mouth  of  a  patient,  its  condition  may  be  readily  observed. 


CHAPTER    IV. 

DISPERSION   AND   ACHROMATISM. 

530.  Decomposition  of  white  lig^ht.  Solar  spectrum.  —  The  pheno- 
menon of  refraction  is  by  no  means  so  simple  as  we  have  hitherto  as- 
sumed ;  when  white  light,  or  that  which  reaches  us  from  the  sun,  passes 
from  one  medium  into  another,  //  is  decomposed  into  several  kinds  of 
lights,  a  phenomenon  to  which  the  name  dispersion  is  given. 

In  order  to  show  that  white  light  is  decomposed  by  refraction,  a  pencil 
of  solar  light,  SA  (fig.  413),  is  allowed  to  pass  through  a  small  aperture 


460 


On  Light. 


[530 


in  the  window  shutter  of  a  dark  chamber.  This  pencil  tends  to  form  a 
round  and  colourless  image  of  the  sun  at  K  ;  but  if  a  flint  glass  prism, 
arranged  horizontally,  be  interposed  in  its  passage,  the  beam,  on  emerging 
from  the  prism,  becomes  refracted  towards  its  base,  and  produces  on  a 
distant  screen  a  vertical  band  rounded  at  the  ends,  coloured  in  all  the 
tints  of  the  rainbow,  which  is  called  the  solar  spectrum,  see  Plate  I.  In 
this  spectrum  there  is,  in  reality,  an  inhnity  of  different  tints,  which  im- 
perceptibly merge  into  each  other,  but  it  is  customary  to  distinguish  seven 
principal  colours.  These  are  violet,  indigo,  blue,  greeii^  yellow,  orange, 
red',  they  are  arranged  in  this  order  in  the  spectrum,  the  violet  being  the 
most  refrangible,  and  the  red  the  least  so.     They  do  not  all  occupy  an 


Fig.  413- 


equal  extent  in  the  spectrum,  violet,  having  the  greatest  extent,  and ' 
orange  the  least. 

With  transparent  prisms  of  different  substances,  or  with  hollow  glass 
prisms  filled  with  various  liquids,  spectra  are  obtained  formed  of  the 
same  colours,  and  in  the  same  order  ;  but  when  the  deviation  produced 
is  the  same,  the  length  ,of  the  spectrum  varies  with  the  substance  of 
which  the  prism  is  made.  The  angle  of  separation  of  two  selected  rays 
(say  in  the  red  and  the  violet)  produced  by  a  prism  is  called  the  disper- 
sion, and  the  ratio  of  this  angle  to  the  mean  deviation  of  the  two  rays  is 
called  the  dispersive  power.  This  ratio  is  constant  for  the  same  sub- 
stance so  long  as  the  refracting  angle  of  the  prism  is  small.  For  the 
deviation  of  the  two  rays  is  proportional  to  the  refracting  angle  ;  their 
difference  and  their  mean  \2,ry  in  the  same  manner,  and,  therefore,  the 
ratio  of  their  difference  to  their  mean  is  constant.  For  flint  glass  this  is 
0-043  '->  for  crown  gla^s  it  is  0*0246  ;  for  the  dispersive  power  of  flint  is 
almost  double  that  of  crown  glass. 

The  spectra  which  are  formed  by  artificial  lights  rarely  contain  all  the 
colours  of  the  solar  spe-ctrum ;  but  their  colours  are  found  in  the  solar 
spectrum,  and  in  the  same  or-dier.  Their  relative  intensity  is  also  modi- 
fied    The  shade  jof  coJboTiW  which  predominates  in  the  flame  predominates 


-532]  Pj'odiiction  of  a  Pure  Spectrum,  461 

also  in  the  spectrum  :  yellow,  red,  and  green  flames  produce  spectra  in 
which  the  dominant  tint  is  yellow,  red,  or  green. 

531.  Production  of  a  pure  spectrum. — In  the  above  experiment, 
when  the  light  is  admitted  through  a  wide  slit,  the  spectrum  formed  is 
built  up  of  a  series  of  overlapping  spectra,  and  the  colours  are  confused 
and  indistinct.  In  order  to  obtain  a  pure  spectrum,  the  slit  in  the  shutter 
of  the  dark  room  through  which  light  enters,  should  be  from  15  to  25"""  in 
height  and  from  i  to  2"*™  in  breadth.  The  sun's  rays  are  directed  upon  the 
slit  by  a  mirror,  or  still  better  by  a  heliostat  (502).  An  achromatic  double 
convex  lens  is  placed  at  a  distance  from  the  slit  of  double  its  own  focal 
length,  which  should  be  about  a  metre,  and  a  screen  is  placed  at  the 
same  distance  from  the  lens.  An  exact  image  of  the  slit  is  thus  formed 
on  the  screen  (528).  If  now  there  is  placed  near  the  lens,  between  it  and 
the  screen,  a  prism  with  an  angle  of  about  60°  and  with  its  refracting  edge 
parallel  to  the  slit,  a  very  beautiful  sharp  and  pure  spectrum  is  formed  on 
the  screen. 

The  prism  should  be  free  from  stride,  and  should  be  placed  so  that  it 
produces  the  minimum  deviation. 

532.  The  colours  of  the  spectrum  are.  simple,  and  unequally  re- 
frangrihle. — If  one  of  the  colours  of  the  spectrum  be  isolated  by  inter- 
cepting the  others  by  means  of  a  screen,  E,  as  shown  in  fig.  414,  and  if 


Fig.  414. 

the  light  thus  intercepted  be  allowed  to  pass  through  a  second  prism,  B, 
a  refraction  will  be  observed,  but  the  light  remains  unchanged  ;.  that  is, 
the  image  received  on  the  screen  H  is  violet  if  the  violet  pencil  has  been 
allowed  to  pass,  blue  if  the  blue  pencil,  and  so  on.  Hence  the  colours  of 
the  spectrum  are  simple  ;  that  is,  they  cannot  further  be  decomposed  by 
the  prism. 

Moreover,  the  colours  of  the  spectrum  are  unequally  refrangible  ;  that 
is,  they  possess  different  refractive  indices.  The  elongated  shape  of  the 
spectrum  would  be  sufficient  to  prove  the  unequal  refrangibihty  of  the 
simple  colours,  for  it  is  clear  that  the  violet,  which  is  most  deflected 
towards  the  base  of  the  prism,  is  also  most  refrangible,  and  that  red 
which  is  least  deflected  is  least  refrangible.  But  the  unequal  refrangi- 
bihty of  simple  colours  may  be  shewn  by  numerous  experiments,  of  which 
the  two  following  may  be  adduced  : — 

i.  Two  narrow  strips  of  coloured  paper,  one  red  and  the  other  violet 
are  fastened  close  to  each  other  on  a  sheet  of  black  paper.     On  looking 


462 


On  Light. 


[532- 


at  them  through  a  prism,  they  are  seen  to  be  unequally  displaced,  the  red 
band  to  a  less  extent  than  the  violet  ;  hence  the  red  rays  are  less  refran- 
gible than  the  violet. 

ii.  The  same  conclusion  may  be  drawn   from  Newton's  experiment 
with  crossed  prisms.     On  a  prism,  A  (fig.  415),  in  a  horizontal  position, 


Fig.  415- 


a  pencil  of  white  light,  S,  is  received,  which,  if  it  had  merely  traversed 
the  prism  A,  would  form  the  spectrum  rr,  on  a  distant  screen.  But  if  a 
second  prism,'  B,  be  placed  in  a  vertical  position  behind  the  first,  in  such 
a  manner  that,  the  refracted  pencil  passes  through  it,  the  spectrum  vr 
becomes  deflected  towards  the  base  of  the  vertical  prism  :  but,  instead  of 
being  deflected  in  a  direction  parallel  to  itself,  as  would  be  the  case  if  the 
colours  of  the  spectrum  were  equally  refracted,  it  is  obliquely  refracted  in 
the  direction  rV,  proving  that  from  red  to  violet  the  colours  are  more 
and  more  refrangible. 

•  These  difterent  experiments  show  that  the  refractive  index  differs  in 
different  colours  ;  even  rays  which  are  to  perception  undistinguishable 
have  not  the  same  refractive  index.     In  the  red  band,  for  instance,  the 


rays  at  the  extremity  of  the  spectrum  are  less  refracted  than  those  which 
are  nearer  the  orange  zone.  In  calculating  indices  of  refraction  (506),  it 
is  usual  to  take  as  the  index  of  any  particular  substance  the  refrangibility 
of  the  yellow  ray  in  a  prism  formed  of  that  substance. 

533.  Re  composition  of  white  light. — Not  merely  can  white  light  be 


-533] 


Recoinposition  of  White  Light. 


463 


resolved  into  lights  of  various  colours,  but  by  combining  the  different 
pencils  separated  by  the  prism,  white  light  can  be  reproduced.  This  may 
be  effected  in  various  ways  : — 

i.  If  the  spectrum  produced  by  one  prism  be  allowed  to  fall  upon  a 
second  prism  of  the  same  material,  and  the  same  refracting  angle  as  the 
first,  but  inverted,  as  shown  in  fig.  417,  the  latter  reunites  the  different 
colours  of  the  spectrum,  and  it  is  seen  that 
the  emergent  pencil  E,  which  is  parallel 
to  the  pencil  S,  is  colourless. 

ii.  If  the  spectrum  falls  upon  a  double 
convex  lens  (fig.  416),  a  white  image  of 
the  sun  will  be  formed  on  a  white  screen 
placed  in  the  focus  of  the  lens  ;  a  glass 
globe  filled  with  water  produces  the  same 
effect  as  the  lens. 

iii.  When  the  spectrum  falls  upon  a  concave  mirror,  a  white  image 
is  formed  on  a  screen  of  ground  glass  placed  in  its  focus  (fig.  418). 


Fig.  419 


iv.  Light  may  be  recomposed  by  means  of  a  pretty  experiment,  which 
consists  in  receiving  the  seven  colours  of  the  spectrum  on  seven  small 
glass  mirrors  with  plane  faces,  and  which  can  be  so  inclined  in  all 
positions  that  the  reflected  light  may  be  transmitted  in  any  given  direc- 
tion (fig.  419).  When  these  mirrors  are  suitably  arranged,  the  seven 
reflected  pencils  may  be  caused  to  fall  on  the  ceiling  in  such  a  manner 
as  to  form  seven  distinct  images — red,  orange,  yellow,  etc.  When  the 
mirrors  are  moved  so  that  the  separate  images  become  superposed,  a 
single  image  is  obtained,  which  is  white. 

v.  By  means  of  Newtojis  disc,  fig.  420,  it  may  be  shown  that  the  seven 
colours  of  the  spectrum  form  white.  This  is  a  cardboard  disc  of  about  a 
foot  in  diameter  ;  the  centre  and  the  edges  are  covered  with  Mack  paper, 
while  in  the  space  between  there  are  pasted  strips  of  papers  of  the  colours 
of  the  spectrum.    They  proceed  from  the  centre  to  the  circumference,  and 


464 


On  Light. 


[533 


their  relative  dimensions  and  tints  are  such  as  to  represent  five  spectra 
(fig.  421).  When  this  disc  is  rapidly  rotated,  the  efi"ect  is  the  same  as  if 
the  retina  received  simultaneously  the  impression  of  the  seven  colours. 


Fig.  420. 

If  by  a  mechanical  arrangement,  a  prism,  on  which  the  sun's  light  falls, 
is  made  to  oscillate  rapidly  so  that  the  spectrum  also  oscillates  the  middle 
of  the  spectrum  appears  white. 

These  latter  phenomena  depend  on  the  physiological  fact,  that  sensa- 
tion always  lasts  a  little  longer  than  the  impression  from  which  it  results. 
If  a  new  impression  is  allowed  to  act,  before  the  sensation  arising  from 
the  former  one  has  ceased,  a  sensation  is  obtained  consisting  of  tAvo  im- 
pressions. And  by  choosing  the  time  short  enough,  three,  four,  or  more 
impressions  may  be  mixed  with  each  other.  With  a  rapid  rotation  the 
disc  is  nearly  white.  It  is  not  quite  so,  for  the  colours  cannot  be  exactly 
arranged  in  the  same  proportions  as  those  in  which  they  exist  in  the 
spectrum,  and  pigment  colours  are  not  pure.  A  similar  explanation 
applies  to  the  experiment  of  the  oscillating  prism. 

534.  ITewton's  theory  of  tlie  composition  of  li^lit. — Newton  was  the 
first  to  decompose  white  light  by  the  prism,  and  to  recompose  it.  From 
the  various  experiments  which  we  have  described,  he  concluded  that 
white  light  was  not  homogeneous,  but  formed  of  seven  lights  unequally 
refrangible,  which  he  called  simple  or  primitive  lights.  Owing  to  their 
difference  in  refrangibility  they  become  separated  in  traversing  the 
prism. 

The  designation  of  the  various  colours  of  the  spectrum  is  to  a  very 
great  extent  arbitrary  ;  for  in  strict  accuracy,  the  spectrum  is  made  up  of 


-536]  Colour  of  Bodies.  465 

an  infinite  number  of  simple  colours,  which  pass  into  one  another  by 
imperceptible  gradations  of  colour  and  refrangibility.  _ 

535.  Colour  of  bodies. — The  natural  colour  of  bodies  results  from  the 
fact  that  of  the  coloured  rays  contained  in  white  light,  one  portion  is 
absorbed  at  the  surface  of  the  body.  If  the  unabsorbed  portion  traverses 
the  body,  it  is  coloured  and  transparent ;  if,  on  the  contrary,  it  is  reflected 
it  is  coloured  and  opaque.  In  both  cases  the  colour  results  from  the 
constituents  which  have  not  been  absorbed.  Those  which  reflect  or 
transmit  all  colours  in  the  propoition  in  which  they  exist  in  the  spectrum 
are  white  ;  those  which  reflect  or  transmit  none  are  black.  JBetween 
these  two  limits  there  are  infinite  tints  according  to  the  greater  or  less 
extent  to  which  bodies  reflect  or  transmit  some  colours  and  absorb 
others.  Thus  a  body  appears  yellow,  because  it  absorbs  all  colours  with 
the  exception  of  yellow.  In  like  manner,  a  solution  of  ammoniacal  oxide  of 
copper  absorbs  preferably  the  red  and  yellow  rays,  transmits  the  blue 
rays  almost  completely,  the  green  and  violet  less  so,  hence  the  light  seen 
through  it  is  blue. 

Hence  bodies  have  no  colour  of  their  own ;  with  the  nature  of  the 
incident  light  the  colour  of  the  body  changes.  Thus,  if  in  a  dark  room 
a  white  body  be  successively  illuminated  by  each  of  the  colours  of  the 
spectrum,  it  has  no  special  colour  but  appears  red,  orange,  green,  etc., 
according  to  the  position  in  which  it  is  placed.  If  homogeneous  light 
falls  upon  a  body,  it  appears  brighter  in  the  colour  of  this  light,  if  it  does 
not  absorb  this  colour;  but  black  if  it  does  absorb  it.  In  the  light  of  a 
lamp  fed  by  spirit  in  which  some  common  salt  is  dissolved,  everything 
white  and  yellow  seems  bright,  while  most  of  the  other  colours  are  black. 
This  is  well  seen  in  the  case  of  a  stick  of  red  sealing-wax  viewed  in  such 
a  light.  In  the  light  of  lamps  and  of  candles,  which  from  the  want  of  blue 
rays  appear  yellow,  yellow  and  white  appear  the  same,  and  blue  seems 
like  green.  In  bright  twilight  or  in  moonshine,  the  light  of  gas  has  a 
reddish  tint. 

536.  Mixed  colours.  Complementary  colours. — By  mixed  colours  we 
understand  the  impression  of  colour  which  results  from  the  coincident 
action  of  two  or  more  colours  on  the  same  position  of  the  retina.  This 
new  impression  is  single  ;  it  cannot  be  resolved  into  its  components  ;  in 
this  respect  it  differs  from  a  complex  sound  in  which  the  ear  by  practice 
can  distinguish  the  constituents.  Mixed  colours  may  be  produced  by 
causing  different  parts  of  the  spectrum  to  cover  each  other  ;  they  may  also 
be  produced  by  looking  in  an  oblique  direction  through  a  vertical  glass 
plate  at  a  coloured  surface  \  while  at  the  same  time,  the  observer's  side  of 
the  plate  reflects  towards  his  eye  light  of  a  different  colour.  The  method 
of  the  coloured  disc  affords  another  means  of  producing  mixed  colours. 

If  in  any  of  the  methods  by  which  the  impression  of  mixed  spectral 
colours  is  produced,  One  or  more  colours  be  suppressed,  the  residue 
corresponds  to  one  of  the  tints  of  the  spectrum  ;  and  the  mixture  of  the 
colours  taken  away  produces  the  impression  of  another  spectral  colour. 
Thus,  if  in  fig.  416  the  red  rays  are  cut  off  from  the  lens  L,  the  light  on 
the  focus  is  no  longer  white  but  greenish  blue.     In  like  manner  if  the 

X3 


466  On  Light.  [536- 

violet,  indigo,  and  blue  of  tlie  colour  disc  be  suppressed,  the  rest  seems 
yellow,  while  the  mixture  of  that  which  has  been  taken  out  is  a  bluish 
violet.  Hence  white  can  always  be  compounded  of  two  tints  ;  and  two  tints 
which  together  give  white  are  called  covipleinentary  colours.  Thus  of 
spectral  tints  red  and  greenish  yellow  are  complementary,  so  are  orange 
and  Prussian  blue ;  yellow  and  indigo  blue ;  greenish  yellow  and 
violet. 

A  distinction  must  be  made  between  spectral  colours  and  pigment 
colours.  Thus  a  mixture  of  pigment  yellow  and  pigment  blue  produces 
green  and  not  white,  as  is  the  case  when  the  blue  and  yellow  of  the 
spectrum  are  mixed.  The  reason  of  this  is  that  in  the  mixture  of  pigments 
we  have  a  case  of  substraction  of  colours  and  not  of  addition.  For  in 
the  mixture  the  pigment  blue  absorbs  almost  entirely  the  yellow  and  red 
light  ;  and  the  pigment  yellow  absorbs  the  blue  and  violet  light  so  that 
only  the  green  remains. 

If  the  complementary  spectral  colours  are  mixed  in  other  proportions 
than  is  requisite  for  the  production  of  white,  intermediate  colours  are 
obtained  which  lie  in  the  spectrum  between  the  tints  of  the  complementary 
colours.  Thus  a  mixture  of  red  and  greenish  blue,  in  which  the  former 
predominates,  produces  a  tint  which  is  nearer  orange  ;  while  when  the 
latter  is  in  excess,  the  tint  comes  nearer  yellow  and  ultimately  green. 
These  colours,  however,  are  not  so  pure  as  the  corresponding  spectral 
tints.  They  are  less  saturated,  as  it  is  called  ;  that  is,  mixed  with 
white. 

In  the  above  series  are  two  spectral  colours  very  remote  in  the  spec- 
trum which  have  nearly  the  same  complementary  colours  :  these  are  red, 
the  complementary  colour  to  which  is  greenish  blue,  and  violet,  whose 
complementary  colour  is  greenish  yellow.  Now  when  two  pairs  of  com- 
plementary colours  are  mixed  together,  they  must  produce  white,  just  as  if 
only  two  complementary  colours  were  mixed.  But  a  mixture  of  greenish 
blue  and  of  greenish  yellow  is  green.  Hence  it  follows  that  from  a 
mixture  of  red,  green,  and  violet  white  must  be  formed.  This  may  easily 
be  ascertained  to  be  the  case,  by  means  of  a  colour  disc  on  which  are 
these  three  colours  in  suitable  proportions. 

From  the  above  facts  it  follows  that  from  a  mixture  of  red,  green,  and 
violet  all  possible  colours  may  be  constructed,  and  hence  these  three 
spectral  colours  are  called  t\\e^  fundainetital  colours.  It  must  be  remarked 
that  the  tints  resulting  from  the  mixture  of  these  three  have  never  the 
saturation  of  the  individual  spectral  colours. 

We  have  to  discriminate  three  points  in  regard  to  colour.  In  the  first 
place,  the  tint  or  colour  proper  by  which  we  mean  that  special  property 
which  is  due  to  a  definite  refrangibility  producing  it  ;  secondly,  the  satu- 
ration  which  depends  on  the  greater  or  less  admixture  of  white  light  with 
the  colours  of  the  spectrum,  these  being  colours  which  are  fully  saturated  ; 
and  thirdly,  there  is  the  intensity  which  depends  on  the  amplitude  of 
vibration. 

537.  Bomog:eneous  ligrht. — The  light  emitted  from  luminous  bodies 
is  seldom  or  never  quite  pure,  on  being  examined  by  the  prism  it  will  be 


-  538]  Properties  of  the  Spectrum.  •     467 

found  to  contain  more  than  one  colour.  In  optical  researches  it  is  fre- 
quently of  great  importance  to  procure  homogeneous  or  monocIu'omatic_ 
light.  Common  salt  in  the  flame  of  a  Bunsen's  lamp  gives  a  yellow  of 
great  purity.  For  red  light,  ordinary  light  is  transmitted  through  glass 
coloured  with  suboxide  of  copper,  which  absorbs  nearly  all  the  rays  ex- 
cepting the  red,  A  very  pure  blue  is  obtained  by  transmitting  ordinary 
light  through  a  glass  trough  containing  an  ammoniacal  solution  of 
sulphate  of  copper. 

538.  Properties  of  the  spectrum. — Besides  its  luminous  properties, 
the  spectrum  is  found  to  produce  calorific  and  chemical  effects. 

Lu?ni7ious properties.  It  appears  from  the  experiments  of  Fraunhofer 
and  of  Herschel,  that  the  light  in  the  yellow  part  of  the  spectrum  has 
the  greatest  intensity,  and  that  in  the  violet  the  least. 

Caloripc  effects.  It  was  long  known  that  the  various  parts  of  the 
spectrum  differed  in  their  calorific  effects.  Leshe  found  that  a  thermo- 
meter placed  in  different  parts  of  the  spectrum  indicated  a  higher  tem- 
perature as  it  moved  from  violet  towards  red.  Herschel  fixed  the 
maximum  intensity  of  the  heating  effects  just  outside  the  red  ;  Berard 
in  the  red  itself.  Seebeck  showed  that  those  different  effects  depend  on 
the  nature  of  a  prism  :  with  a  prism  of  water  the  greatest  caloritic  effect 
is  produced  in  the  yellow  ;  with  one  of  alcohol  it  is  in  the  orange-yellow  ; 
and  with  a  prism  of  crown  glass  it  is  in  the  middle  of  the  red. 

Melloni,  by  using  prisms  and  lenses  of  rock  salt,  and  by  availing  him- 
self of  the  extreme  delicacy  of  the  thermo-electric  apparatus,  first  made 
a  complete  investigation  of  the  calorific  properties  of  the  thermal  spec- 
trum. This  result  led,  as  we  have  seen,  to  the  confirmation  and  extension 
of  Seebeck'?  observations. 

Chemical  properties.  In  numerous  phenomena,  light  acts  as  a  chemical 
agent.  For  instance,  chloride  of  silver  blackens  under  the  influence  of 
light,  transparent  phosphorus  becomes  opaque,  vegetable  colouring 
matters  fade,  hydrogen  and  chlorine  gases,  when  mixed,  combine  slowly 
in  diffused  Hght,  and  with  explosive  violence  when  exposed  to  direct 
sunlight.  The  chemical  action  differs  in  different  parts  of  the  spectrum. 
Scheele  found  that  when  chloride  of  silver  was  placed  in  the  violet,  the 
action  was  more  energetic  than  in  any  other  part.  Wollaston  observed 
that  the  action  extended  beyond  the  violet,  and  concluded  that,  besides 
the  visible  rajs  there  are  some  invisible  and  more  highly  refrangible 
rays.     These  are  the  chemical  or  actinic  rays. 

Th«  researches  of  Bunsen  and  Roscoe  show  that  whenever  chemical 
action  is  induced  by  light,  an  absorption  of  light  takes  place,  preferably 
of  the  more  refrangible  parts  of  the  spectrum.  Thus,  when  chlorine 
and  hydrogen  unite,  under  the  action  of  light,  to  form  hydrochloric  acid, 
light  is  absorbed,  and  the  quantity  of  chemically  active  rays  consumed  is 
directly  proportional  to  the  amount  of  chemical  action. 

There  is  a  curious  difference  in  the  action  of  the  different  rays.  Moser 
placed  an  engraving  on  an  iodised  silver  plate,  and  exposed  it  to  the 
light  until  an  action  had  commenced,  and  then  placed  it  under  a  violet 
glass  in  the  sunlight.     After  a  few  minutes  a  picture  was  seen  with  great 


468      ♦  On  Light.  [538- 

distinctness,  while  when  placed  under  a  red  or  yellow  glass,  it  required 
a  very  long  time,  and  was  very  indistinct.  When,  however,  the  iodized 
silver  plate  was  tirst  exposed  in  a  camera  obscura  to  blue  light  for  two 
minutes,  and  was  then  brought  under  a  red  or  yellow  glass,  an  image 
quickly  appeared,  but  not  when  placed  under  a  green  glass.  It  appears 
as  if  there  are  vibrations  of  a  certain  velocity  which  could  commence  an 
action,  and  that  there  are  others  which  are  devoid  of  the  property  of 
commencing,  but  can  continue  and  complete  an  action  when  once  set  up. 
Becquerel,  who  discovered  these  properties  in  luminous  rays,  called  the 
former  exciting  rays,  and  the  latter  contiiiuijig  or  phosphorogenic  rays. 
The  phosphorogenic  rays,  for  instance,  have  the  property  of  rendering 
certain  objects  self-luminous  in  the  dark  after  they  have  been  exposed 
for  some  time  to  the  light.  Becquerel  found  that  the  phosphorogenic 
spectrum  extended  from  indigo  to  beyond  the  violet. 

539.  Bark  lines  of  the  spectrum. — The  colours  of  the  solar  spectrum 
are  not  continuous.  For  several  grades  of  refrangibility  rays  are  wanting, 
and  in  consequence,  throughout  the  whole  extent  of  the  spectrum,  there 
are  a  great  number  of  very  narrow  dark  lines.  To  observe  them,  a  pencil 
of  solar  rays  is  admitted  into  a  darkened  room,  through  a  narrow  slit. 
At  a  distance  of  three  or  four  yards,  we  look  at  this  slit  through  a  prism 
of  flint  glass,  which  must  be  very  free  from  flaws,  taking  care  to  hold  its 
edge  parallel  to  the  slit.  We  then  observe  a  great  number  of  very 
delicate  dark  lines  parallel  to  the  edge  of  the  prism,  and  at  very  unequal 
intervals. 

The  existence  of  the  dark  lines  was  first  observ^ed  by  WoUaston  in 
1802  ;  but  Fraunhofer,  a  celebrated  optician  of  Miinich,  first  studied  and 
gave  a  detailed  description  of  them.  Fraunhofer  mapped  the  lines,  and 
indicated  the  most  marked  of  them  by  the  letters  A,  a,  B,  C,  D,  E,  b.,  F, 
G,  H  ;  they  are  therefore  generally  known  as  Fraunhofer's  lines. 

The  dark  line  A  (see  fig.  2  of  Plate  I.),  is  at  the  extremity  and 
B  in  the  middle  of  the  red  ray  ;  C  at  the  boundary  of  the  red  and 
orange  ray  ;  D  is  in  the  yellow  ray  ;  E,  in  the  green  ;  F,  in  the  blue  ; 
G,  in  the  indigo  ;  H,  in  the  violet.  There  are  certain  other  noticeable 
dark  lines,  such  as  <^  in  the  red,  and  b  in  the  green.  In  the  case  of  solar 
light  the  positions  of  the  dark  lines  are  fixed  and  definite  ;  on  this  ac- 
count they  are  used  for  obtaining  an  exact  determination  of  the  refractive 
index  (506)  of  each  colour  ;  for  example,  the  refractive  index  of  the 
blue  ray  is,  strictly  speaking,  that  of  the  dark  line  F.  In  the  spectra 
of  artificial  fights,  and  of  the  stars,  the  relative  positions  of  the  dark  lines 
are  changed.  In  the  electric  light  the  dark  lines  are  replaced  by  brilliant 
lines.  In  coloured  flames,  that  is  to  say,  flames  in  which  certain  chemi- 
cal substances  undergo  evaporation,  the  dark  lines  are  replaced  by  very 
brilliant  lines  of  light,  which  differ  for  different  substances.  Lastly,  of 
the  dark  lines,  some  are  constant  in  position  and  distinctness,  such  are 
Fraunhofer's  lines ;  but  some  of  the  lines  only  appear  as  the  sun  nears 
the  horizon,  and  others  are  strengthened.  They  are  also  influenced  by 
the  state  of  the  atmosphere.     The  fixed  lines  are  due  to  the  sun  ;  the 


-541J 


FraunJwfer  s  Lines, 


469 


variable  lines  have  been  proved  by  Jannsen  and  Secchi  to  be  due  to  the 
aqueous  vapour  in  the  air,  and  are  called  atmospheric  or  teliiiric  lines. 

F'raunhofer  counted  in  the  spectrum  more  than  600  dark  lines,  more  or 
less  distinct,  distributed  irregularly  from  the  extreme  red  to  the  extreme 
violet  ray,     Brewster  counted  2,000.     By  causing  the  refracted  rays  to 


Fig.  422, 

pass  successively  through  several  analysing  prisms,  not  merely  has  the 
existence  of  3,000  dark  lines  been  ascertained,  but  several  which  had  been 
supposed  single  have  been  shown  to  be  double. 

540.  iLpplications  of  Fraunhofer's  lines. — Subsequently  to  Fraun- 
hofer,  several  physicists  studied  the  dark  lines  of  the  spectrum.  In  1822 
Sir  J.  Herschel  remarked  that  by  volatilising  substances  in  a  flame  a  very 
delicate  means  is  aflbrded  of  detecting  certain  ingredients  by  the  colours 
they  impart  to  certain  of  the  dark  lines  of  the  spectrum  ;  and  Fox  Talbot 
in  1834  suggests  optical  analysis  as  probably  the  most  delicate  means  of 
detecting  minute  portions  of  a  substance.  To  Kirchoff  and  Bunsen, 
however  is  really  due  the  merit  of  basing  on  the  observation  of  the  lines 
of  the  spectrum  a  method  of  analysis.  They  ascertained  that  the  salts 
of  the  same  metal,  when  introduced  into  a  flame,  always  produce  lines 
identical  in  colour  and  position,  but  different  in  colour,  position,  or  num- 
ber for  different  metals,  and  finally  that  an  exceedingly  small  quantity  of 
a  metal  sufflces  to  disclose  its  existence.  Hence  has  arisen  a  new  method 
of  analysis,  known  by  the  name  of  spectral  a?ialysis. 

541.  Spectroscope. — The  name  of  spectroscope  has  been  given  to 
the  apparatus  employed  by  Kirchhoff  and  Bunsen  for  the  study  of  the 


4/0 


On  Light. 


[541- 


spectrum.  One  of  the  forms  of  this  apparatus  is  represented  in  fig.  422 
It  is  composed  of  three  telescopes  mounted  on  a  common  foot,  and  whose 
axes  converge  towards  a  prism,  P,  of  flint-glass.  The  telescope  A  is  the 
only  one  which  can  turn  round  the  prism.  It  is  fixed  in  any  required 
position  by  a  clamping  screw  n.  The  screw-head,  ;;/,  is  used  to  shift  the 
position  of  the  eye-piece,  so  that  a  clear  image  of  the  spectrum  may  be 
obtained,  or  in  other  words,  to  focus  the  eyepiece.  The  screw-head  ?i  is 
used  to  change  the  inclination  of  the  axis. 

To  explain  the  use  of  the  telescopes  B  and  C,  we  must  refer  to  fig. 
423,  which  shows  the  passage  of  the  light  through  the  apparatus.  The 
rays  emitted  by  the  flame  G  falls  on  the  lens  a,  and  are  caused  to  converge 
to  a  point,  b,  which  is  the  principal  focus  of  a  second  lens  c.  Conse- 
quently the  pencil,  on  leaving  the  telescope  B,  is  formed  of  parallel  rays. 
This  pencil  enters  the  prism  P.  On  leaving  the  prism,  the  light  is 
decomposed,  and  in  this  state  falls  on  the  lens  x.  By  this  lens  x,  a  real 
and  reversed  image  of , the  spectrum  is  formed  at  t.  This  image  is  seen 
by  the  observer  through  a  magnifying  glass  which  forms  at  ss'  a  virtual 
image  of  the  spectrum  magnified  about  eight  times. 

The  telescope  C  serves  to  measure  the  relative  distances  of  the  lines 
of  the  spectrum.       For  this  purpose  there  is  placed  at  7n  a  micrometer 


Fig,  423- 


divided  into  23  equal  parts.  The  micrometer  is  formed  thus  : — A  scale 
of  250  millimetres  is  divided  with  great  exactness  into  25  equal 
parts.  A  photographic  negative  on  glass  of  this  scale  is  taken,  reduced 
to  15  millimetres.  The  negative  is  taken  because  then  the  scale  is 
light  on  a  dark  ground.  The  sqale  is  then  placed  at  w.  in  the  principal 
focus  of  the  lens  e  :  consequently,  when  the  scale  is  lighted  by  the  candle 
F,  the  rays  emitted  from  it  leave  the  lens  e  in  parallel  pencils  ;  a  portion 
of  these,  being  reflected  from  a  face  of  the  prism,  passes  through  the  lens 
X,  and  forms  a  perfectly  distinct  image  of  the  micrometer  at  z,  thereby 
furnishing  the  means  of  measuring  exactly  the  relativ^e  distances  of  the 
different  spectral  lines. 


I 


-541] 


Spectroscope. 


471 


Fig.  424. 


The  micrometric  telescope  C  (fig.  422)  is  furnished  with  several  adjust- 
ing screws,  /,  o^  r\  of  these  /  adjusts  the  focus;  o  displaces  the  micro- 
meter in  the  direction  of  the  spectrum  laterally ;  r  raises  or  lowers 
the  micrometer,  which  it  does  by  giving  ditferent  inclinations  to  the 
telescope. 

The  opening  whereby  the  light  of  the  flame  G  enters  the  telescope  B 
consists  of  a  narrow  vertical  slit,  which  can  be  opened  more  or  less  by 
causing  the  moveable  piece  a  to  ad- 
vance or  recede  by  means  of  the 
screw  V  (fig.  424).  When  for  pur- 
poses of  comparison  two  spectra  are 
to  be  examined  simultaneously,  there 
is  placed  over  the  upper  part  of  the 
sht  a  small  prism,  whose  refracting 
angle  is  60°.  Rays  from  one  of  the 
flames,  H,  fall  at  right  angles  on  one 
face  of  the  prism,  they  then  experi- 
ence total  reflection  on  a  second  face, 
and  leave  the  prism  by  the  third  face, 
and  in  a  direction  at  right  angles  to 
that  face.  By  this  means  they  pass  into 
the  telescope  in  a  direction  parallel  to  its  axis,  .without  in  any  degree  .nixing 
with  the  rays  which  proceed  from  the  second  flame,  G.  Consequently, 
the  two  pencils  of  rays  traverse  the  prism  P  (fig.  423),  and  form  two  hori- 
zontal spectra  which  are  viewed  simultaneously  through  the  telescope  A. 
In  the  flames  G  and  H  are  platinum  wires,  <;',  c  .  These  wires  have  been 
dipped  beforehand  into  solution  of  the  salts  of  the  metals  on  which 
experiment  is  to  be  made;  and  by  the  vaporisation  of  these  salts  the 
metals  modify  the  transmitted  light,  and  gave  rise  to  definite  lines. 

Each  of  the  flames  H  and  G  is  a  jet  of  ordinary  gas.  The  apparatus 
through  which  the  gas  is  supplied  is  known  as  a  Bimseiis  burner.  The 
gas  comes  through  the  hollow  stem  k  (fig.  422).  At  the  lower  part  of 
this  there  is  a  lateral  orifice  to  admit  air  ";o  support  the  combustion  of 
the  gas.  This  orifice  can  be  more  or  less  closed  by  a  small  diaphragm, 
which  acts  as  a  regulator.  If  we  allow  a  moderate  amount  of  air  to  enter, 
the  gas  burns  with  a  luminous  flame,  and  the  fines  are  obscured.  But  if 
a  strong  and  steady  current  of  air  enters,  the  carbon  is  rapidly  oxidised, 
the  flarxie  loses  its  brightness,  and  burns  with  a  pale  blue  light,  but  with 
an  intense  heat.  In  this  state  it  no  longer  yields  a  spectrum.  If,  how- 
ever, a  metallic  salt  is  introduced  either  in  a  solid  state  or  in  a  jtate  of 
solution,  the  spectrum  of  the  metal  makes  its  appearance,  and  in  a  fit 
state  for  observation. 

There  are  three  chief  types  of  spectra  :  the  co7itimioiis  spectrum,  or 
those  furnished  by  ignited  sohds  and  liquids  (fig.  i,  Plate  I.) ;  the  band  or 
line  spectrum,  consisting  of  a  number  of  bright  lines,  and  produced  by 
ignited  gases  or  vapours ;  and  absorption  spectra,  or  those  furnished  by 
the  sun  or  fixed  stars.  For  an  explanation  of  these,  see  art.  543.  Bodies 
at  a  red  heat  give  only  a  small  spectrum,  extending  at  most  to  the  orange ; 


472  On  Light.  [541  • 

as  the  temperature  gradually  rises,  yelbw,  green,  blue,  and  violet  success- 
ively appear,  while  the  intensity  of  the  lower  colours  increases. 

Instead  of  the  prism  very  pure  spectra  may  also  be  obtained  by 
means  of  a  grating  (6io). 

542.  Experiments  witb  tlie  spectroscope. — The  coloured  plate  at 
the  beginning  shows  certain  spectra  observed  by  means  of  the  spectro- 
scope.    No.  I  represents  the  continuous  spectrum. 

No.  2  shows  the  spectrum  of  sodium.  The  spectrum  contains  neither 
red,  orange,  green,  blue,  nor  violet.  It  is  marked  by  a  very  brilliant 
yellow  ray  in  exactly  the  same  position  as  Fraunhofer's  dark  line  D.  Of 
all  metals  sodium  is  that  which  possesses  the  greatest  spectral  sensibility. 
In  fact,  it  has  been  ascertained  that  one  two  hundred  millionth  of  a 
grain  of  sodium  is  enough  to  cause  the  appearance  of  the  yellow  line. 
Consequently,  it  is  very  difficult  to  avoid  the  appearance  of  this  line.  A 
very  little  dust  scattered  in  the  apartment  is  enough  to  produce  it, — a 
circumstance  which  shows  how  abundantly  sodium  is  distributed  though- 
out  nature. 

No.  3  is  the  spectrum  of  lithium.  It  is  characterised  by  a  well- 
marked  line  in  the  red  called  Li^/,  and  by  the  feebler  orange  line  Li(-\ 

Nos.  4  and  5  show  the  spectra  of  cccsium  and  rutiidiiun,  metals  dis- 
covered by  Bunsen  and  Kirchhoff  by  means  of  spectral  analysis.  The 
former  is  distinguished  by  tw.o  blue  lines  Cs7  and  Cs3,  the  latter  by  two 
very  brilliant  dark  red  lines  Rbv  and  Rbc^,  and  by  two  less  intense  violet 
lines  RbrandRb^.  A  third  metal,  thaltiunr,  has  been  discovered  by 
the  same  method  by  Mr.  Crookes  in  England,  and  independently  by 
M.  Lamy  in  France.  Thallium  is  characterised  by  a  single  green  line. 
Still  more  recently  Richter  and  Reich  have  discovered  a  new  metal 
associated  with  zinc,  and  which  they  call  indium  from  a  couple  of  charac- 
teristic lines  which  it  forms  in  the  indigo. 

The  extreme  delicacy  of  the  spectrum  reactions,  and  the  ease  with 
which  they  are  produced,  constitute  them  a  most  valuable  help  in  the 
quantitative  analysis  of  the  alkalies  and  alkaline  earths.  It  is  sufficient  to 
place  a  small  portion  of  the  substance  under  examination  on  platinum 
wire  as  represented  in  tig.  424,  and  compare  the  spectrum  thus  obtained 
either  directly  with  that  of  another  substance,  or  with  the  charts  in  which 
the  positions  of  the  lines  produced  by  the  various  metals  are  laid  down. 

With  other  metals  the  production  of  their  spectra  is  more  difficult, 
especially  in  the  case  of  some  of  their  compounds.  The  heat  of  a  Bunsen's 
burner  is  insurincient  to  vaporise  the  metals,  and  a  more  intense  tempera- 
ture must  be  used.  'This  is  effected  by  taking  electric  sparks  between 
wires  consisting  of  the  metal  whose  spectrum  is  required,  and  the  electric 
sparks  are  most  conveniently  obtained  by  means  of  Ruhmkorff's  coil. 
Thus  all  the  metals  may  be  brought  within  the  sphere  of  spectrum  obser- 
vations. 

The  power  of  the  apparatus  has  great  influence  on  the  nature  of  the 
spectrum  ;  while  an  apparatus  with  one  prism  only  gives  in  a  sodium  flame 
the  well  known  yellow  line,  an  apparatus  with  more  prisms  resolves  it  into 
two  or  three  lines. 


-542]  Experiments  with  the  Spectroscope.  473 

It  has  been  observed  that  the  character  of  the  spectrum  changes  with 
the  temperature;  thus  chloride  of  lithium  in  the  flame  of  a  Bunsen's 
burner  gives  a  single  intense  peach-coloured  line  ;  in  a  hotter  flame,  as 
that  of  hydrogen,  it  gives  an  additional  orange  line  ;  while  in  the  oxy- 
hydrogen  jet  or  the  voltaic  arc  a  broad  brilliant  blue  band  comes  out  in 
addition.  The  sodium  spectrum  produced  by  a  Bunsen's  burner  con- 
sists of  a  single  yellow  line  ;  if,  by  the  addition  of  oxygen,  the  heat  be  gra- 
dually increased,  more  bright  lines  appear  ;  and  with  the  aid  of  the  oxy- 
hydrogen  flame  the  spectrum  is  continuous.  Sometimes  also,  in  addition 
to  the  appearance  of  new  lines,  an  increase  in  temperature  resolves  those 
bands  which  exist  into  a  number  of  fine  lines,  which  in  some  cases  are 
more  and  in  some  less  refrangible  than  the  bands  from  which  they  are 
formed.  It  may  be  supposed  that  the  glowing  vapour  found  at  the  low- 
temperature  consists  of  the  oxide  of  some  difficultly  reducible  metal, 
whereas  at  the  enormously  high  temperature  of  the  spark  these  com- 
pounds are  decomposed,  and  the  true  bright  lines  of  the  metal  are 
formed. 

The  delicacy  of  the  reaction  increases  very  considerably  with  the  tem- 
perature. With  the  exception  of  the  alkalies,  it  is  from  40  to  300  times 
greater  at  the  temperature  of  the  electric  spark  than  at  that  of  Bunsen's 
burner. 

The  spectra  of  the  permanent  gases  are  best  obtained  by  taking  the 
electric  spark  of  a  Ruhmkorff's  coil,  or  Holtz's  apparatus,  through  glass 
tubes  of  a  special  construction,  provided  with  electrodes  of  platinum  and 
filled  with  the  gas  in  question  in  a  state  of  great  attenuation,  known  as 
Geissler's  tubes  ;  if  the  spark  be  passed  through  hydrogen,  the  light  emitted 
is  bright  red,  and  its  spectrum  consists  of  one  bright  red,  one  green,  and 
one  blue  line  No.  7,  the  first  two  of  which  appear  to  coincide  with  Fraun- 
hofer's  lines  C  and  F,  and  the  third  with  a  line  between  F  and  G, 
No.  6  represents  the  spectrum  of  oxygen.  No.  8  is  the  spectrum  of 
nitrogen.  The  light  of  this  gas  in  a  Geissler's  tube  is  purple  and  the 
spectrum  very  complicated. 

If  the  electric  discharge  take  place  through  a  compound  gas  or- 
vapour,  the  spectra  are  those  of  the  elementary  constituents  of  the  gas. 
It  seems  as  if  at  very  intense  temperatures  chemical  combination  was 
impossible,  and  oxygen  and  hydrogen,  chlorine  and  the  metals,  could 
coexist  in  a  separate  form,  although  mechanically  mixed  with  each  other. 

The  nature  of  the  spectra  of  the  elementary  gases  is  very  materially 
influenced  by  alterations  of  temperature  and  pressure.  Wiillner  made  a 
series  of  very  accurate  observations  on  the  gases  oxygen,  hydrogen,  and 
nitrogen.  He  not  only  used  gases  in  closed  tubes,  which  by  various 
electrical  means  he  raised  to  different  temperatures  ;  but  in  one  and  the 
same  series  of  experiments,  in  which  a  small  inductorium  was  used,  he 
employed  pressures  varying  from  100  millimetres  to  a  fraction  of  a  milli- 
metre ;  while,  in  another  series,  in  which  a  larger  apparatus  was  used, 
he  extended  the  pressure  to  2,000  millimetres.  At  the  lowest  pressure  of 
less  than  one  millimetre,  the  spectrum  of  hydrogen  was  found  to  be  green, 
and  consisting  of  six  splendid  groups  of  lines,  which  at  a  higher  pressure 


474  On  Light.  [542- 

than  I  millimetre  changed  to  continuous  bands  ;  at  2  to  3  millimetres 
the  spectrum  consisted  of  the  often-mentioned  three  Hnes,  which  did  not 
disappear  under  a  higher  pressure,  but  gradually  became  less  brilliant  as 
the  continuous  spectrum  increased  in  extent  and  lustre.  From  this  point 
the  light,  and  therefore  the  spectrum,  became  feebler.  Using  the  larger 
apparatus,  the  band  spectrum  appeared  only  under  a  higher  pressure ;  at 
the  highest  pressuie  of  2,000  millimetres  it  gave  place  to  the  continuous 
spectrum,  since  the  bright  lines  continually  extended  and  ultimately 
merged  into  each  other. 

543.  Explanation  of  tbe  dark  lines  of  tlie  solar  spectrum. — It  has 
been  already  seen  that  incandescent  sodium  vapour  gives  a  bright  yellow 
line  corresponding  to  the  dark  line  D  of  the  solar  spectrum.  Kirchhoff 
found  that,  when  the  brilliant  light  produced  by  incandescent  lime  passes 
through  a  flame  coloured  by  sodium  in  the  usual  manner,  a  spectrum  is 
produced  in  which  is  a  dark  line  coinciding  with  the  dark  line  D  of  the 
solar  spectrum  ;  what  would  have  been  a  bright  yellow  line  becomes  a 
dark  line  when  formed  on  the  back  ground  of  the  lime  light.  By 
allowing  in  a  similar  manner  the  lime  light  to  traverse  vapours  of  potas- 
sium, barium,  strontium,  etc.,  the  bright. lines  which  they  would  have 
formed  were  found  to  be  converted  into  dark  lines  :  such  spectra  are 
called  absorption  spectra. 

It  appears  then  that  the  vapour  of  sodium  has  the  power  of  absorbing 
rays  of  the  same  refrangibility  as  that  which  it  emits.  And  the  same  is 
true  of  the  vapours  of  potassium,  barium,  strontium,  etc.  This  absorptive 
power  is  by  no  n>eans  an  isolated  phenomenon.  These  substances  share 
it,  for  example,  with  the  vapour  of  nitrous  acid,  which  Brewster  found  to 
possess  the  following  property  :  when  a  tube  filled  with  this  vapour  is 
placed  in  the  path  of  the  light  either  of  the  sun  or  of  a  gas  flame,  and  the 
light  is  subsequently  decomposed  by  a  prism,  a  spectrum  is  produced 
which  is  full  of  dark  lines  (No.  9,  Plate  I.)  ;  and  Miller  showed  that  iodine 
and  bromine  vapour  produced  analogous  effects. 

Hence  the  origin  of  the  above  phenomenon  is,  doubtless,  the  absorption 
by  the  sodium  vapour  of  rays  of  the  same  kind,  that  is,  as  the  same  re- 
frangibility, as  those  which  it  has  itself  the  power  of  emitting.  Other 
rays  it  allows  to  pass  unchanged,  but  these  it  either  totally  or  in  great 
part  suppresses.  Thus  the  particular  lines  in  the  spectrum  to  which  these 
rays  would  converge  are  illuminated  only  by  the  feebly  luminous  sodium 
flame,  and  accordingly  appear  dark  by  contrast  with  the  other  portions 
of  the  spectrum  which  receive  light  from  the  powerful  flame  behind. 

By  replacing  one  of  the  flames,  G  or  H  (fig.  420),  by  a  ray  of  solar  light 
reflected  from  a  heliostat,  Kirchhoff  ascertained  by  direct  comparison 
that  the  bright  lines  which  characterise  iron  correspond  to  dark  lines 
in  the  solar  spectrum.  He  also  found  the  same  to  be  the  case  with 
sodium,  magnesium,  calcium,  nickel,  and  some  other  metals. 

From  these  observations  we  may  draw  important  conclusions  with 
respect  to  the  constitution  of  the  sun.  Since  the  solar  spectrum  has  dark 
lines  where  sodium,  iron,  etc.,  give  bright  ones  (No.  1 1.  Plate  I.),  it  is  prob- 
able that  around  the  solid,  or  more  probably  liquid,  body  of  the  sun,  which 


-543]  Dark  Lines  of  the  Solar  Spectrum.  475 

throws  out  the  hght,  there  exists  a  vaporous  envelope  which,  like  the  sodium 
flame  in  the  experiment  described  above,  absorbs  certain  rays,  namely, 
those  which  the  envelope  itself  emits.  Hence  those  parts  of  the  spectrum 
which,  but  for  this  absorption,  would  have  been  illuminated  by  these 
particular  rays,  appear  feebly  luminous  in  comparison  with  the  other 
parts,  since  they  are  illuminated  only  by  the  light  emitted  by  the  envelope, 
and  not  by  the  solar  nucleus  ;  and  we  are  at  the  same  time  led  to  con- 
clude that  in  this  vapour  there  exists  the  metals  sodium,  iron,  etc. 

Huggins  and  Miller  have  applied  spectrum  analysis  to  the  investigation 
of  the  heavenly  bodies.  The  spectra  of  the  moon  and  planets,  whose 
light  is  reflected  from  the  sun,  give  the  same  lines  as  those  of  the  sun. 
Uranus  proves  an  exception  to  this,  and  is  probably  still  in  a  self- 
luminous  condition.  The  spectra  of  the  fixed  stars  contain,  however, 
dark  lines  differing  from  the  solar  lines,  and  from  one  another.  Four 
distinct  types  of  spectra  are  distinguished  by  Pere  Secchi.  The  first 
embraces  the  white  stars  and  includes  the  well-known  Sirius  and  a  Lyrae. 
Their  spectra  (No.  12,  Plate  I.)  usually  contain  a  number  of  very  fine 
lines,  and  always  contain  four  broad  dark  lines,  which  coincide  with  the 
bright  lines  of  hydrogen.  Out  of  346  stars  164  were  found  to  belong  to 
this  group.  The  second  group  embraces  those,  having  spectra  intersected 
by  numerous  fine  lines  like  those  of  our  sun.  About  140  stars,  among 
them  Pollux,  Capella,  (t,  Aquilae,  belong  to  this  group.  The  third  group 
embraces  the  red  and  orange  stars,  such  as  a  Orionis,  o  Pegasi  ;  the 
spectra  of  these  (Nos.  13,  14,  Plate  I.)  are  divided  into  eight  or  ten  parallel 
columnar  clusters  of  dark  and  bright  bands  increasing  in  intensity  to  the 
red.  Group  four  is  made  up  of  small  red  stars  with  spectra,  and  is  con- 
structed of  three  bright  zones  increasing  in  intensity  towards  the  violet. 
It  would  thus  appear  that  these  fixed  stars,  while  differing  from  one 
another  in  the  matter  of  which  they  are  composed,  are  constructed  on  the 
same  general  plan  as  our  sun.  Huggins  has  observed  a  striking  difference 
in  the  spectra  of  the  nebulas  ;  where  they  can  at  all  be  observed,  they  are 
found  to  consist  generally  of  bright  lines,  like  the  spectra  of  the  ignited 
gases,  instead  of  like  the  spectra  of  the  sun  and  stars  consisting  of  a 
bright  ground  intersected  by  dark  lines.  J t  is  hence  probable  that  the 
nebulae  are  masses  of  glowing  gas,  and  do  not  consist,  like  the  sun  and 
stars,  of  a  photosphere  surrounded  by  a  gaseous  atmosphere. 

One  of  the  most  interesting  triumphs  of  spectrum  analysis  has  been  the 
discovery  of  the  true  nature  of  the  protuberances.,  which  appear  during  a 
solar  eclipse  as  mountains  or  cloud-shaped  luminous  objects  varying  in 
size,  and  surrounding  the  moon's  disc. 

During  the  eclipse  of  1868  it  had  been  ascertained  by  Jannsen  that 
they  emitted  certain  bright  fines  coinciding  with  those  of  hydrogen.  They 
have,  however,  been  fully  understood  only  since  Lockyer  and  Jannsen 
have  discovered  a  method  of  investigating  them  at  any  time.  The  prin- 
ciple of  this  method  is  as  follows  : — When  a  line  of  light  admitted  through 
a  slit  is  decomposed  by  a  prism,  the  length  of  the  spectrum  may  be 
increased  by  passing  it  through  two  or  more  prisms  ;  as  the  quantity  of 
light  is  the  same,  it  is  clear  that  the  intensity  of  the  spectrum  will  be 


476  On  Light.  [543-,— 

diminished.  This  is  the  case  with  the  ordinary  sources  of  light,  such  as 
the  sun  ;  if  the  light  be  homogeneous,  it  will  be  merely  deviated,  and  not 
reduced  in  intensity  by  dispersion.  And  if  the  source  of  light  emit  lights 
of  both  kinds,  the  image  of  the  slit  of  light  of  a  definite  refrangibility 
which  the  mixture  may  contain  will  stand  out  by  their  superior  intensity 
on  the  weaker  ground  of  the  continuous  spectrum.  This  is  the  case  with 
the  spectrum  of  the  protuberances.  Viewed  through  an  ordinary  spectro- 
scope, the  light  they  emit  is  overshadowed  by  that  of  the  sun  ;  but  by 
using  prisms  of  great  dispersive  power  the  sun's  light  becomes  weakened, 
and  the  spectrum  of  the  protuberances  may  be  secured.  Lockyer's 
researches  leave  no  doubt  that  they  are  ignited  gas  masses,  principally  of 
hydrogen.  By  altering  the  position  of  the  slit  a  series  of  sections  of  the 
prominences  are  obtained  by  collating  which  the  form  of  the  prominence 
may  be  inferred.  They  are  thus  found  to  enclose  the  sun  usually  to  a 
depth  of  about  5,000  miles,  but  sometimes  in  enormous  local  accumula- 
tions, which  reach  the  height  of  70,000  miles.  Lockyer  has  not  merely 
examined  these  phenomena  right  on  the  edge  of  the  sun  ;  but  he  has 
been  able  to  observe  them  on  the  disc  itself.  He  has  shown  that  some  of 
these  protuberances  are  the  results  of  sudden  outbursts  or  storms,  which 
move  with  the  enormous  velocity  of  120  miles  in  a  second. 

For  a  fuller  account  of  this  branch  of  Physics,  which  is  incompatible 
with  the  limits  of  this  work,  the  reader  is  referred  to  Roscoe's  '  Lectures 
on  Spectrum  Analysis,'  and  to  the  same  writer's  articles  in  Watts's 
'-  Dictionary  of  Chemistry,'  or  to  Schellen's  '  Spectrum  Analysis,'  translated 
by  Lassell. 

544.  Uses  of  the  spectroscopec — When  a  liquid  placed  in  a  glass 
tube  or  in  a  suitable  glass  cell  is  interposed  between  a  source  of  light  and 
the  slit  of  the  spectroscope,  on  looking  through  the  telescope,  the  spec- 
trum observed  will  in  many  cases  be  found  to  be  traversed  by  dark  bands. 
No  10,  Plate  I,  represents  the  appearance  of  the  spectrum  when  a 
solution  of  chlorophylle,  the  green  colouring  matter  of  plants,  is  thus 
interposed.  Both  in  the  red,  the  yellow  and  the  violet  parts  dark  bands 
are  formed,  and  the  blue  gives  way  to  a  reddish  shimmer.  If  instead  of 
chlorophylle  arterial  blood  greatly  diluted  be  used,  the  red  of  the  spec- 
trum appears  brighter,  but  green  and  violet  are  nearly  extinguished.  As 
these  bands  thus  differ  in  different  liquids  as  regards  position,  breadth, 
and  intensity,  in  many  cases  they  afford  the  most  suitable  means  of 
identifying  bodies.  Sorby  and  Browning  have  devised  a  combination 
of  the  microscope  and  spectroscope,  called  the  microspectroscope,  which 
renders  it  possible  to  examine  even  very  minute  traces  of  substances. 

This  application  of  the  spectroscope  has  been  very  useful  in  inves- 
tigating substances  which  have  special  importance  in  physiology  and 
pathology  ;  thus,  in  examining  normal  and  diseased  blood,  in  detecting 
albumen  in  urine,  and  in  ascertaining  the  rate  at  which  certain  substances 
pass  into  the  various  fluids  of  the  system.  The  characteristic  absorption 
bands  which  certain  liquids,  such  as  wine,  beer,  etc.,  present  in  their 
normal  state,  compared  with  those  yielded  by  adulterated  substances 
furnishes  a  delicate  and  certain  means  of  detecting  the  latter. 


•^ —  -545]  Fluorescence.  477 

545.  Fluorescence. — Professor  Stokes  has  made  the  remarkable  dis- 
covery that  under  certain  circumstances  the  rays  of  hght  are  capable  of 
undergoing  a  change  of  refrangibility.  The  discovery  originated  in  the 
study  of  a  phenomenon  observed  by  Sir  J,  Herschel,  that  certain  solutions 
when  looked  at  by  transmitted  light  appear  colourless,  but  when  viewed 
in  reflected  light  present  a  bluish  appearance.  Stokes  has  found  that  this 
property  which  he  calls  fluorescence,  is  characteristic  of  a  large  class  of 
bodies. 

The  phenomenon  is  best  seen  when  a  solution  of  sulphate  of  quinine, 
•  contained  in  a  trough  with  parallel  sides,  is  placed  in  different  positions 
in  the  solar  spectrum.  No  change  is  observed  in  the  upper  part  of  the 
spectrum,  but  from  about  the  middle  of  the  lines  G  and  H  (coloured  Plate) 
to  some  distance  beyond  the  extreme  range  of  the  violet,  rays  of  a  beau- 
tiful sky-blue  colour  are  seen  to  proceed.  These  invisible  ultra-violet  rays 
also  become  visible  when  the  spectrum  is  allowed  to  fall  on  paper  im- 
pregnated with  a  solution  of  cpsculine  (a  substance  extracted  from  horse 
chestnut),  an  alcoholic  solution  of  stramonium,  or  a  plate  of  canary  glass 
(which  is  coloured  by  means  of  uranium).  This  change  arises  from  a 
diminution  in  the  refrangibility  of  those  lays  outside  the  violet,  which  are 
ordinarily  too  refrangible  to  affect  the  eye. 

Glass  appears  to  absorb  many  of  these  more  refrangible  rays,  which  is 
not  the  case  nearly  to  the  same  extent  with  quartz.  When  prisms  and 
troughs  formed  of  plates  of  quartz  are  used,  a  spectrum  may  be  obtained 
which,  outside  the  line  H,  is  double  the  length  of  the  visible  spectrum. 
In  the  spectrum  thus  made  visible  dark  lines  may  be  seen  like  those  in 
the  ordinary  spectrum. 

The  phenomena  may  be  observed  without  the  use  of  a  prism.  When 
an  aperture  in  a  dark  room  is  closed  by  means  of  a  piece  of  blue  glass, 
and  the  light  is  allowed  to  fall  upon  a  piece  of  canary  glass,  it  instantly 
appears  self-luminous  from  the  emission  of  the  altered  rays. 

In  most  cases  it  is  the  violet  and  ultra-violet  rays  which  undergo  an 
alteration  of  refrangibility,  but  the  phenomenon  is  not  confined  to  them. 
A  decoction  of  madder  in  alum  gives  yellow  and  violet  light  from  about 
the  line  D  to  beyond  the  violet  ;  an  alcoholic  solution  of  chlorophylle 
gives  red  light  from  the  line  B  to  the  Hmit  of  the  spectrum.  In  these 
cases  the  yellow,  the  green,  and  the  blue  rays  experience  diminution 
of  refrangibility  ;  the  change  never  produces  more  highly  refrangible  rays. 
The  electric  light  gives  a  very  remarkable  spectrum.  With  quartz 
apparatus  Stokes  obtained  a  spectrum  six  or  eight  times  as  long  as  the 
ordinary  one.  Several  flames  of  no  great  illuminating  power  emit  very 
peculiar  light.  Characters  traced  on  paper  with  solution  of  stramonium, 
which  are  almost  invisible  in  daylight,  appear  instantaneously  when  illumi- 
nated by  the  flame  of  burning  sulphur.  Robinson  has  found  that  the 
light  of  the  aurora  is  peculiarly  rich  in  rays  of  high  refrangibility. 

If  a  pencil  of  rays  be  allowed  to  pass  through  a  condensing  lens,  and 
be  received  on  a  screen  within  the  focus,  the  bright  spot  has  a  red  edge, 
while  if  the  screen  is  placed  beyond  the  focus  the  bright  spot  has  a  violet 
edge. 


478  On  Light.  [546- 

546.  Chromatic  aberration. — The  various  lenses  hitherto  described 
(51  )  possess  the  inconvenience  that,  when  at  a  certain  distance  from 
the  eye,  they  give  images  with  coloured  edges.  This  defect,  which  is 
most  observable  in  condensing  lenses,  is  due  to  the  unequal  refrangibility 
of  the  simple  colours  (532),  and  is  called  chromatic  aberration. 

For,  as  a  lens  may  be  compared  to  a  series  of  prisms  with  infinitely 
small  faces,  and  united  at  their  bases,  it  not  only  refracts  light,  but 
also  decomposes  it  like  a  prism.  On  account  of  this  dispersion,  therefore 
lenses  have  really  a  distinct  focus  for  each  colour.  In  condensing  lenses, 
for  example,  the  red  rays,  which  are  the  least  refrangible,  form  their 
focus  at  a  point,  r,  on  the  axis  of  the  lens  (fig.  425),  while  the  violet  rays, 


Fig.  425. 

which  are  most  refrangible,  coincide  in  the  nearer  point,  v.  The  foci  of 
the  orange,  yellow,  green,  blue,  and  indigo  are  between  these  points.  The 
chromatic  aberration  is  more  perceptible  in  proportion  as  the  lenses  are 
more  convex,  and  as  the  point  at  which  the  rays  are  incident  is  further 
from  the  axis  ;  for  then  the  deviation,  and  therefore  the  dispersion,  are 
increased. 

If  a  pencil  graze  which  has  passed  through  a  condensing  lens  be 
received  on  a  screen  placed  at  in  m  within  the  first  distance,  a  bright  spot 
is  seen  with  a  red  border,  if  it  is  placed  ^X  s  s  the  bright  spot  has  a  violet 
border. 

547.  Acbromatism. — By  combining  prisms  which  have  different  re- 
fracting angles  (512),  and  are  formed  of  substances  of  unequal  dispersive 
powers  (530),  white  light  may  be  refracted  without  being  dispersed.  The 
same  result  is  obtained  by  combining  lenses  of  different  substances,  the 
curvatures  of  which  are  suitably  combined.  The  images  of  objects  viewed 
through  such  lenses  do  not  appear  coloured,  and  they  are  accordingly 
called  achromatic  lenses  ;  achrontatism  being  the  term  applied  to  the 
phenomenon  of  the  refraction  of  light  without  decomposition. 

By  observing  the  phenomenon  of  the  dispersion  of  colours  in  prisms  ot 
water,  of  oil,  ot  turpentine,  and  of  crown  glass,  Newton  was  led  to  sup- 
pose that  dispersion  was  proportional  to  refraction.  He  concluded  that 
there  could  be  no  refraction  without  dispersion,  and,  therefore,  that 
achromatism  was  impossible.  Almost  half  a  century  elapsed  before  this 
was  found  to  be  incorrect.  Hall,  an  Enghsh  philosopher,  in  1733,  was 
the  first  to  construct  achromatic  lenses,  but  he  did  not  publish  his  dis- 
covery. It  is  to  Dolland,  an  optician  in  London,  that  we  owe  the  greatest 
improvement  which  has  been  made  in  optical  instruments.     He  showed 


-547]  Achromatism.  ^  479 

in  1757  that  by  combining  two  lenses,  one  a  double  convex  crown  glass 
lens,  the  other  a  concavo-convex  lens  of  flint  glass  (fig.  426),  a  lens  is 
obtained  which  is  virtually  achromatic. 

To  explain  this  result,  let  two  prisms,  BFC  and  CDF,  be  joined  and 
turned  in  a  contrary  direction,  as  shown  in  fig.  427.  Let  us  suppose,  in 
the  first  case,  that  both  prisms  are  of  the  same  material,  but  that  the 
refracting  angle  of  the  second,  CDF,  is  less  than  the  refracting  angle  of 
the  first ;  the  two  prisms  will  produce  the  same  effect  as  a  single  prism, 
BAF  ;  that  is  to  say,  that  white  light  which  traverses  it  will  not  only  be 
refracted,  but  also  decomposed.  If,  on  the  contrary,  the  first  prism  BCF 
were  of  crown  glass,  and  the  other  of  flint  glass,  the  dispersion  might  be 
destroyed  without  destroying  the  refraction.  For  as  flint  glass  is  more 
dispersive  than  crown,  and  as  the  dispersion  produced  by  a  prism  dimi- 
nishes with  its  refracting  angle  (530),  it  follows  that  by  suitably  lessening 
the  refracting  angle  of  the  flint  glass  prism  CFD,  as  compared  with  the 
refracting  angle  of  the  crown  glass  prism  BCF,  the  dispersive  power  of 


Fig.  426.  Fig.  427. 

these  prisms  maybe  equalised  ;  and  as,  from  their  position,  the  dispersion 
takes  place  in  a  contrary  direction,  it  is  neutralised  ;  that  is,  the  emergent 
rays  EO  are  parallel,  and  therefore  give  white  light.  Nevertheless,  the 
ratio  of  the  angles  BCF  and  CFD,  which  is  suitable  for  the  parallehsm 
of  the  red  rays  and  violet  rays,  is  not  so  for  the  intermediate  rays,  and, 
consequently,  only  two  of  the  rays  of  the  spectrum  can  be  exactly  com- 
bined, and  the  achromatism  is  not  quite  perfect.  To  obtain  perfect 
achromatism,  several  prisms  would  be  necessary,  of  unequally  dispersive 
materials,  and  the  angles  of  which  were  suitably  combined. 

The  refraction  is  not  destroyed  at  the  same  time  as  the  dispersion  ; 
that  could  only  happen  if  the  refracting  power  of  a  bqdy  varied  in  the 
same  ratio  as  its  dispersive  power,  which  is  not  the  case.  Consequently, 
the  emergent  ray  EO  is  not  exactly  parallel  to  the  incident  ray,  and  there 
is  a  refraction  without  appreciable  decomposition. 

Achromatic  lenses  are  made  of  two  lenses  of  unequally  dispersive  ma- 
terials ;  one.  A,  of  flint  glass,  is  a  diverging  concavo-convex  (fig,  422)  ; 
the  other,  B,  of  crown  glass,  is  double  convex,  and  one  of  its  faces  may 
exactly  coincide  with  the  concave  face  of  the  first.  As  with  prisms, 
several  lenses  would  be  necessary  to  obtain  perfect  achromatism  ;  but  for 
optical  instruments  two  are  sufficient,  their  curvature  being  such  as  to 
combine  the  blue  and  orange  rays. 


48o  On  Light.  [548- 


CHAPTER  V. 

OPTICAL    INSTRUMENTS. 

548.  Tbe  different  kinds  of  optical  instruments. — By  the  term 
optical  instrument  is  meant  any  combination  of  lenses,  or  of  lenses  and 
mirrors.  Optical  instruments  may  be  divided  into  three  classes,  accord- 
ing to  the  ends  they  are  intended  to  answer,  viz.: — i.  Microscopes,  which 
are  designed  to  obtain  a  magnified  image  of  any  object  whose  real  dimen- 
sions are  too  small  to  admit  of  its  being  seen  distinctly  by  the  naked  eye. 
ii.  Telescopes,  by  which  very  distant  objects,  whether  celestial  or  terres- 
trial, may  be  observed,  iii.  histruments  designed  to  project  on  a  screen 
a  magnified  or  diminished  image  of  any  object  which  can  thereby  be 
either  depicted  or  rendered  visible  to  a  crowd  of  spectators  :  such  as  the 
camera  lucida,  the  camera  obscura,  photographic  apparatus,  the  7nagic 
lanter?t,  the  solar  microscope,  the  photo-electric  microscope,  etc.  The  two 
former  classes  yield  virtual  images  ;  the  last,  with  the  exception  of  the 
camera  lucida,  yield  real  images. 

MICROSCOPES. 

549.  Tlie  simple  microscope.— The  simple  microscope,  or  jnagnifying 
glass  is  merely  a  convex  lens  of  short  focal  length,  by.  means  of  which  we 
look  at  objects  placed  between  the  lens  and  its  principal  focus.  Let  AB 
(fig.  428)  be  the  object  to  be  observed  placed  between  the  lens  and  its 


Fig.  428. 

principal  focus,  F.  Draw  the  secondary  axes  AO  and  BO,  and  also  from 
A  and  B  rays  parallel  to  the  axis  of  the  lens  FO.  Now  these  rays,  on 
passing  out  of  the  lens,  tend  to  pass  through  the  second  principal  focus 
F',  consequently  they  are  divergent  with  reference  to  the  secondary  axes, 
and  therefore,  when  produced,  will  cut  those  axes  in  A'  and  B'  respec- 
tively. These  points  are  the  virtual  foci  of  A  and  B  respectively.  The 
lens  therefore  produces  at  A'  B'  an  erect  and  magnified  virtual  image  of 
the  object  AB. 

The  position  and  magnitude  Df  this  image  depend  on  the  distance  of 


J 


-560] 


Optical  Instruments. 


481 


the  object  from  the  focus.  Thus,  if  AB  is  moved  to  ab  nearer  the  lens, 
the  secondary  axes  will  contain  a  greater  angle,  and  the  image  will  be 
formed  at  a'b',  and  will  be  much  smaller,  and  nearer  the  eye.  On  the 
other  hand,  if  the  object  is  moved  farther  from  the  lens  the  angle  between 
the  secondary  axes  is  diminished,  and  their  intersection  with  the  pro- 
longation of  the  refracted  rays  taking  place  beyond  A'B',  the  image  is 
formed  farther  from  the  lens,  and  is  larger. 

In  a  simple  microscope  both  chromatic  aberration  and  spherical 
aberration  increase  with  the  degree  of  magnification.  We  have  already 
seen  that  the  former  can  be  corrected  by  using  achromatic  lenses 
(547),  and  the  latter  by  using  diaphragms,  which  allow  the  passage  of 
such  rays  only  as  are  nearly  parallel  to  the  axis,  the  spherical  aberration 
of  these  rays  being  nearly  inappreciable.     Spherical  aberration  may  be 


Fig.  429. 

still  further  corrected  by  using  two  plano-convex  lenses,  instead  of 
one  very  convergent  lens.  When  this  is  done,  the  plane  face  of  each 
lens  is  turned  towards  the  object  (fig.  429).  Although  each  lens  is  less 
convex  than  the  simple  lens  which  together  they  replace,'^  yet  their  joint 
magnifying  power  is  as  great,  and  with  a  less  amount  of.  sphei-ical  aber- 
ration, since  the  first  lens  draws  towards  the  axis  the,  ray^which  fall  on 
the  second  lens.  This  combination 
of  lenses  is  known  as  Wollaston's 
doublet. 

There  are  many  forms  of  the  simple 
microscope.  One  of  the  best  is  that 
represented  in  fig.  430.  On  a  hori- 
zontal support,  E,  which  can  be  raised 
and  lowered  by  a  rack  and  pinion, 
there  is  a  black  eyepiece,  w,  in  the 
centre  of  which  is  fitted  a  small  con- 
vex lens.  Below  this  is  the  stage, 
which  is  fixed,  and  on  which  the  object 
is  placed  between  glass  plates.  In 
order  to  illuminate  the  object  power- 
fully, diffused  light  is  reflected  from  a 
concave  glass  mirror,  M,  so  that  the 
reflected    rays   fall  upon   the   object.  ~  — — ^-=-- 

In   using    this    microscope,    the    eye  ^^'  ^^°' 

is  placed  very  near  the  lens,  which  is  lowered  or  raised  until  the  position 
is  found  at  which  the  object  appears  in  its  greatest  distinctness. 

550.  Conditions   of  distinctness   of  tlie    imagres. — In    order    that 
objects  looked  at  through  a  microscope  should  be  seen  with  distinctness 

Y  _ 


4^2 


On  Light, 


[550 


they  must  have  a  strong  light  thrown  upon  them,  but  this  is  by  no  means 
enough.  It  is  necessary  that  the  image  be  formed  at  a  determinate 
distance  from  the  eye.  In  fact,  there  is  for  each  person  2,  distance  of 
most  distinct  vision,  a  distance,  that  is  to  say,  at  which  an  object  must  be 
placed  from  an  observer's  eye,  in  order  to  be  seen  with  greatest  dis- 
tinctness. This  distance  is  different  for  different  observers,  but  ordi- 
narily is  between  lo  and  12  inches.  It  is,  therefore,  at  this  distance 
from  the  eye  that  the  image  ought  to  be  formed.  Moreover,  this  is  why 
each  observer  has  to  focus  the  instrument,  that  is,  to  adapt  the  microscope 
to  his  own  distance  of  most  distinct  vision.  This  is  effected  by  slightly 
varying  the  distance  from  the  lens  to  the  object,  for  we  have  seen  above 
that  a  slight  displacement  of  the  object  causes  a  great  displacement  of 
the  image.  With  a  common  magnifying  glass,  such  as  is  held  in  the  hand, 
the  adjustment  is  effected  by  merely  moving  it  nearer  to  or  farther  from 
the  object.  In  the  microscope  the  adjustment  is  effected  by  means  of  a 
rack  and  pinion,  which  in  the  case  of  the  instrument  shown  in  fig.  430 
moves  the  instrument,  but  moves  the  object  in  the  case  of  the  instrument 
depicted  in  fig.  435.  What  has  been  said  ?^iovXfocHssi7tg  the  microscope 
applies  equally  to  telescopes.     In  the  latter  instruments  the  eyepiece  is 


Fig.  432. 

generally  adjusted  with  respect  to  the  image  formed  in  the  focus  of  the 
object  glass. 

551.  Apparent  magrnitude  of  an  object. — The  apparent  magnitude 
of  apparent  diameter  pf  a  body  is  the  angle  it  subtends  at  the  eye  of  the 
observer.  Thus,  if  AB  is  the  object,  and  O  the  observer's  eye  (figs.  431, 
432),  the  apparent  magnitude  of  the  object  is  the  angle  AOB  contained 
by  two  visual  rays  drawn  from  the  centre  of  the  pupil  to  the  extremities 
of  the  object. 

In  the  case  of  objects  seen  through  optical  instruments,  the  angles 
which  they  subtend  are  so  small  that  the  arcs  which  measure  the  angles 
do  not  differ  sensibly  from  their  tangents.  The  ratio  of  two  such  angles 
is  therefore  the  same  as  that  of  their  tangents.  Hence  we  deduce  the 
two  following  principles  : — 


-552]  Measure  of  Magnification.  483 

I.  When  the  same  object  is  seen  at  itmquat distafices,  the  apparent  dia- 
7ueter  varies  rnversely  as  the  distance  from  the  observer's  eye.  — - 

II.  In  the  case  of  two  objects  seen  at  the  sam'^  distance,  the  ratio  of  the 
apparent  diaj?ieters  is  the  sam3  as  that  of  their  absolute  magnitudes. 

These  principles  may  be  proved  as  follows  :  i.  In  fig.  431,  let  AB 
be  the  object  in  its  first  position,  and  ab  the  same  object  in  its  second 
position.  For  the  sake  of  distinctness  these  are  represented  in  such 
positions  that  the  line  OC  passes  at  right  angles  through  their  middle 
points  C  and  c  respectively.  It  is,  however,  sufficient  that  ab  and  AB 
should  be  the  bases  of  isosceles  triangles  having  a  common  vertex  at  O. 
Now  by  what  has  been  said  above,  AB  is  virtually  an  arc  of  a  circle 
described  with  centre  O  and  radius  OC  ;  likewise  ab  is  virtually  an  arc  of 
a  circle  whose  centre  is  O  and  radius  O^.     Therefore, 

AOB:^0^  =  ^:^'^-=  -^^  :    ^. 
OC     O^     OC     Oc 

Therefore,  AOB  varies  inversely  as  OC. 

ii.  Let  AB  and  A'B'  be  two  objects  placed  at  the  same  perpendicular 
distance,  OC,  from  the  eye,  O,  of  the  observer  (fig.  332).  Then  they  are 
virtually  arcs  of  a  circle  whose  centre  is  O  and  radius  OC.     Therefore, 

AOB  :  A'OB'  =  ^^  :  ^'^-  =  AB  :  A^B, 

a  proportion  which  expresses  the  second  principle. 

552.  Measure  of  magrnification. — In  the  simple  microscope,  the  mea - 
sure  of  the  magnification  produced  is  the  ratio  of  the  apparent  diam.eter 
of  the  image  to  that  of  the  object,  both  being  at  the  distance  of  most  dis 


tinct  vision.*  The  same  rule  holds  good  for  other  microscopes.  It  is 
however,  important  to  obtain  an  expression  for  the  magnification  depend- 
ing on  data  that  are  of  easier  determination. 

*  A  simpler  and  more  general  definition  may  be  stated  thus  —Let  a  be  the  angular 
magnitude  of  the  object  as  seen  by  the  naked  eye,  ^  the  angular  magnitude  of  the 
image,  whether  real  or  virtual,  actually  present  to  the  eye,  then  the  magnification  is 
^  -r-  a.     This  rule  appJies  to  telescopes., 

Y2 


484  On  Light.  [552- 

In  fig.  433  let  AB  be  the  object,  and  A'B'  its  image  formed  at  the  dis- 
tance of  most  distinct  vision.  Let  a'b'  be  the  projection  of  AB  on  A'B'. 
Then,  since  the  eye  is  very  near  the  glass,  the  magnification  equals 

1^^-,  or  — ,5-,  that  is,  ^ ^  .     But  since  the  triangles  A'OB'  and  AOB 
a'Ob'^         a'b'  AB  ^ 

are  similar,  A'B'  :  AB  =  DO  :  CO.     Now  DO  is  the  distance  of  most 

distinct  vision,  and  CO  is  very  nearly  equal  to  FO,the  focal  length  of  the 

lens.     Therefore  the  magnification  equals  the  ratio  of  the  distance  of 

most  distinct  vision  to  the  focal  length  of  the  lens.     Hence  we  conclude 

that  the  magnification  is  greater  : — ist,  as  the  focal  length  of  the  lens  is 

smaller,  in  other  words,  as  the  lens  is  more  convergent ;  2ndly,  as  the 

observer's  distance  of  most  distinct  vision  is  greater. 

By  changing  the  lens  the  magnification  can  be  increased,  but  only 
within  certain  limits  if  we  wish  to  obtain  a  distinct  image.  By  means  of 
a  simple  microscope  distinct  magnification  maybe  obtained  up  to  120 
diameters. 

The  magnification  we  have  now  considered  is  linear  magnification. 
Stiperjicial  magnification  equals  the  square  of  the  linear  magnification  : 
for  instance,  the  former  will  be  i  ,600  when  the  latter  is  40. 

553.  Compound  microscope. — The  compound  microscope  in  its  sim- 
plest form  consists  of  two  condensing  lenses  :  one,  with  a  short  focus,  is 
called  the  object  glass  ox  objective^  because  it  is  turned  towards  the  object ; 
the  other  is  less  condensing,  and  is  called  the  eyepiece  or  power,  because 
it  is  close  to  the  observer's  eye. 

Fig.  434  represents  the  path  of  the  luminous  rays,  and  the  formation 
of  the  image  in  the  simplest  form  of  a  compound  microscope.     An  object 


Fig.  434 

AB,  being  placed  very  near  the  principal  focus  of  the  object  glass,  M,  but 
a  little  farther  from  the  glass,  a  real  image,  ab,  inverted  and  somewhat 
magnified,  is  formed  on  the  other  side  of  the  object  glass  (524).  Now 
the  distance  of  the  two  lenses  M  and  N,  is  such  that  the  position  of  the 
image,  ab,  is  between  the  eyepiece  N,  and  its  focus,  F.  From  this  it 
follows  that  for  the  eye  at  E,  looking  at  the  image  through  the  eyepiece 
this  glass  produces  the  same  effect  as  a  simple  microscope,  and  instead 
of  this  image,  ab,  another  image,  a'b' ,  is  seen,  which  is  virtual,  and  still 
more  magnified.  This  second  image,  although  erect  as  regards  the  first, 
is  inverted  in  reference  to  the  object.  It  may  thus  be  said,  that  the  com- 
pound microscope  is  nothing  more  than  a  simple  microscope  applied  not 
to  the  object,  but  to  its  image  already  magnified  by  the  first  lens.' 

554.  Amici's  compound  microscope. — The  principle  of  the  compound 


-554] 


Microscope, 


485 


microscope  has  been  already  (553)  explained  ;  the  principal  accessories  to 
the  instrument  remain  to  be  described. 

Fig.  435  represents  a  perspective  view,  and  fig.  436  a  section  of  a  com- 
pound microscope.  The  body  of  the  microscope  consists  of  a  series  of 
brass  tubes,  DD',  H,  and  I,  in  the  former  of  these  is  fitted  the  eyepiece, 
and  in  the  lower  part  of  the  latter  the  object  glass,  0.  The  tube  I  moves 
with  gentle  friction  in  the  tube  DD',  which  in  turn  can  also  be  moved  in 


Fig.  435- 

a  larger  tube  fixed  in  the  ring  E.  This  latter  is  fixed  to  a  piece,  BB, 
which  by  means  of  a  very  fine  screw,  worked  by  the  milled  head  T,  can 
be  moved  up  and  down  an  inner  rod  r,  not  represented  in  the  figure. 
The  whole  body  of  the  microscope  is  raised  and  lowered  with  the  piece 
BB',  so  that  it  can  be  placed  near  or  far  from  the  object  to  be  examined. 
Moreover,  the  rod,  t,  and  all  the  other  pieces  of  the  apparatus  rest  on 
a  horizontal  axis,  A,  with  which  they  turn  under  so  much  friction  as  to 
remain  fixed  in  any  position  in  which  they  may  be  placed. 


486  On  Light,  [554- 

The  objects  to  be  observed  are  placed  between  two  glass  plates,  V,  on 
a  stage,  R.  This  is  perforated  in  the  centre  so  that  light  can  be  reflected 
upon  it  by  a  concave  reflecting  glass  mirror,  M.  The  mirror  is  mounted 
on  an  articulated  support,  so  that  it  can  be  placed  in  any  position  what- 
ever, so  as  to  reflect  to  the  object  either  the  diffused  light  of  the  atmo- 
sphere, or  that  from  a  candle  or  lamp.  Between  the  reflector  and  the  stage 
is  a  diaphragm  or  stop,  K,  perforated  by  four  holes  of  different  sizes,  anyone 
of  which  can  be  placed  over  the  perforation  in  the  stage,  and  thus  the 
light  faUing  on  the  object  may  be  regulated;  the  light  can  moreover  be 
regulated  by  raising  by  a  lever,  ;/,  the  diaphragm,  K,  which  is  movable 
in  a  slide.  Above  the  diaphragm  is  a  piece,  ;;/,  to  which  can  be  attached 
either  a  very  small  stop,  so  that  only  very  little  light  can  reach  the  object, 
or  a  condensing  lens,  which  illuminates  it  strongly,  or  an  oblique  prism, 
represented  at  X.  The  rays  from  the  reflector  undergo  two  total  reflec- 
tions in  this  prism,  and  emerge  by  a  lenticular  face  that  concentrates  them 
on  the  object,  but  in  an  oblique  direction,  which  in  some  microscopic  ob- 
servations is  an  advantage.  Objects  are  generally  so  transparent  that 
they  can  be  lighted  from  below  ;  but  where,  owing  to  their  opacity,  this 
is  not  possible,  they  are  lighted  from  above  by  means  of  a  condensing 
lens  mounted  on  a  jointed  support,  and  so  placed  that  they  receive  the 
diffused  light  of  the  atmosphere. 

Fig.  436  shows  the  arrangement  of  the  lenses  and  the  path  of  the 
rays  in  the  microscope.  At  0  is  the  object  glass,  consisting  of  three  small 
condensing  lenses,  represented  on  a  larger  scale  at  L,  on  the  right  of 
the  figure.  The  effects  of  these  lenses  being  added  to  each  other  they  act 
like  a  single  very  powerful  condensing  lens.  The  object  being  placed  at 
/,  a  very  little  beyond  the  principal  focus  of  the  system,  the  emerging 
rays  fall  upon  a  fourth  condensing  lens,  Ji,  the  use  of  which  will  be  seen 
presently  (555,  556).  Having  become  more  convergent,  owing  to  their  pas- 
sage through  the  lens,  ;/,  the  rays  form  at  aa'  a  real  and  amplified  image 
of  the  object  /.  This  image  is  between  a  fifth  condensing  lens,  O,  and 
the  principal  focus  of  this  lens.  Hence,  on  looking  through  this,  it  acts  as 
a"  magnifier  (524),  and  gives  at  AA',  a  virtual  and  highly  magnified 
image  of  aa',  and  therefore  of  the  object.  The  two  glasses  71  and  O, 
constitute  the  eyepiece  in  the  same  manner  as  the  three  glasses,  0,  con- 
stitute the  object  glass. 

The  first  image,  aa',  must  not  merely  be  formed  between  the  glass,  O, 
and  its  principal  focus,  but.  at  such  a  distance  from  this  glass  that  the 
second  image,  AA^,  is  formed  at  the  observer's  distance  of  distinct  vision. 
This  result  is  obtained  in  moving,  by  the  hand  the  body,  DH,  of  the 
microscope  in  the  larger  tube  fixed  to  the  ring,  E,  until  a  tolerably  dis- 
tinct image  is  obtained  ;  then  turning  the  milled  head,  T,  in  one  direction 
or  the  other,  the  piece,  BB,  and  with  it  the  whole  microscope,  are  moved 
until  the  image,  AA',  attains  its  greatest  distinctness,  which  is  the  case 
when  the  image,  aa\  is  formed  at  the  distance  of  distinct  vision  :  a  distance 
which  can  always  be  ultimately  obtained,  for  as  the  object  glass  ap- 
proaches or  recedes  from  the  object,  the  image,  aa'  recedes  from  or 
approaches  the  eyepiece,  and  at  the  same  time  the  image,  AA'. 


565] 


Achromatism  of  the  Microscope. 


487 


This  operation  is  called  the  focussing.  In  the  microscope,  where  the 
distance  from  the  object  glass  to  the  eyepiece  is  constant,  it  is  effected 
by  altering  their  distance  from  the  object.  In  telescopes,  where  the 
objects  are  inaccessible,  the  object  is  effected  by  varying  the  distance  of 
the  eyepiece  and  the  object  glass. 

The  microscope  possesses  numerous  eyepieces  and  object  glasses,  by 
means  of  which  a  great  variety  of  magnifying  power  is  obtained.  A  small 
magnifying  power  is  also  obtained  by  removing  one  or  two  of  the  lenses 
of  the  object  glass. 

The  above  contains  the  essential  features  of  the  microscope  ;  it  is  made 
in  a  great  variety  of  forms,  which  differ  mainly  in  the  construction  of  the 
stand,  the  arrangement  of  the  lenses,  and  in  the  illumination.  For 
descriptions  of  these,  the  student  is  referred  to  special  works  on  the 
microscope. 

555.  Achromatism  of  tlie  microscope.  Campani's  eyepiece. — 
When  a  compound  microscope  consists  of  two  single  lenses,  as  in  fig.  435, 
not  only  is  the  spherical  aberration  uncorrected,  but  also  the  chromatic 
aberration,  the  latter  defect  causing  the  images  to  be  surrounded  by 
fringes  of  the  prismatic  colours,  these  fringes  being  larger  as  the  magnifi- 
cation is  greater.  It  is  with  a  view  to  correcting  these  aberrations 
that  the  object  glass  (see  fig.  424)  is  composed  of  three  achromatic 
lenses,  and  the  eyepiece  of  two  lenses,  ?t  and  w,  for  the  first  of  these,  n^ 
would  be  enough  to  produce  colour  unless  the  magnifying  power  were  low. 

The  effect  of  this  eyepiece  in  correcting  the  colour  may  be  explained  as 
follows  : — It  will  be  borne  in  mind  that  with  respect  to  red  rays  the  focal 
length  of  a  lens  is  greater  than  the  focal  length  of  the  same  lens  with 
reference  to  the  violet  rays. 

In  fact,  if  in  the  equation  (4)  (527),  we  write  R'  =  00 ,  we  obtain  /  = 

n  —  V 

which  gives  the  focal  length  of  a  plano-convex  lens  whose  refractive 


Fig.  437- 


index  is  ;/.     Now,  in  flint  glass,  and  for  the  red  ray,  n—\   equals  0-63, 
and  for  the  violet  ray  71  —  i  equals  0-67 

Let  ab  be  the  object,  O  the  object  glass  which  is  corrected  for  colour. 
Consequently,  a  pencil  of  rays  falling  from  ^  on  O  would  converge  to  a 
focus.  A,  without  any  separation  of  colours,  but  falling  on  ihtjield glass  C, 
the  red  rays  would  converge  to  r,  the  violet  rays  to  v,  and  intermediate 
colours,  to  intermediate  points.  In  like  manner  the  rays  from  b,  after 
passing  through  the  field  glass,  would  converge  to  r',  v\  and  intermediate 
points.     So  that  on  the  whole  there  would  be  formed  a  succession  of 


488  On  Light.  [555- 

coloured  images  of  ab,  viz.  a  red  image  at  rr' ,  a  violet  image  at  vv' .,  and 
between  them  images  of  intermediate  colours.  Let  d  be  the  point  of  the 
object  which  is  situated  on  the  axis.  The  rays  from  d  will  converge  to 
R,  V,  and  intermediate  points.  Now  suppose  the  eyeglass  O'  to  be  placed 
in  such  a  manner  that  R  is  the  principal  focus  of  O'  for  the  red  rays,  then 
will  V  be  its  principal  focus  for  the  violet  rays.  Consequently,  the  red 
rays,  after  emerging  from  O',  will  be  parallel  to  the  axis,  and  so  will  the 
violet  rays  emerging  from  V,  and  so  of  any  other  colour.  Consequently, 
the  colours  of  ^,  which  are  separated  by  C,  are  again  combined  by  O'. 
The  same  is  very  nearly  true  of  r  and  ?y,  and  of  r'  and  v'.  Hence  com- 
bination of  lenses  C  and  O'  corrects  the  chromatic  aberration  that 
would  be  produced  by  the  use  of  a  single  eyeglass.  Moreover,  by 
drawing  the  rays  towards  the  axis,  it  diminishes  the  spherical  aberration, 
and,  as  we  shall  see  in  the  next  article,  enlarges  the  field  of  view. 

In  all  eyepieces  consisting  of  two  lenses  the  lens  to  which  the  eye  is 
applied  is  called  the  eye  lens,  the  one  towards  the  object  glass  is  called 
thtjield  lens.  The  eyepiece  above  described  was  invented  by  Huyghens, 
who  was  not,  however,  aware  of  its  property  of  achromatism.  He  de- 
signed it  for  use  with  the  telescope.  It  was  applied  to  the  microscope  by 
Campani.  The  relation  between  the  focal  lengths  of  the  lenses  is  as 
follows  : — The  focal  length  of  the  field  glass  is  three  times  that  of  the  eye 
lens,  and  the  distance  between  their  centres  is  half  the  sum  of  the  focal 
length.  It  easily  follows  from  this  that  the  image  of  the  point  d  would 
but  for  the  interposition  of  the  field  lens,  be  formed  at  D,  which  is  so 
situated  that  CD  is  three  times  DO',  then  the  mean  of  the  coloured 
images  will  be  formed  midway  between  C  and  O^ 

556.  Field  of  view. — By  the  field  of  view  of  an  optical  instrument  is 
meant  all  those  points  which  are  visible  through  the  eyepiece..  ; The 
advantage  obtained  by  the  use  of  an  eyepiece  in  enlarging  the/  jfield  of 


Fig-  438.  lL^ 

view  will  be  readily  understood  by  an  inspection  of  the  accompanying 
figure.  As  before,  O  is  the  object  glass,  C  the  field  lens,  O'  the  eye  le^s, 
and  E  the  eye  placed  on  the  axis  of  the  instrument.  Let  ^z  be  a  point  of 
the  object ;  if  we  suppose  the  field  lens  removed,  the  pencil  of  rays  from  a 
would  be  brought  to  a  focus  at  A,  and  none  of  them  would  fall  on  the  eye 
lens  O',  nor  pass  into  the  eye  E.  Consequently,  a  is  beyond  the  field  of 
view.  But  when  the  field  glass  C  is  interposed,  the  pencil  of  rays  is 
brought  to  a  focus  at  A',  and  emerges  from  O'  into  the  eye.  Conse- 
quently, a  is  now  within  the  field  of  view.  It  is  in  this  manner  that  the 
substitution  of  an  eyepiece  for  a  single  eye  lens  enlarges  the  field  of  view. 


557] 


Magnifying  Power.     Micrometer, 


489 


557.  Magrnifyingr  power.  Micrometer. — The  magnifying  power  of 
any  optical  instrument  is  the  ratio  of  the  magnitude  of  the  image  to  the 
magnitude  of  the  object.  The  magnifying  power  in  a  compound  micro- 
scope is  the  product  of  the  respective  magnifying  powers  of  the  object 
glass  and  of  the  eyepiece  ;  that  is,  if  the  first  of  these  magnifies  20  times, 
and  the  other  10,  the  total  magnifying  power  is  200.  The  magnifying 
power  depends  on  the  greater  or  less  convexity  of  the  object  glass  and  of 
the  eyepiece,  as  well  as  on  the  distance  between  these  two  glasses,  to- 
gether with  the  distance  of  the  object  from  the  object  glass.  A  magni- 
fying power  of  1,500  and  even  upwards  has  been  obtained  ;  but  the  image 
then  loses  in  sharpness  what  it  gains  in  extent.  To  obtain  precise  and 
well  illuminated  images,  the  magnifying  power  ought  not  to  exceed  500 
to  600  diameters,  which  gives  a  superficial  enlargement  25o,cxx)  to 
360,000  times  that  of  the  object. 

The  magnifying  power  is  determined  experimentally  by  means  of  the 
micrometer  ;  this  is  a  small  glass  plate,  on  which,  by  means  of  a  diamond, 
a  series  of  lines  is  drawn  at  a  distance  from  each  other  of  ^^  or  j^^  of  a 
millimetre.  The  micrometer  is  placed  in  front  of  the  object  glass,  and 
then  instead  of  viewing  directly  the  rays  emerging  from  the  eyepiece,  Q, 
they  are  received  on  a  piece  of  glass,  A  (fig.  439),  inclined  at  an  angle  of 
45°,  and  the  eye  is  placed  above  so  as  to  see  the  image  of  the  micrometer 
lines  which  is  formed  by  reflection  on  a  screen,  E,  on  whidr  is  a  scaje 
divided  into  millimetres.  By  counting  the  number  of  di^yiSions  of 
scale  corresponding  to  a  certain  number  of  lines  of  the  iHiage,  the  rifa 
nifying  power  may  be  deduced.  Thus,  if  the  image  occupies  a  space  of  45 
millimetres  on  the  scale,  and  contains  1 5  lines  of  the  micrometer,  the  dis- 
tance between  each  of  which  shall  be  assumed  at 
j^5  millimetre,  the  absolute  magnitude  of  the 
object  will  be  {^-^  millimetre  ;  and  as  the  image 
occupies  a  space  of  45  millimetres,  the  magnifi- 
cation will  be  the  quotient  of  45  by  ~~  or  300. 
The  eye  in  this  experiment  ought  to  be  at 
such  a  distance  from  the  screen,  E,  that  the 
screen  is  distinctly  visible  :  this  distance  varies 
with  different  observers,  but  is  usually  10  to  12 
inches.  The  magnifying  power  of  the  micro- 
scope can  also  be  determined  by  means  of  the 
camera  lucida. 

When  once  the  magnifying  power  is  known, 
the  absolute  magnitude  of  objects  placed  before  the  microscope  is  easily 
deduced.  For,  as  the  magnifying  power  is  nothing  more  than  the 
quotient  of  the  size  of  the  image  by  the  size  of  the  object,  it  follows  that 
the  size  of  the  image  divided  by  the  magnifying  power  gives  the  size 
of  the  object  ;  it  is  in  this  manner  that  the  diameter  of  all  microscopic 
objects  is  determined. 


Fig-  439- 


Y  3 


490 


On  Light. 


[558- 


TELESCOPES. 


558,  Astronomical  telescope. — 1\it.  asironomicaltelescope'xs  used  for 
observing  the  heavenly  bodies  ;  hke  the  microscope,  it  consists  of  a  con- 
densing eyepiece  and  object  glass.     The  object  glass,  M  (fig.  440),  forms 


Fig.  440. 

between  the  eyepiece,  N,  and  its  principal  focus  an  inverted  image  of  the 
heavenly  body,  and  this  eyepiece,  which  acts  as  a  magnifying  glass,  then 
gives  a  virtual  and  highly  magnified  image,  a'b\  of  the  image  ab.  The 
astronomical  telescope  appears,  therefore,  analogous  to  the  microscope  ; 
but  the  two  instruments  difter  in  this  respect :  that  in  the  microscope,  the 
object  being  very  near  the  object  glass,  the  image  is  formed  much  beyond 
the  principal  focus,  and  is  greatly  magnified,  so  that  both  the  object  glass 
and  the  eyepiece  magnify  :  while  in  the  astronomical  telescope,  the 
heavenly  body  being  at  a  great  distance,  the  incident  rays  are  parallel, 
and  the  image  formed  in  the  principal  focus  of  the  object  glass  is  much 
smaller  than  the  object.  There  is,  therefore,  no  magnification  except  by 
the  eyepiece,  and  this  ought,  therefore,  to  be  of  very  short  focal  length. 


Ei£.  441. 

Fig.  441  shows  an  astronomical  telescope  mounted  on  its  stand.  Above 
it  there  is  a  small  telescope,  which  is  called  the  finder.     Telescopes  with 


-559] 


Terrestrial  Telescope. 


49^ 


a  large  magnifying  power  are  not  convenient  for  finding  a  star,  as  they 
have  but  a  small  field  of  view  :  the  position  of  the  star  is,  accordingly, 
first  sought  by  the  finder,  which  has  a  much  larger  field  of  view,  that  is, 
takes  in  a  far  greater  extent  of  the  heavens  :  it  is  then  viewed  by  means 
of  the  telescope. 

ACB 

The  magnification  (note,  art.  552)  equals  - 7^-77  (^0-  44°) ;  that  is,  it  equals 

^,  and  therefore  is  approximately  equal  to  --,  F  beingthe  focus  of  the 
bO  C  OF 

object  glass,  M,  and  being  supposed  very  nearly  to  coincide  with  the  focus 

of  the  eyepiece,  N  ;  it  may,  therefore,  be  concluded  that  the  magnifying 

power  is  greater  in  proportion  as  the  object  glass  is  less  convergent,  and 

the  eyepiece  more  so. 

When  the  telescope  is  used  to  make  an  accurate  observation  of  the 
stars,  for  example,  their  zenith  distance  or  their  passage 
over  the  meridian,  a  C7'0ss  wire  is  added.  This  consists  of 
two  very  fine  metal  wires  or  spider  threads  stretched 
across  a  circular  aperture  in  a  small  metal  plate  (fig.  442). 
The  wires  ought  to  be  placed  in  the  position  where  the 
inverted  image  is  produced  by  the  object  glass,  and  the 
point  where  the  wires  cross  ought  to  be  on  the  optical  axis  ^'^"  '*'*^' 
of  the  telescope,  which  thus  becomes  the  line  of  sight  or  collimaiion. 

559.  Terrestrial  telescope.  — The  terrestrial  telescope  di^trsirom  the 
astronomical  telescope  in  producing  images  in  their  right  positions. 
This  is  effected  by  means  of  two  condensing  glasses,  P  and  O   (fig.  443), 


Fig.  443- 


placed  between  the  object  glass,  M,  and  the  eyepiece,  R.  The  object 
being  supposed  to  be  at  AB,  at  a  greater  distance  than  can  be  shown  in 
the  drawing,  an  inverted  and  much  smaller  image  is  formed  at  ba  on  the 
other  side  of  the  object  glass.  But  the  second  lens,  P,  is  at  such  a 
distance  that  its  principal  focus  coincides  with  the  image  ab  ;  from  which 
it  follows  that  the  luminous  rays  which  pass  through  b,  for  example,  after 
traversing  the  lens,  P,  take  a  direction  parallel  to  the  secondary  axis,  bO 
(520).  Similarly  the  rays  passing  by  a  take  a  direction  parallel  to  the 
axis  aO.  After  crossing  on  H,  these  various  rays  traverse  a  third  lens. 
O,  whose  principal  focus  coincides  with  the  point  H.  The  pencil  BbH 
converges  towards  b\  on  a  secondary  axis  O'  b',  parallel  to  its  direction  ; 
the  pencil  A^H  converging  in  the  same  manner  at  ^ ,  an  erect  image  of 
the  object,  AB,  is  produced  at  a'  b'.  This  image  is  viewed,  as  in  the 
astronomical  telescops,  through  a  condensing  eyepiece,  R,  so  placed  that . 


492  On  Light.  [559- 

it  acts  as  a  magnifying  glass,  that  is,  its  distance  from  the  image,  a'  h\  is 
less  than  the  principal  focal  distance ;  hence,  there  is  formed,  at  a'  b',  a 
virtual  image  of  a'  b',  erect,  and  much  magnified.  The  lenses  P  and  O, 
which  only  serve  to  rectify  the  position  of  the  image,  are  fixed  in  a  brass 
tube,  at  a  constant  distance,  which  is  equal  to  the  sum  of  their  principal 
focal  distances.  The  object  glass,  M,  moves  in  a  tube,  and  can  be  moved 
to  or  from  the  lens  P,  so  that  the  image,  ab,  is  always  formed  in  the  focus 
of  the  lens  whatever  be  the  distance  of  the  object.  The  distance  of  the 
lens,  R,  may  also  be  varied  so  that  the  image  a^'  b'\  may  be  formed  at  the 
distance  of  distinct  vision. 

This  instrument  may  also  be  used  as  an  astronomical  telescope  by  using 
a  different  eyepiece ;  this  must  have  a  much  greater  magnifying  power 
than  the  former  cases. 

In  the  terrestrial  telescope  the  magnifying  power  is  the  same  as  in  the 
astronomical  telescope,  provided  always  that  the  correcting  glasses,  P  and 
O,  have  the  same  convexity. 

560.  Calilean  telescope. — The  Galilean  Telescope  is  the  simplest  of 
all  telescopes,  for  it  only  consists  of  two  lenses,  namely,  an  object  glass, 


Fig.  444. 

M,  and  a  diverging  or  double  concave  eyepiece,  R  (fig.  444),  and  it  gives 
at  once  an  erect  image.     Opera  glasses  are  constructed  on  this  principle. 

If  the  object  be  represented  by  the  right  line  AB,  a  real  but  inverted 
and  smaller  image  would  be  formed  at  ba  ;  but  in  traversing  the  eyepiece, 
R,  the  rays  emitted  from  the  points  A  and  B  are  refracted,  and  diverge 
from  the  secondary  axes  bO'  and  .aO\  which  correspond  to  the  points  b 
and  a  of  the  image.  Hence,  these  rays  produced  backward  meet  their 
axes  in  a'  and  b'\  the  eye  which  receives  them  sees  accordingly  an  erect 
and  magnified  image  in  a'  b',  which  appears  nearer  because  it  is  seen  under 
an  angle,  a'  O'  b',  greater  than  the  angle,  AOB,  under  which  the  object  is 
seen. 

The  magnifying  power  is  equal  to  the  ratio  of  the  angle  a'  O'  b'  to  the 
angle  AOB,  and  is  usually  from  2  to  4. 

The  distance  of  the  eyepiece  R  from  the  image  ab  is  pretty  nearly  equal 
to  the  principal  focal  distance  of  this  eyepiece  ;  it  follows,  therefore,  that 
the  distance  between  the  two  lenses  is  the  difference  between  their  re- 
spective focal  distances  ;  hence,  Galileo's  telescope  is  very  short  and  port- 
able. It  has  the  advantage  of  showing  objects  in  their  right  position  ; 
and,  further,  as  it  has  only  two  lenses,  it  absorbs  very  little  light  :  in  con- 
sequence, however,  of  the  divergence  of  the  emergent  rays,  it  has  only  a 
small  field  of  view,  and  in  using  it  the  eye  must  be  placed  very  near  the 


562] 


Reflecting  Telescopes. 


493 


eyepiece.  The  eyepiece  can  be  moved  to  or  from  the  object  glass,  so  that 
the  image  a'  b'  is  always  formed  at  the  distance  of  distinct  vision.  ^ 

The  opera  glass  is  usually  double,  so  as  to  produce  an  image  in  each 
eye,  by  which  greater  brightness  is  attained. 

The  time  at  which  telescopes  were  invented  is  not  known.  Some  at- 
tribute their  invention  to  Roger  Bacon  in  the  13th  century;  others  to 
J.  B.  Porta  at  the  end  of  the  i6th ;  others  again  to  a  Dutchman,  Jacques 
Metius,  who,  in  1609,  accidentally  found  that  by  combining  two  glasses, 
one  concave  and  the  other  convex,  distant  objects  appeared  nearer  and 
much  larger. 

Galileo's  was  the  first  telescope  directed  towards  the  heavens.  By  its 
means  Galileo  discovered  the  mountains  of  the  moon,  Jupiter's  satellites, 
and  the  spots  on  the  sun. 

561.  Reflecting:  telescopes, — The  telescopes  previously  described  are 
refractmg  or  dioptric  telescopes.  It  is,  however,  only  in  recent  times  that 
it  has  been  possible  to  construct  achromatic  lenses  of  large  size  ;  before 
this,  a  concave  metallic  mirror  was  used  instead  of  the  object  glass. 
Telescopes  of  this  kind  are  called  reflecting  or  catoptric  telescopes.  The 
principal  forms  are  those  devised  by  Gregory,  Newton,  Herschel,  and 
Cassegrain. 

562.  The  Gregrorlan  telescope. — Figure  445  is  a  representation  of 
Gregory's  telescope  ;  it  is  mounted  on  a  stand,  about  which  it  is  mov- 


Fig.  445. 


able,  and  can  be  inclined  at  any  angle.  This  mode  of  mounting  is 
optional  ;  it  may  be  equatorially  mounted.  Fig.  446  gives  a  longitudinal 
section.  It  consists  of  a  long  brass  tube  closed  at  one  end  by  a  concave 
metallic  mirror,  M,  which  is  perforated  in  the  centre  by  a  round  aperture 


494 


On  Light. 


[562 


through  which  rays  reach  the  eye.     There  is   a   second  concave  metaikOr 
mirror,  N,  near  the  end  of  the  tube;    it  is  somewhat  larger  than  the 
central  aperture  in  the  large  mirror,  and  its  radius  of  curvature  is  iinici.  . 


S 


Fig.  446. 


smaller  than  that  of  the  large  mirror.  The  axes  of  both  mirrors  coi| 
with  the  axis  of  the  tube.  As  the  centre  of  curvature  of  the  large  mir/or 
is  at  O,  and  its  focus  at  ab,  rays,  such  as  SA,  emitted  from  a  heavenly 
body,  are  reflected  from  the  mirror,  M,  and  form  at  ab  an  inverted  and! 
very  small  image  of  the  heavenly  body.  The  distance  of  the  mirrors  and 
their  curvatures  is  so  arranged  that  the  position  of  this  image  is  between 
the  centre,  0,  and  the  focus,/,  of  the  small  mirror  ;  hence  the  rays,  after 
being  reflected  a  second  time  from  the  mirror  N,  form  at  a'  b'  a  magnified 
and  inverted  image  oiab^  and  therefore  in  the  true  position  of  the  heavenly 
body.  This  image  is  viewed  through  an  eyepiece,  P,  which  may  either 
be  single  or  compound,  its  object  being  to  magnify  it  again  so  that  it  is 
seen  at  a"  b''. 

As  the  objects  viewed  are  not  always  at  the  same  distance,  the  focus 
of  the  large  mirror,  and  therefore  that  of  the  small  one,  vary  in  position. 

And  as  the  distance  of  distinct  vision  is  not  the  same  with  all  eyes,  the 
image  a"  b"  ought  to  be  formed  at  different  distances.  The  required  ad- 
justments may  be  obtained  by  bringing  the  small  mirror  nearer  or  farther 
from  the  larger  one  ;  this  is  effected  by  means  of  a  milled  head,  A  (fig.  445), 
which  turns  a  rod,  and  this  by  a  screw  moves  a  piece  to  which  the  mirror 
is  fixed. 

563.  The  ITewtonian  telescope. — This  instrument  does  not  differ 
much  from  that  of  Gregory ;  the  large  mirror  is  not  perforated  and  there 


IS  a  sman^i^ne  mirror  mc'hped  at  an  angle  of  45°  towards  an  eyepiece 
placed  in  the  side  of  theJele*(iope.  The  difficulty  of  constructing  metallic 
mirrors  has  caused . t^escxa^  of  Gregorian  and  Newtonian  constructioa 


J 


-563] 


Telescopes. 


495 


to  fall  into  disuse.  Of  late,  however,  the  process  of  silvering  glass  mirrors 
has  been  carried  to  a  high  state  of  perfection,  and  M.  Foucault  has  applied 
these  mirrors  to  Newtonian  telescopes  with  great  success.  His  first  mirror 
was  only  four  inches  in  diameter,  but  he  has  successively  constructed 
mirrors  of  8,  1 2,  and  1 3  inches,  and  at  the  time  of  his  death  had  completed 
one  of  32  inches  diameter. 

Fig.  448  represents  a  Newtonian  telescope  mounted  on  an  equatoriaL 


Fij.  448. 


stand,  and  fig.  447  gives  a  horizontal  section  of  it.  This  section  shows  how 
the  luminous  rays  reflected  from  the  parabolic  mirror,  M,  meet  a  small 
rectangular  prism,  ;//;/,  which  replaces  the  inclined  plane  mirror  used  in 


49^  On  Light.  [563- 

the  old  form  of  Newtonian  telescope.  After  undergoing  a  total  reflection 
from  ;««,  the  rays  form  at  ab  a  very  small  image  of  the  heavenly  body. 
This  image  is  viewed  through  an  eyepiece  with  four  lenses  placed  on  the 
side  of  the  telescope,  and  magnifying  from  50  to  800  times,  according  to 
the  sizeof  the  silvered  mirror. 

In  reflectors  the  mirror  acts  as  object  glass,  but  there  is,  of  course,  no 
chromatic  aberration.  The  spherical  aberration  is  corrected  by  the 
form  given  to  the  reflector,  which  is  paraboloid,  but  slightly  modified  by 
trial  to  suit  the  eye-piece  fitted  to  the  telescope. 

The  mirror  once  polished  is  immersed  in  a  silvering  liquid,  which  con- 
sists essentially  of  ammoniacal  solution  of  nitrate  of  silver,  to  which  some 
reducing  agent  is  added.  When  a  polished  glass  surface  is  immersed  in 
this  solution,  silver  is  deposited  on  the  surface  in  the  form  of  a  brilliant 
metallic  layer,  which  adheres  so  firmly  that  it  can  be  polished  with  rouge 
in  the  usual  manner.  These  new  telescopes  with  glass  mirrors  have  the 
advantage  over  the  old  ones  that  they  give  purer  images,  they  weigh 
less,  and  are  much  shorter,  their  focal  distance  being  only  about  six  times 
the  diameter  of  the  mirror. 

These  details  known,  the  whole  apparatus  remains  to  be  described. 
The  body  of  the  telescope  (fig.  448)  consists  of  an  octagonal  wooden 
tube.  The  end,  G,  is  6pen  ;  the  mirror  is  at  the  other  end.  At  a  certain 
distance  from  this  end,  two  axles  are  fixed,  which  rest  on  bearings  sup- 
ported by  two  wooden  uprights,  A  and  B.  These  are  themselves  fixed 
to  a  table,  PO,  which  turns  on  a  fixed  plate,  RS,  placed  exactly  parallel 
to  the  equator.  On  the  circumference  of  the  turning  table  there  is  a 
brass  circle,  divided  into  360  degrees,  and  beneath  it,  but  also  fixed  to 
the  turning  table,  there  is  a  circular  toothed  wheel,  in  which  an  endless 
screw,  V,  works.  By  moving  this  in  either  direction  by  means  of  the 
handle  w,  the  table  PQ,  and  with  it  the  telescope,  can  be  turned.  A 
vernier,  x.,  fixed  to  the  plate  RS,  gives  the  fractions  of  a  degree.  On  the 
axis  of  the  motion  of  the  telescope  there  is  a  graduated  circle,  O,  which 
serves  to  measure  the  declitiation  of  the  star,  that  is,  its  angular  distance 
from  the  equator;  while  the  degrees  traced  round  the  table,  RS,  serve  to 
measure  the  fight  ascension,  that  is,  the  angle  which  the  declination 
circle  of  the  star  makes  with  the  declination  circle  passing  through  the 
first  point  of  Aries. 

In  order  to  fix  the  telescope  in  declination,  there  is  a  brass  plate,  E, 
fixed  to  the  upright ;  it  is  provided  with  a  clamp,  in  which  the  limb  O 
works,  and  which  can  be  screwed  tight  by  means  of  a  screw  with  a  milled 
head,  r.  On  the  side  of  the  apparatus  there  is  the  eyepiece,  0,  which  is 
mounted  on  a  sliding  copperplate,  on  which  there  is  also  the  small  prism 
inn,  represented  in  section  in  fig.  447.  To  bring  the  image  to  the  right 
place,  this  plate  may  be  moved  by  means  of  a  rack  and  a  milled  head,  a. 
The  handle,  n,  serves  to  clamp  or  unclainp  the  screw,  V.  The  drawing 
was  one  taken  from  a  telescope,  the  mirror  of  which  is  only  6^  inches  in 
diameter,  and  which  gives  a  magnifying  power  of  1 50  to  200. 

564.  The  Kerscbelian  telescope. — SirW.  Herschel's  telescope,  which, 


I 


565] 


Camera  Obscura. 


A97 


until  recently,  was  the  most  celebrated  instrument  of  modern  times,  was 
constructed  on  a  method  differing  from  those  described.  The  mirror  was 
so  inclined  that  the  image  of  the  star  was  formed  at  ab  on  the  side  of  the 
telescope  near  the  eyepiece,^;  hence  it  is  termed the/r6';z/7/2V7£/ telescope. 


As  the  rays  in  this  telescope  only  undergo  a  single  reflection,  the  loss  of 
light  is  less  than  in  either  of  the  preceding  cases,  and  the  image  is  there- 
fore brighter.  The  magnifying  power  is  the  quotient  of  the  principal  focal 
distance  of  the  mirror  by  the  focal  distance  of  the  eyepiece. 

Herschel's  great  telescope  was  constructed  in  1789  ;  it  was  40  feet  in 
length,  the  great  mirror  was  50  inches  in  diameter.  The  quantity  of 
light  obtained  by  this  instrument  was  so  great  as  to  enable  its  inventor 
to  use  magnifying  powers  far  higher  than  anything  which  had  hitherto 
been  attempted. 

Herschel's  telescope  has  been  exceeded  by  one  constructed  by  the  late 
Earl  of  Rosse.  This  magnificent  instrument  has  a  focal  length  of  53 
feet,  the  diameter  of  the  speculum  being  six  feet.  It  is  at  present  used  as 
a  Newtonian  telescope,  but  it  can  also  be  arranged  as  a  front  view 
telescope. 


INSTRUMENTS   FOR    FORMING   PICTURES   OF   OBJECTS. 

565.  Camera  obscura. — The  camera  obscura  (dark  chamber)  is,  as  its 
name  implies,  a  closed  space  impervious  to  light.  There  is,  however,  a 
small  aperture  by  which  luminous  rays  enter,  as  shown  in  fig.  450.  The 
rays,  proceeding  from  external  objects,  and  entering  by  this  aperture,  form 
on  the  opposite  side  an  image  of  the  object  in  its  natural  colours,  but  of 
reduced  dimensions,  and  in  an  inverted  position. 

Porta,  a  Neapolitan  physician,  the  inventor  of  this  instrument,  found 
that  by  fixing  a  double  convex  lens  in  the  aperture,  and  placing  a  white 
screen  in  the  focus,  the  image  was  much  brighter,  and  more  definite. 

Fig.  450  represents  a  camera  obscura,  such  as  is  used  for  drawing.  It 
consists  of  a  rectangular  wooden  box,  formed  of  two  parts  which  slide  in 
and  out.  The  luminous  rays,  R,  pass  into  the  box  by  a  lens,  B,  and  form 
an  image  on  the  opposite  side,  O,  which  is  at  the  focal  distance  of  the  lens. 
But  the  rays  are  reflected  from  a  glass  mirror,  M,  inclined  at  an  angle  of 
45°,  and  form  an  image  on  the  ground  glass  plate,  N.     When  a  piece  of 


On  Light. 


[565- 


tracing  paper  is  placed  on  this  screei),  a  drawing  of  the  image  is  easily 
made.     A  wooden  door,  A,  cuts  off  extraneous  light. 


The  box  is  formed  of  two  parts,  sliding  one  within  the  other,  like  the 
joints  of  a  telescope,  so  that,  by  elongating  it  more  or  less,  the  reflected 

image  may  be  made  to  fall 
exactly  on  the  screen,  N ,  at 
whatever  distance  the  object 
may  be  situated. 

Fig.  451  shows  another 
kind  of  camera  obscura, 
which  is  occasionally  erected 
in  summer  houses.  In  a 
brass  case,  A,  there  is  a  tri- 
angular prism,  P  (fig.  452), 
which  acts  both  as  condens- 
ing lens  and  as  mirror.  One 
of  its  faces  is  plane,  but  the 
others  have  such  curvatures 
that  the  combined  refrac- 
tions on  entering  and  emerg- 
ing from  the  prism  produce 
the  effect  of  a  meniscus  lens. 
Hence  rays  from  an  object, 
AB,  after  passing  into  the 
prism  and  undergoing  total 
reflection  from  the  face  cd^ 
form  at  abdi  real  image  of  AB. 
In    fig.    451,   the     small 


I 


t'ig-  451 


table  B  corresponds  to  the  focus  of  the  prism  in  the  case  A,  and  an  image 


566] 


Camera  Obsciira. 


499 


for.ns  on  a  piece  of  paper  placed  on  the  table.  The  whole  is  surrounded 
by  a  black  curtain,  so  that  the  observer  can  place  himself  in  complete 
darkness. 

566.  Camera  lucida.— The  camera  lucida  is  a  small  instrument  de- 
pending on  internal  reflection,  and  serves  for  taking  an  outline  of  any 
object.  It  was  invented  by  Dr.  Wollaston,  in  1804.  It  consists  of  a  smal 
four-sided  glass  prism,  of  which  fig.  453  gives  a  section  perpendicular  to 
the  edges.     A   is  a  right  angle,  and  C  an 

angle  of  135°;  the  other  angles  B  and  D,       a 

are  67^°.  The  prism  rests  on  a  stand,  on  [—- 
which  it  can  be  raised  or  lowered,  and  turned  ^ 
more  or  less  about  an  axis  parallel  to  the 
prismatic  edges.  When  the  face,  AB,  is 
turned  towards  the  object,  the  rays  from  the 
object  fall  nearly  perpendicular  on  this  face, 
pass  into  the  prism  without  any  appreciable 
reifraction,  and  are  totally  reflected  from  BC; 
for  as  the  line  ab  is  perpendicular  to  BC,  and 
«L   to   AB,  the   angle  a«L   will   equal  the 

an ^^rg?:^j[^  is.  it  will  contain  67^°,  and  this  being  greater  than  the  critical 
^g^feoYglas^^joS),  the  ray  L?/ will  undergo  total  reflection.  The  rays 
i*are  again  totally  reflected  from  o,  and  emerge  near  the  summit,  D,  in  a 
direction  ^almost  .perpendicular  to  the  face  DA,  so  that  the  eye  which  re- 
ceives the  i-ays  sees  at  U  an  image  of  the  object  L.    If  the  outlines  of  the 


Fig.  452. 


(k 


Fig-  453- 


Fig.  454- 


image  are  traced  with  a  pencil,  a  very  correct  design  is  obtained;  but  un- 
fortunately there  is  a  great  difficulty  in  seeing  both  the  image  and  the 
point  of  the  pencil,  for  the  rays  from  the  object  give  an  image  which  is 
farther  from  the  eye  than  the  pencil.  This  is  corrected  by  placing  be- 
tween the  eye  and  prism  a  lens,  I,  which  gives  to  the  rays  from  the  pencil 
and  those  from  the  object  the  same  divergence.  In  this  case,  however, 
it  is  necessary  to  place  the  eye  very  near  the  edge  of  the  prism,  so  that 
the  aperture  of  the  pupil  is  divided  into  two  parts,  one  of  which  sees  the 
image  and  the  other  the  pencil. 

Amici's  camera  lucida,  represented  in  fig.  454,  is  preferable  to  that  of 
Wollaston,  inasmuch  as  it  allows  the  eye  to  change  its  position  to  a  con- 


500 


On  Light. 


[566- 


siderable  extent,  without  ceasing  to  see  the  image  and  the  pencil  at  the 
same  time.  It  consists  of  a  rectangular  glass  prism,  ABC,  having  one  of 
its  perpendicular  faces  turned  towards  the  object  to  be  depicted,  while 
the  other  is  at  right  angles  to  an  inclined  plate  of  glass,  mn.  The  rays, 
LI,  proceeding  from  the  object,  and  entering  the  prism,  are  totally  re- 
flected from  its  base  at  D,  and  emerge  in  the  direction  KH.  They  are 
then  partially  reflected  from  the  glass  plate  mn  at  H,  and  form  a  vertical 
image  of  the  object,  L,  which  is  seen  by  the  eye  in  the  direction  OL''.  The 
eye  at  the  same  time  sees  through  the  glass  the  point  of  a  pencil  applied 
to  the  paper,  and  thus  the  outline  of  the  picture  may  be  traced  with  great 
exactness. 

567.  IMEagrlc  lantern. — This  is  an  apparatus  by  which  a  magnified 
image  of  small  objects  may  be  projected  on  a  white  screen  in  a  dark 
room.  It  consists  of  a  tin  plate  box,  in  which  there  is  a  lamp  placed  in 
the  focus  of  a  concave  mirror,  A  (fig.  456).  The  reflected  rays  fall  upon 
a  condensing  lens,  B  (fig.  455),  which  concentrates  them  on  the  figure 
painted  on  a  glass  plate,  V.  There  is  a  double  convex  lens,  C,  at  a  dis- 
tance from  V  of  rather  more  than  its  focal  distance,  and,  consequently,  a 
real  and  very  much  magnified  image  of  the  figure  on  the  glass  is  produced 
on  the  screen  (524). 

Dissolving  views  are  obtained  by  arranging  two  magic  lanterns,  which 
are  quite  alike,  with  diflerent  pictures,  in  such  a  manner  that  both  pictures 

Fig.  455. 


Fig.  456. 

are  produced  on  exactly  the  same  part  of  a  screen.  The  object  glasses  of 
both  lanterns  are  closed  by  screens,  which  are  so  arranged  that  according 
as  one  is  raised  the  other  is  lowered,  and  vice  versa.  In  this  way  one 
picture  is  gradually  seen  to  change  into  the  other. 

The  magnify.ng  power  of  the  magic  lantern  is  obtained  by  dividing 
the  distance  of  the  lens  C  from  the  image  by  its  distance  from  the  object. 
If  the  image  is  100  or  1,000  times  farther  from  the  lens  than  the  object,  the 
image  will  be  100  or  1,000  times  as  large.  Hence  a  lens  with  a  very  short 
focus  can  produce  a  very  large  image,  provided  the  screen  is  sufficiently 
large. 


I 


■**     ^^^ 


-568] 


Solar  Microscope. 


501 


568.  Solar  microscope. — The  solar  microscope  is  in  reality  a  magic 
lantern  illuminated  by  the  sun's  rays  ;  it  serves  to  produce  highly  magnified 
images  of  very  small  objects.     It  is  worked  in  a  dark  room ;  fig.   457 


Fig.  457- 

represents  it  fitted  in  the  shutter  of  a  room,  and  fig.  458  gives  the  internal 
details. 

The  sun's  rays  fall  on  a  plane  mirror,  M,  placed  outside  the  room,  and 
are  reflected  towards  a  condensing  lens,  /,  and  from  thence  to  a  second 


Fig.  458. 

lens,  0  (fig.  458),  by  which  they  are  concentrated  at  its  focus.  The  object 
to  be  magnified  is  at  this  point  ;  it  is  placed  between  two  glass  plates, 
which,  by  means  of  a  spring,  ;z,  are  kept  in  a  firm  position  between  two 
metal  plates,  ;;z.  The  object  thus  strongly  illuminated  is  very  near  the 
focus  of  a  system  of  three  condensing  lenses,  x,  which  forms  upon  a 
screen  at  a  suitable  distance  an  inverted  and  greatly  magnified  image,  ab. 
The  distance  of  the  lenses,  0  and  x^  from  the  object  is  regulated  by  means 
of  screws,  C  and  D. 

As  the  direction  of  the  sun's  hght  is  continually  varying,  the  position 


502  On  Light.  [568- 

of  the  mirror  outside  the  shutter  must  also  be  changed,  so  that  the  re- 
flection is  always  in  the  direction  of  the  axis  of  the  microscope.  The 
most  exact  apparatus  for  this  purpose  is  the  heliostat  (502)  ;  but  as  this 
instrument  is  very  expensive,  the  object  is  usually  attained  by  inclining 
the  mirror  to  a  greater  or  less  extent  by  means  of  an  endless  screw  B, 
and  at  the  same  time  turning  the  mirror  itself  round  the  lens,  /,  by  a  knob 
A,  which  moves  in  a  fixed  slide. 

The  solar  microscope  labours  under  the  objection  of  concentrating 
great  heat  on  the  object,  which  soon  alters  it.  This  is  partially  obviated 
by  interposing  a  layer  of  a  saturated  solution  of  alum,  which,  being  a 
powerfully  athermanous  substance  (407),  cuts  off  a  considerable  portion 
of  the  heat. 

The  magnifying  power  of  the  solar  microscope  may  be  deduced  experi- 
mentally by  substituting  for  the  object  a  glass  plate  marked  with  lines  at 
a  distance  of  Y(>  or,  ^^^  of  a  millimetre.  Knowing  the  distance  of  these 
lines  on  the  image,  the  magnifying  power  may  be  calculated.  The  same 
method  is  used  with  the  photoelectric  light.  According  to  the  magnify- 
ing power  which  it  is  desired  to  obtain,  the  objective  x  is  formed  of  one. 
two,  or  three  lenses,  which  are  all  achromatic. 

The  solar  microscope  furnishes  the  means  of  exhibiting  to  a  large 
audience  many  curious  phenomena,  such  for  instance,  as  the  circulation 
of  blood  in  the  smaller  animals,  the  crystallisation  of  salts,  the  occur- 
rence of  animalculae  in  water,  vinegar,  etc. 

569.  Pbotoelectric  microscope. — This  is  nothing  more  than  the  solar 
microscope,  which  is  illuminated  by  the  electric  Hght  instead  of  by  the 
sun's  rays.  The  electric  light,  by  its  intensity,  its  steadiness,  and  the 
readiness  with  which  it  can  be  procured  at  any  time  of  the  day,  is  far 
preferable  to  the  solar  light.  The  photoelectric  microscope  alone  .will  be 
described  here :  the  electric  light  will  be  considered  under  the  head  of 
Galvanism. 

Fig.  459  represents  the  arrangement  devised  by  M.  Duboscq.  A  solar 
microscope,  ABD,  identical  with  that  already  described,  is  fixed  on  the 
outside  of  a  brass  box.  In  the  interior  are  two  charcoal  points  which 
do  not  quite  touch,  the  space  between  them  being  exactly  on  the  axis 
of  the  lenses.  The  electricity  of  one  end  of  a  powerful  battery  reaches 
the  charcoal,  a,  by  means  of  a  copper  wire,  K  ;  while  the  electricity 
from  the  opposite  end  of  the  battery  reaches  ^  by  a  second  copper 
wire,  H. 

During  the  passage  of  the  electricity,  a  luminous  arc  is  formed  between 
the  two  ends  of  the  carbons,  which  gives  a  most  brilliant  light,  and 
powerfully  illuminates  the  microscope.  This  is  effected  by  placing  at  D 
in  the  inside  of  the  tube  a  condensing  lens,  whose  principal  focus  corre- 
sponds to  the  space  between  the  two  charcoals.  In  this  manner  the 
luminous  rays,  which  enter  the  tubes,  D  and  B,  are  parallel  to  their  axis, 
and  the  same  effects  are  produced  as  with  the  ordinary  solar  microscope ; 
a  magnified  image  of  the  object  placed  between  two  plates  of  glass  is 
produced  on  the  screen. 

In  continuing  the  experiment  the  two  carbons  become  consumed,  and 


570] 


Lighthoitse  Lenses. 


503 


to  an  unequal  extent,  a  more  quickly  than  c.  Hence,  their  distance 
increasing,  the  light  becomes  weaker,  and  is  ultimately  extinguished.  In 
speaking  afterwards  of  this  electric  light,  the  working  of  the  apparatus, 


i''ig-  459- 

P,  which  keeps  these  charcoals  at  a  constant  distance,  and  thus  ensures 
a  constant  light,  will  be  explained. 

The  part  of  the  apparatus,  MN,  may  be  considered  as  a  universal 
photogenic  appaj'atiis.  The  microscope  can  be  replaced  by  the  head  pieces 
of  the  phantasmagoria,  the  polyorama,  the  megascope,  by  polarising  ap- 
paratus, etc.,  and  in  this  manner  is  admirably  adapted  for  exhibiting 
optical  phenomena  to  a  large  auditory.  Instead  of  the  electric  light, 
we  may  use  with  this  apparatus  the  oxy-hydrogen  or  Drummond's  light, 
which  is  obtained  by  heating  a  cylinder  of  lime  in  the  flame  produced 
by  the  combustion  of  a  mixture  of  hydrogen  and  oxygen  gases. 

570.  Kigrbtbouse  lenses. — Lenses  of  large  dimensions  are  very  dif- 
ficult of  construction  ;  they  further  produce  a  considerable  spherical  aber- 
ration, and  their  thickness  causes  the  loss  of  much  light.  In  order  to 
avoid  these  inconveniences,  Echelon  lenses  have  been  constructed.  They 
consist  of  a  plano-convex  lens,  C  (figs.  460,  and  461),  surrounded  by  a 
series  of  annular  and  concentric  segments,  A,  B,  each  of  which  has  a 


504 


Oil  LigJit. 


[570- 


plane  face  on  the  same  side  as  the  plane  face  of  the  central  lens,  while  the 
faces  on  the  other  side  have  such  a  curvature  that  the  foci  of  the  different 
segments  coincide  in  the  same  point.  These  rings  form,  together  with  the 
central  lens,  a  single  lens,  a  section  of  which  is  represented  in  fig.  461. 
The  drawing  was  made  from  a  lens  of  about  2  feet  in  diameter,  the 
segments  of  which  are  formed  of  a  single  piece  of  glass  ;  but  with  larger 
lenses,  each  segment  is  likewise  formed  of  several  pieces. 

Behind  the  lens  there  is  a  support  fixed  by  three  rods,  on  which  a  body- 


Fig.  460 

can  be  placed  and  submitted  to  the  sun's  rays.  As  the  centre  of  the 
support  coincides  with  the  focus  of  the  lens,  the  substances  placed  there 
are  melted  and  volatilised  by  the  high  temperature  produced.  Gold, 
platinum,  and  quartz  are  rapidly  melted.  The  experiment  proves  that 
heat  is  refracted  in  the  same  way  as  light :  for  the  position  of  the  calor- 
ific focus  is  identical  with  that  of  the  luminous  focus. 

Formerly  parabolic  mirrors  were  used  in  sending  the  light  of  beacons 
and  lighthouses  to  gi'eat  distances,  but  they  have  been  supplanted  by  the 
use  of  lenses  of  the  above  construction. 


-571]  PJiGiooraphy.  505 

lamp  of  peculiar  construction,  which  gives  as  much  light  as  20  moderators. 
The  light  is  placed  in  the  principal  focus  of  the  lens  so  that  the  emergent 
rays  form  a  parallel  beam  (fig.  401),  which  loses  intensity  only  by  passing 
through  the  atmosphere,  and  can  be  seen  at  a  distance  of  above  40  miles. 
In  order  that  all  points  of  the  horizon  may  be  successively  illuminated,  the 
lens  is  continually  moved  round  the  lamp  by  a  clockwork  motion,  the  rate 
of  which  varies  with  different  lighthouses.  Hence,  in  different  parts,  the 
light  alternately  appears  and  disappears  after  equal  intervals  of  time. 
These  alternations  serve  to  distinguish  lighthouses  from  an  accidental 
fire  or  a  star.  By  means  too  of  the  number  of  times  the  light  disappears 
in  a  given  time,  and  by  the  colour  of  the  light,  sailors  are  enabled  to 
distinguish  the  lighthouses  from  one  another,  and  hence  to  know  their 
position. 

Of  late  years  the  use  of  the  electric  light  has  been  substituted  for  that 
of  oil  lamps;  a  description  of  the  apparatus  will  be  given  in  a  subsequent 
chapter. 

PHOTOGRAPHY. 

571 .  Dag-uerreotype. — Photography  is  the  art  of  fixing  the  images  of 
the  camera  obscura  on  substances  sensitive  to  light.  The  various  photo- 
graphic processes  may  be  classed  under  three  heads  :  photography  on 
metal,  photography  on  paper,  and  photography  on  glass. 

Wedgwood  was  the  first  to  suggest  the  use  of  chloride  of  silver  in 
fixing  the  image,  and  Davy,  by  means  of  the  solar  microscope,  obtained 
images  of  small  objects  on  paper  impregnated  with  chloride  of  silver; 
but  no  method  was  known  of  preserving  the  images  thus  obtained,  by 
preventing  the  further  action  of  light.  Niepce,  in  18 14,  obtained  per- 
manent images  of  the  camera  by  coating  glass  plates  with  a  layer  of 
a  varnish  composed  of  bitumen  dissolved  in  oil  of  lavender.  This  pro- 
cess was  tedious  and  inefficient,  and  it  was  not  until  1839  ^^^^-^  the  pro- 
blem was  solved.  In  that  year,  Daguerre  described  a  method  of  fixing 
the  images  of  the  camera,  which,  with  the  subsequent  improvements 
of  Talbot  and  Archer,  has  rendered  the  art  of  photography  one  of  the 
most  marvellous  discoveries  ever  made,  either  as  to  the  beauty  and  per- 
fection of  the  results,  or  as  to  the  celerity  with  which  they  are  produced. 

In  Daguerre's  process,  the  Daguerreotype^  the  picture  is  produced  on 
a  plate  of  copper  coated  with  silver.  This  is  first  very  carefully  polished, 
an  operation  on  which  much  of  the  success  of  the  subsequent  operations 
depends.  It  is  then  rendered  sensitive  by  exposing  it  to  the  action  of 
iodine  vapour,  which  forms  a  thin  layer  of  iodide  of  silver  on  the  surface. 
The  plate  is  now  fit  to  be  exposed  in  the  camera  ;  it  is  sensitive  enough 
for  views  which  require  an  exposure  of  ten  minutes  in  the  camera,  but 
when  greater  rapidity  is  required,  as  for  portraits,  etc.,  it  is  further 
exposed  to  the  action  of  an  accelerator^  such  as  bromine  or  hypobromite 
of  calcium.  All  these  operations  must  be  performed  in  a  room  lighted 
by  a  candle,  or  by  the  daylight  admitted  through  yellow  glass,  which 
cuts  off  all  chemical  rays.     The  plate  is  preserved  from  the  action  of 

z 


5o6 


On  Light. 


[571- 


light  by  placing  it  in  a  small  wooden  case  provided  with  a  slide  on  the 
sensitive  side. 

The  third  operation  consists  in  exposing  the  sensitive  plate  to  the 
action  of  light,  placing  it  in  that  position  in  the  camera  where  the  image 
is  produced  with  greatest  delicacy.  For  photographic  purposes  a  camera 
obscura  of  peculiar  construction  is  used.     The  brass  tube,  A  (fig.  462), 

l> 


Fig.  462. 

contains  an  achromatic  condensing  lens,  which  can  be  moved  by  means 
of  a  rackwork  motion,  to  which  is  fitted  a  milled  head,  D.  At  the  op- 
posite end  of  the  box  is  a  ground-glass  plate,  E,  which  slides  in  a  groove, 
B,  in  which  the  case  containing  the  plate  also  fits.  The  camera  being 
placed  in  a  proper  position  before  the  object,  the  sliding  part  of  the  box 
is  adjusted  until  the  image  is  produced  on  the  glass  with  the  utmost 
sharpness  ;  this  is  the  case  when  the  glass  slide  is  exactly  in  the  focus. 
The  final  adjustment  is  made  by  means  of  the  milled  head,  D. 

The  glass  slide  is  then  replaced  by  the  case  containing  the  sensitive 
plate ;  the  slide  which  protects  it  is  raised  ;  and  the  plate  exposed  for  a 
time,  the  duration  of  which  varies  in  different  cases,  and  can  only  be 
hit  exactly  by  great  practice.  The  plate  is  then  removed  to  a  dark  room. 
No  change  is  perceptible  to  the  eye,  but  those  parts  on  which  the  light 
has  acted  have  acquired  the  property  of  condensing  mercury :  the  plate 
is  next  placed  in  a  box  and  exposed  to  the  action  of  mercurial  vapour  at 
60  or  70  degrees. 

The  mercury  is  deposited  on  the  parts  affected,  in  the  form  of  globules 
imperceptible  to  the  naked  eye.  The  shadows,  or  those  parts  on  which 
the  light  has  not  acted,  remain  covered  with  the  layer  of  iodide  of  silver. 
This  is  removed  by  treatment  with  hyposulphite  of  sodium,  which  dis- 
solves iodide  of  silver  without  affecting  the  rest  of  the  plate.  The  plate  is 
next  immersed  in  a  solution  of  chloride  of  gold  in  hyposulphite  of  sodium, 
which  dissolves  the  silver,  while  some  gold  combines  with  the  mercury 
and  silver  of  the  parts  attacked,  and  greatly  increases  the  intensity  of  the 
lustre. 

Hence  the  light  parts  of  the  image  aie  those  on  which  the  mercury 


572] 


Photography. 


507 


has  been  deposited,  and  the  shaded  those  on  which  the  metal  has  retained 
its  reflecting  lustre.  -^ 

Fig.  463  represents  a  section  of  the  camera  and  the  object  glass.  At 
first  it  consisted  of  a  double  convex  lens,  but  now  double  achromatic 
lenses,  L  L',  are  used  as  object  glasses.     They  act  more  quickly  than  ob- 


Fig.  463- 


jectives  with  a  single  lens,  have  a  shorter  focus,  and  can  be  more  easily 
focussed  by  moving  the  lens,  L',  by  means  of  the  rack  and  pinion,  D. 

572.  Photographs  on  paper. — In  Daguerre's  process,  which  has  just 
been  described,  the  images  are  produced  directly  on  metal  plates. 
With  paper  and  glass,  photographs  of  two  kinds  may  be  obtained  : 
those  in  which  an  image  is  obtained  with  reversed  tints,  so  that  the 
lightest  parts  have  become  the  darkest  on  paper,  and  vice  versa ;  and 
those  in  which  the  lights  and  shades  are  in  their  natural  position.  The 
former  are  called  negative  and  the  \2XX.^x  positive  pictures. 

A  negative  may  be  taken  either  on  glass  or  on  paper  ;  it  serves  to  pro- 
duce a  positive  picture. 

Negatives  on  glass. — A  glass  plate  of  the  proper  size  is  carefully  cleaned  ; 
collodion  impregnated  with  iodide  of  potassium  is  then  poured  upon  it  ; 
and  the  plate  moved  about  till  a  layer  of  collodion  of  uniform  thickness 
is  obtained.  The  plate  is  then  immersed  for  about  a  minute  in  a  bath  of 
nitrate  of  silver  containing  30  grains  of  the  salt  in  an  ounce  of  water. 
This  operation  must  be  performed  in  a  dark  room.  The  plate  is  then 
removed,  allowed  to  drain,  and  when  somewhat  dry,  placed  in  the  closed 
frame,  and  afterwards  exposed  in  the  camera,  for  a  shorter  time  than  in 
the  case  of  a  Daguerreotype.  On  removing  the  plate  to  a  dark  room, 
no  change  is  visible,  but  on  pouring  over  it  a  solution  called  the  developer^ 
an  image  gradually  appears.  The  principal  substances  used  for  developing 
are  protosulphate  of  iron  and  pyrogallic  acid.  The  action  of  light  on 
iodide  of  silver  appears  to  produce  some  molecular  change,  in  virtue  ©f 
which  the  developers  have  the  property  of  reducing  to  the  metallic  state 
those  parts  of  the  iodide  of  silver  which  have  been  most  acted  upon 
by  the  light.  When  the  picture  is  sufficiently  brought  out,  water  is 
poured  over  the  plate,  in  order  to  prevent  the  further  action  of  the  de- 
veloper. The  parts  on  which  light  has  not  acted  are  still  covered  with 
iodide  of  silver,  which  would  be  affected  if  the  plate  were  now  exposed 

z  2 


5o8  On  Light.  [672- 

to  the  light.  It  is,  accordingly,  washed  with  solution  of  hyposulphite 
of  sodium,  which  dissolves  the  iodide  of  silver  and  leaves  the  image  un- 
altered. The  picture  is  then  coated  with  a  thin  layer  of  spirit-varnish, 
to  protect  it  from  mechanical  injury. 

When  once  the  negative  is  obtained,  it  may  be  used  for  printing  an 
indefinite  number  of  positive  pictures.  For  this  purpose,  paper  is  impreg- 
nated with  chloride  of  silver,  by  immersing  it  first  in  solution  of  nitrate 
of  silver  and  then  in  one  of  chloride  of  sodium  ;  chloride  of  silver  is  thus 
formed  on  the  paper  by  double  decomposition.  The  negative  is  placed  on 
a  sheet  of  this  paper  in  a  copying  frame,  and  exposed  to  the  action  of  light 
for  a  certain  time.  The  chloride  of  silver  becomes  acted  upon — the  light 
parts  of  the  negative  being  most  affected,  and  the  dark  parts  least  so.  A 
copy  is  thus  obtained,  on  which  the  lights  of  the  negative  are  replaced  by 
shades,  and  inversely.  In  order  to  fix  the  picture,  it  is  washed  in  a  solu- 
tion of  hyposulphite  of  sodium,  which  dissolves  the  unaltered  chloride  of 
silver.  The  picture  is  afterwards  immersed  in  a  bath  of  chloride  of  gold 
which  gives  it  tone. 

573.  Positives  on  grlass. — Very  beautiful  positives  are  obtained  by 
preparing  the  plates  as  in  the  preceding  cases  ;  the  exposure  in  the  camera, 
however,  is  not  nearly  so  long  as  for  the  negatives.  The  picture  is  then 
developed  by  pouring  over  it  a  solution  of  protosulphate  of  iron,  which 
produces  a  negative  image ;  and  by  afterwards  pouring  a  solution  6f 
cyanide  of  potassium  over  the  plate,  this  negative  is  rapidly  converted 
into  a  positive.  It  is  then  washed  and  dried,  and  a  coating  of  varnish 
poured  over  the  picture. 

574.  Pbotog-raplis  on  albumenised  paper  and  g^lass. — In  some 
cases,  paper  impregnated  with  a  solution  of  albumen  containing  iodide  of 
potassium  is  used  instead  of  collodion,  over  which  it  has  the  advantage 
that  it  can  be  prepared  for  some  time  before  it  is  used,  and  that  it  pro- 
duces certain  effects  in  the  middle  tints.  It  has  the  disadvantage  of  not 
being  nearly  so  sensitive.  It  requires,  therefore,  longer  exposure,  and  is 
unsuitable  for  portraits,  but  can  be  advantageously  used  for  views. 


CHAPTER  VI. 

THE   EYE  CONSIDERED   AS  AN   OPTICAL   INSTRUMENT. 

575.  Structure  of  the  human  eye. — The  eye  is  the  organ  of  vision — 
thdt  is  to  say,  of  the  phenomenon  by  virtue  of  which  the  light  emitted 
or  reflected  from  bodies  excites  in  us  the  sensation  which  reveals  their 
presence. 

The  eye  is  placed  in  a  bony  cavity  called  the  orbit  ;  it  is  maintained 
in  its  position  by  the  muscles  which  serve  to  move  it,  by  the  optic  nerve, 
the  conjunctiva,  and  the  eyelids.  Its  size  is  much  the  same  in  all  persons  : 
it  is  the  varying  aperture  of  the  eyelids  that  makes  the  eye  appear  larger 
or  smaller. 


-575]  Structure  of  the  Human  Eye.  509 

Fig.  464  represents  a  transverse  section  of  the  eye  from  back  to  front. 
The  general  shape  is  that  of  a  spheroid,  the  curvature  of  which  is  greater 
in  the  anterior  than  in  the  posterior  part.  It  is  composed  of  the  follow- 
ing parts  :  the  ^^r;/^^,the  sclerotica^  the  iris^  thepupil^  the  aqueous  humour^ 


the  crystalline,  the  vitreous  body,  the  hyaloid  membrane,  the  choroid,  the 
retina,  and  the  optic  7ierve. 

Cornea. — The  cornea,  a,  is  a  transparent  membrane  situated  in  front  of 
the  ball  of  the  eye.  In  shape  it  resembles  a  small  watch  glass,  and  it  fits 
into  the  sclerotica,  z;  in  fact,  these  membranes  are  so  connected  that  some 
anatomists  have  considered  them  as  one  and  the  same,  and  have  distin- 
guished them  by  calling  the  cornea  the  transpare7it,  and  the  sclerotica 
the  opaque  cornea. 

Sclerotica.— T\iQ  sclerotica,  /,  ox  sclerotic  coat,  is  a  membrane  which 
together  with  the  cornea,  envelopes  all  parts  of  the  eye.  In  front  there 
is  an  almost  circular  aperture  into  which  the  cornea  fits  ;  a  perforation 
behind  gives  passage  to  the  optic  nerve. 

Iris. — The  iris,  d,  is  an  annular,  opaque  diaphragm,  placed  between  the 
cornea  and  the  crystalline  lens.  It  constitutes  the  coloured  part  of  the 
eye,  and  is  perforated  by  an  aperture  called^  the  pupil,  which  in  man  is 
circular.  In  some  animals,  especially  those  belonging  to  the  genus  felis, 
it  is  narrow  and  elongated  in  a  vertical  direction  ;  in  the  ruminants  it 
is  elongated  in  a  transverse  direction.  It  is  a  contractile  membrane, 
and  its  diameter  varies  in  the  same  individual  between  o'i2  and  0-28  of 
an  inch  ;  but  these  limits  may  be  exceeded.  The  luminous  rays  pass  into 
the  eye  through  the  pupil.  The  pupil  enlarges  in  darkness,  but  contracts 
under  the  influence  of  a  bright  light.  These  alterations  of  contraction 
and  enlargement  take  place  with  extreme  rapidity ;  they  are  very  frequent, 
and  play  an  important  part  in  the  act  of  vision.  The  movements  of  the 
iris  are  involuntary. 

It  appears  from  this  description  that  the  iris  is  a  screen  with  a  variable 
aperture,  whose  function  is  to  regulate  the  quantity  of  light  which  pene- 
trates into  the  eye  ;  for  the  size  of  the  pupil  diminishes  as  the  intensity 


510  On  Light.  [575- 

of  light  increases.  The  iris  serves  also  to  correct  the  spherical  aberration, 
as  it  prevents  the  marginal  rays  from  passing  through  the  edges  of  the 
crystalline  lens.  It  thus  plays  the  same  part  with  reference  to  the  eye 
that  a  diaphragm  does  in  optical  instruments  (526). 

Aqueous  huinour. — Between  the  posterior  part  of  the  cornea  and  the 
front  of  the  crystalline  there  is  a  transparent  liquid  called  the  aqueous 
humour.  The  space,  e,  occupied  by  this  humour  is  divided  into  two 
parts  by  the  iris  ;  the  part  b,  between  the  cornea  and  the  iris,  is  called 
the  anterior  chamber ;  the  part  c,  which  is  between  the  iris  and  the  crys- 
talline, is  \hQ  posterior  chamber. 

Crystalline  lens. — This  is  a  double  convex  transparent  body  placed 
immediately  behind  the  iris  ;  the  inner  margin  of  which  is  in  contact 
with  its  anterior  surface,  though  not  attached  to  it.  The  lens  is  enclosed 
in  a  transparent  membrane,  called  its  capsule ;  it  is  less  convex  on  its 
anterior  than  on  its  posterior  surface,  and  is  composed  of  almost  con- 
centric layers,  which  decrease  in  density  and  refracting  power  from  the 
centre  to  the  circumference. 

To  the  anterior  surface  of  the  capsule,  near  its  margin,  is  fixed  a  firm 
transparent  membrane,  which  is  attached  behind  to  the  front  of  the 
hyaloid  membrane,  and  is  known  as  the  suspensory  ligament.  This 
ligament  exerts  a  traction,  all  round,  on  the  front  surface  of  the  lens, 
and  renders  it  less  convex  than  it  would  otherwise  be,  and  its  relaxation 
plays  an  important  part  in  the  adaptation  of  the  eye  for  sight  at  different 
distances. 

Vitreous  body.  Hyaloid  7nembrane. — The  vitreous  body,  or  vitreous 
humour,  is  a  transparent  mass  resembling  the  white  of  an  ^%%,  which 
occupies  all  the  part  of  the  ball  of  the  eye,  h,  behind  the  crystalline. 
The  vitreous  humour  is  surrounded  by  the  hyaloid  membrane,  /,  which 
lines  the  posterior  face  of  the  crystalline  capsule,  and  also  the  internal 
face  of  another  membrane  called  the  retina. 

Retina.  Optic  nerve. — The  retina, ;;?,  is  a  membrane  which  receives  the 
impression  of  light,  and  transmits  it  to  the  brain  by  the  intervention  of 
a  nerve,  n,  called  the  optic  nerve,  which,  proceeding  from  the  brain, 
penetrates  into  the  eye,  and  extends  over  the  retina  in  the  form  of  a 
nervous  network.  The  nerve  fibres  themselves  are  not  sensitive  to  light, 
but  are  only  stimulated  by  it  indirectly  through  the  intervention  of  certain 
structures  called  the  7'ods  aiid  cones.  Where  the  optic  nerve  enters,  there 
are  no  rods  or  cones  ;  this  part  of  the  retina  therefore  is  insensitive  to 
light  and  is  called  the  punctum  ccEcum. 

The  only  property  of  the  retina  and  optic  nerve  is  that  of  receiving  and 
transmitting  to  the  brain  the  impression  of  objects.  These  organs  have 
been  cut  and  pricked  without  causing  any  pain  to  the  animals  submitted 
to  these  experiments  ;  but  there  is  reason  to  believe  that  irritation  of  the 
optic  nerve  causes  the  sensation  of  a  flash  of  light. 

Choroid. — The  choroid,  k,  is  a  membrane  between  the  retina  and  the 
sclerotica.  It  is  completely  vascular,  and  is  covered  on  the  internal  face 
by  a  black  substance  which  resembles  the  colouring  matter  of  a  negro's 


-578] 


Path  of  Rays  in  the  Eye. 


Sir 


skin,  and  which  absorbs  all  rays  not  intended  to  co-operate  in  producing 
vision. 

The  choroid  elongates  in  front,  and  forms  a  series  of  convoluted  folds, 
called  ciliary  processes,  which  penetrate  between  the  iris  and  the  crystal- 
line capsule  to  which  they  adhere,  forming  round  it  a  disc,  resembling  a 
radiated  flower.  By  its  vascular  tissue,  the  choroid  serves  to  carry  the 
blood  into  the  interior  of  the  eye,  and  especially  to  the  ciliary  processes. 

576.  Refractive  indices  of  the  transparent  media  of  tbe  eye. — The 
refractive  indices  from  air  into  the  transparent  parts  of  the  eye  have  been 
determined  by  Brewster.  His  results  are  contained  in  the  following 
table,  compared  with  water  as  a  standard : — 

Water .  1-3358 

Aqueous  humour i'3366 

Vitreous  humour     ........  i'3394 

Exterior  coating  of  the  crystalline 1*3767 

Centre  of  the  crystalline i*399o 

Mean  refraction  of  the  crystalline 1*3839 


577.  Curvatures  and  dimensions  of  various  parts  of  tbe  buman 


eye. 


Radius  of  curvature  of  the  sclerotica 

„  „  cornea 

„  „  anterior  face  of  the 

crystalline 

„  „  posterior  face 

Dianieter  of  the  iris    .        .         .         , 

„  „        pupil         ... 

„  „         crystalline 

Thickness  of  the  crystalline 
Distance  from  the  pupil  to  the  cornea 
Length  of  the  axis  of  the  eye 


0-40  to  0-44  in. 
0-28  to  0-32  „ 

0*28  to  0-40  „ 
0-20  to  0*24  „ 
0-44  to  0-48  „ 
0-12  to  0-28  „ 
0-40  „ 

0*20    „ 

o'o8  „ 
0-88  to  0-96  „ 


The  curvature  of  the  cornea,  according  to  M.  Chossat,  is  that  of  an 
ellipsoid  of  revolution  round  its  major  axis,  and  the  curvature  of  the 
crystalline  that  of  an  ellipsoid  of  revolution  round  its  minor  axis. 

578.  Path  of  rays  in  the  eye. — From  what  has  been  said  as  to  the 
structure  of  the  eye  it  may  be  compared  to  a  camera  obscura  (565),  of 


Fig,  465. 

which  the  pupil  is  the  aperture,  the  crystalline  is  the  condensing  lens, 
and  the  retina  is  the  screen  on  which  the  image  is  formed.  Hence,  the 
effect  is  the  same  as  when  the  image  of  an  object  placed  in  front  of  a 


512  On  Light,  [578- 

double  convex  lens  is  formed  in  its  conjugate  focus.  Let  AB  (fig.  465) 
be  an  object  placed  before  the  eye,  and  let  us  consider  the  rays  emitted 
from  any  point  of  the  object  A.  Of  all  these  rays  those  which  are 
directed  towards  the  pupil  are  the  only  ones  which  penetrate  the  eye, 
and  are  operative  in  producing  vision.  These  rays,  on  passing  into  the 
aqueous  humour,  experience  a  first  refraction  which  brings  them  near  the 
secondary  axis  ha,  drawn  through  the  optic  centre  of  the  crystalline  ; 
they  then  traverse  the  crystalline,  which  again  refracts  them  like  a  double 
convex  lens,  and  having  experienced  a  final  refraction  by  the  vitreous 
humour,  they  meet  in  a  point,  a,  and  form  the  image  of  the  point  A. 
The  rays  issuing  from  the  point  B  form  in  like  manner  an  image  of  it  at 
the  point  b^  so  that  a  very  small,  real,  and  inverted  image  is  formed 
exactly  on  the  retina,  provided  the  eye  is  in  its  normal  condition. 

579.  Inversion  of  imag-es. — In  order  to  show  that  the  images  formed 
on  the  retina  are  really  inverted,  the  eye  of  an  albino  or  any  animal 
with  pink  eyes  may  be  taken  ;  this  has  the  advantage  that,  as  the 
choroid  is  destitute  of  pigment,  light  can  traverse  it  without  loss.  This 
is  then  deprived  at  its  posterior  part  of  the  cellular  tissue  surrounding  it, 
and  fixed  in  a  hole  in  the  shutter  of  a  dark  room  ;  by  means  of  a  lens  it 
may  be  seen  that  the  inverted  images  of  external  objects  are  depicted  on 
the  retina. 

The  inversion  of  images  in  the  eye  has  greatly  occupied  both  physicists 
and  physiologists,  and  many  theories  have  been  proposed  to  explain 
how  it  is  that  we  do  not  see  inverted  images  of  objects.  The  chief  diffi- 
culty seems  to  have  arisen  from  the  conception  of  the  mind  or  brain  as 
something  behind  the  eye  looking  into  it  and  seeing  the  image  upon  the 
retina  ;  whereas  really  this  image  simply  causes  a  stimulation  of  the  optic 
nerve,  which  produces  some  molecular  change  in  some  part  of  the  brain, 
and  it  is  only  of  this  change,  and  not  of  the  image,  as  such,  that  we  have 
any  consciousness.  The  mind  has  thus  no  direct  cognisance  of  the  image 
upon  the  retina,  nor  of  the  relative  positions  of  its  parts,  and  sight  being 
supplemented  by  touch  in  innumerable  cases,  it  learns  from  the  first  to 
associate  the  sensations  brought  about  by  the  stimulation  of  the  retina 
(although  due  to  an  inverted  image),  with  the  correct  position  of  the 
object  as  taught  by  touch. 

580.  Optic  axis,  optic  angrle,  visual  angrle. — T\\q  prvicipal  optic  axis 
of  an  eye  is  the  axis  of  its  figure  ;    that  is  to  say,  the  straight  line  in 


Fig.  466. 


reference  to  which  it  is  symmetrical.      In  a  well-shaped  eye  it  is  the 
straight  line  passing  through  the  centre  of  the  pupil  and  of  the  crystal- 


-581]      Estimation  of  the  Size  and  Distance  of  Objects.      5 1 3 

line,  such  as  the  line  Oo  (fig.  465).  The  lines  Aa,  B5,  which  are  almost 
rectilinear  are  secondary  axes.  The  eye  sees  objects  most  distinctly  in 
the  direction  of  the  principal  optic  axis. 

The  optic  -angle  is  the  angle  BAC  (fig.  466),  formed  between  the 
principal  optic  axes  of  the  two  eyes  when  they  are  directed  towards  the 
same  point.  This  angle  is  smaller  in  proportion  as  the  objects  are  more 
distant. 

The  visual  angle  is  the  angle  AOB  (fig.  467),  under  which  an  object  is 


seen  ;  that  is  to  say,  the  angle  formed  by  the  secondary  axes  drawn  from 
the  optic  centre  of  the  crystalline  to  the  opposite  extremities  of  the  object. 
For  the  same  distance,  this  angle  increases  with  the  magnitude  of  the 
object,  and  for  the  same  object  it  decreases  as  the  distance  increases,  as  is 
the  case  when  the  object  passes  from  AB  to  A'B.^  It  follows,  therefore, 
that  objects  appear  smaller  in  proportion  as  they  are  more  distant  ;  for 
as  the  secondary  axes,  AO,  BO,  cross  in  the  centre  of  the  crystalline,  the 
size  of  the  image  projected  on  the  retina  depends  on  the  size  of  the  visual 
angle,  AOB. 

5S1.  Estimation  of  tbe  distance  and  size  of  objects.— The  estima- 
tion of  distance  and  of  size  depends  on  numerous  circumstances  ;  these 
are — the  visual  angle,  the  optic  angle,  the  comparison  with  objects  whose 
size  is  familiar  to  us,  the  diminution  of  the  precision  of  the  image  by  the 
interposition  of  a  more  or  less  vaporous  medium. 

When  the  size  of  an  object  is  known,  as  the  figure  of  a  man,  the  height 
of  a  tree  or  of  a  house,  the  distance  is  estimated  by  the  magnitude  of  the 
visual  angle  under  which  it  is  seen.  If  its  size  is  unknown,  it  is  judged 
relatively  to  that  of  objects  which  surround  it. 

A  colonnade,  an  avenue  of  trees,  the  gas  lights  on  the  side  of  a  road, 
appear  to  diminish  in  size  in  proportion  as  their  distance  increases, 
because  the  visual  angle  decreases  ;  but  the  habit  of  seeing  the  columns, 
trees,  etc.,  in  their  proper  height,  leads  our  judgment  to  rectify  the  im- 
pression produced  by  vision.  Similarly,  although  distant  mountains  are 
seen  under  a  very  small  angle,  and  occupy  but  a  small  space  in  the  field 
of  view,  our  familiarity  with  the  effects  of  aerial  perspective  enables  us  to 
form  a  correct  idea  of  their  real  magnitude. 

The  optic  angle  is  also  an  essential  element  in  appreciating  distance. 
This  angle  increasing  or  diminishing  according  as  objects  approach  or 
recede,  we  move  our  eyes  so  as  to  make  their  optic  axes  converge  towards 
the  object  which  we  are  looking  at,  and  thus  obtain  an  idea  of  its  distance. 
Nevertheless,  it  is  only  by  long  custom  that  we  can  establish  a  relation 
between  our  distance  from  the  objects  and  the  corresponding  motion  of  the 
eyes.     It  is  a  curious  fact  that  persons  bom  bhnd,  and  whose  sight  has 

Z3 


514  On  Light.  [581- 

been  restored  by  the  operation  for  cataract,  imagine  at  first  that  all  objects 
are  at  the  same  distance. 

582.  Distance  of  distinct  vision. — The  distance  of  distinct  vision  is, 
as  already  stated,  the  distance  at  which  objects  must  be  placed  so  as  to 
be  seen  with  the  greatest  distinctness.  It  varies  in  different  individuals, 
and  in  the  same  individual  it  is  often  different  in  the  two  eyes.  For  small 
objects,  such  as  print,  it  is  from  10  to  12  inches  in  normal  cases. 

In  order  to  obtain  an  approximate  measurement  of  the  least  distance  of 
distinct  vision,  two  small  parallel  slits  are  made  in  a  card  at  a  distance  of 
0*03  of  an  inch.  These  apertures  are  held  close  before  the  eye,  and  when 
a  fine  slit  in  another  card  is  held  very  near  these  apertures,  the  slit  is  seen 
double,  because  the  rays  of  light  which  have  traversed  both  apertures  do 
not  intersect  each  other  on  the  retina,  but  behind  it.  But,  if  the  latter 
card  is  ;gradually  removed,  the  distance  is  ultimately  reached  at  which 
both  images  coincide  and  form  one  distinct  image.  Stampfer  has  con- 
structed an  optometer  on  this  principle. 

Persons  <who  see  only  at  a  very  short  distance  are  called  my  optic,  or 
shoi't-^^ghted,  and  those  who  see  only  at  a  long  distance  are  presbyoptic, 
or  long-sightad. 

Sharpness  .ef  sight  may  be  compared,  by  reference  to  that  of  a  normal 
eye  taken  as  a^unit.  Such  a  standard  eye,  according  to  Snellen,  recog- 
nises quadrangular  letters  when  they  are  seen  under  an  angle  of  5' ;  if  for 
instance  such  letters  are  15""^  high  at  a  distance  of  10  metres.  The 
sharpness  of  vision  of  one  who  recognises  these  letters  at  a  distance  of  3 

metres  is  then  ^ . 
I® 

583.  Accommodation. — By  this  term  is  meant  the  changes  which  occur 
in  the  eye  to  fitdt  for  seeing  distinctly  objects  at  different  distances  from  it. 

If  the  eye  be  supposed  fixed  and  its  parts  immovable,  it  is  evident  that 
there  could  only  be  one  surface  whose  image  would  fall  exactly  upon  the 
retina  ;  the  distance  of  this  surface  from  the  eye  being  dependent  on  the 
refractive  indices  of  the  media  and  the  curvatures  of  the  refracting  sur- 
faces of  the  eye.  The  image  of  any  point  nearer  the  eye  than  this  dis- 
tinctly seen  surface  would  fall  behind  the  retina  ;  the  image  of  any  more 
distant  point  would  be  formed  in  front  of  it :  in  each  case  the  section  of  a 
luminous  cone  would  be  perceived  instead  of  the  image  of  the  point,  and 
the  latter  would  appear  diffused  and  indistinct 

Experience,  however,  shows  us  that  a  normal  eye  can  see  distinct 
Milages  of  objects  at  very  different  distances.  We  can,  for  example,  see  a 
distant  tree  through  a  window,  and  also  a  scratch  on  the  pane,  though  not 
both  distinctly  at  the  same  moment ;  for  when  the  eye  is  arranged  to  see 
ooie  clearly,  the  image  of  the  other  does  not  fall  accurately  upon  the  retina. 
An  eye  completely  at  rest  seems  adapted  for  seeing  distant  objects  ;  the 
sense  of  effort  is  greater  in  a  normal  eye  when  a  near  object  is  looked  at, 
after  a  distant  one,  than  in  the  reverse  case  ;  and  in  paralysis  of  the 
nerves  governing  the  accommodating  apparatus  the  eye  is  persistently 
adapted  for  dist-am  sight.  There  must,  therefore,  be  some  mechanism  in 
the  eye  by  which  it  can  be  voluntarily  altered,  so  that  the  more  divergent 


-584]  Binocular  Vision,  515 

rays  proceeding  from  near  objects  shall  come  to  a  focus  upon  the  retina. 
There  are  several  conceivable  methods  by  which  this  might  be  effected  ;:, 
it  is  actually  brought  about  by  a  drawing  forwards  of  the  crystalline  lens 
and  a  greater  convexity  of  its  anterior  surface. 

This  is  shown  by  the  following  experiment  :  if  a  candle  be  placed  on 
one  side  of  the  eye  of  a  person  looking  at  a  distant  object,  and  his  eye  be 
observed  from  the  other  side,  three  distinct  images  of  the  flame  will  be 
seen  ;  the  first,  virtual  and  erect,  is  reflected  from  the  anterior  surface  of 
the  cornea  ;  the  next,  erect  and  less  bright,  is  reflected  from  the  anterior 
surface  of  the  lens  ;  the  third,  inverted  and  brilliant,  is  formed  on  the  pos- 
terior surface  of  the  lens.  If  now  the  person  look  at  a  near  object,  no 
change  is  observed  in  the  first  and  third  images,  but  the  second  image 
becomes  smaller  and  approaches  the  first  ;  which  shows  that  the  anterior 
surface  of  the  crystalline  lens  becomes  more  convex  and  approaches  the 
cornea.  In  place  of  the  candle,  Helmholtz  throws  light  through  two  holes 
in  the  screen  upon  the  eye,  and  observes*  the  distance  on  the  eye  between 
the  two  shining  points,  instead  of  the  size  of  the  flame  of  the  candle. 

This  change  in  the  lens  is  effected  chiefly  by  means  of  a  circular 
muscle  (ciliary  muscle),  the  contraction  of  which  relaxes  the  suspensory 
ligament,  and  so  allows  the  front  surface  of  the  lens  to  assume  more  or 
less  of  that  greater  convexity  which  it  would  normally  exhibit  were  it 
not  for  the  drag  exercised  upon  it  by  the  ligament.  Certain  other  less 
important  changes  tending  to  make  the  lens  more  convex  and  to  push  it 
forwards  occur,  which  cannot,  however,  be  explained  without  entering 
into  minute  anatomical  details.  When  the  eye  is  accommodated  for  near 
vision,  the  pupil  contracts  and  so- partially  remedies  the  greater  spherical 
aberration. 

The  ratige  of  accommodation  called  by  Bonders  — ,  is   measured  by 

first  of  all  determining  the  greatest  distance,  R,  at  which  a  person  can 
read  without  spectacles,  and  then  the  smallest,  P,  at  which  he  can  read  ; 

*u  III 

then  -A  =  P-R- 

584.  Binocular  vision. — A  single  eye  sees  most  distinctly  any  point 
situated  on  its  optical  axis,  and  less  distinctly  other  points  also,  towards 
which  it  is  not  directly  looking,  but  which  still  are  within  its  circle  of 
vision. 

It  is  able  to  judge  of  the  direction  of  any  such  point,  but  unable  by 
itself  to  estimate  its  distance.  Of  the  distance  of  an  object  it  may  indeed 
learn  to  judge  by  such  criteria  as  loss  of  colour,  indistinctness  of  outline 
decrease  in  magnitude,  etc. ;  but  if  the  object  i"s  near,  the  single  eye  is 
not  infallible,  even  with  these  aids. 

When  the  two  eyes  are  directed  upon  a  single  point,  we  then  gain  the 
power  of  judging  of  its  distance  as  compared  with  that  of  any  other 
point,  and  this  we  seem  to  gain  by  the  sense  of  greater  or  less  effort 
required  in  causing  the  optical  axes  to  converge  upon  the  one  point  or 
upon  the  other.     Now  a  solid  object  may  be  regarded  as  composed  of 


«;i6 


On  Light. 


[584- 


points  which  are  at  different  distances  from  the  eye.  Hence,  in  looking 
at  such  an  object,  the  axes  of  the  two  eyes  are  rapidly  and  insensibly 
varying  their  angle  of  convergence,  and  we  as  rapidly  are  gaining  ex- 
perience in  the  difference  in  distance  of  the  various  points  of  which  the 
object  is  composed,  or,  in  other  words,  an  assurance  of  its  sohdity.  Such 
kind  of  assurance  is  necessarily  unattainable  in  monocular  vision. 

585.  The  principle  of  tbe  stereoscope. — Let  any  solid  object,  such  as 
a  small  box,  be  supposed  to  be  held  at  some  short  distance  before  the  two 
eyes.  On  whatever  point  of  it  they  are  fixed,  they  will  see  that  point 
the  most  distinctly,  and  other  points  more  or  less  clearly.  But  it  is 
evident  that,  as  the  two  eyes  see  from  different  points  of  view,  there  will 
be  formed  in  the  right  eye  a  picture  of  the  object  different  from  that 


M\ 


Fig.  468. 

formed  in  the  left  ;  and  it  is  by  the  apparent  union  of  these  two  dissimilar 
pictures  that  we  see  the  object  in  relief.  If,  therefore,  we  delineate  the 
object,  first  as  seen  by  the  right  eye,  and  then  as  seen  by  the  left,  and 
afterwards  present  these  dissimilar  pictures  again  to  the  eyes,  taking  care 
to  present  to  each  eye  that  picture  which  w^as  drawn  from  its  point 
of  view,  there  would  seem  to  be  no  reason  why  we  should  not  see  a 
representation  of  the  object  as  we  saw  the  object  itself,  in  relief.  Ex- 
periment confirms  the  supposition.  If  the  object  held  before  the  eyes  were 
a  truncated  pyramid,  r  and  /,  fig.  468,  would  represent  its  principal  lines, 
as  seen  by  the  right  and  left  eyes  respectively.  If  a  card  be  held  between 
the  figures,  and  they  are  steadily  looked  at  r  by  the  right  eye,  and  / 
simultaneously  by  the  left,  for  a  few  seconds,  there  will  be  seen  a  single 
picture  having  the  unmistakable  appearance  of  relief  Even  without  a 
card  interposed,  the  eye,  by  a  little  practice,  may  soon  be  taught  so  to  com- 
bine the  two  as  to  form  this  solid  picture.  Three  pictures  will  in  that  case 
be  seen,  the  central  being  solid,  and  the  two  outside  ones  plane.  Fig.  469 
will  explain  this.  Let  r  and  /  be  any  two  corresponding  points,  say 
the  points  marked  by  a  large  dot  in  the  figures  drawn  above  ;  R  and  L 
the  positions  of  the  right  and  left  eyes ;  then  the  right  eye  sees  the 
point  r  in  the  direction  R^,  and  the  left  eye  the  point  /  in  the  direction 
L^,  and  accordingly,  each  by  itself  judging  only  by  the  direction,  they 
together  see  these  two  points  as  one,  and  imagine  it  to  be  situated  at  o. 
But  the  right  eye,  thcugh  looking  in  the  direction  Rr,  also  receives  an 


-587] 


Stereoscope. 


517 


image  of  /  on  another  part  of  the  retina,  and  the  left  eye  in  tlie  same  way 
an  image  of  r,  and  thus  three  images  are  seen. 
A  card,  however,  placed  in  the  position 
marked  by  the  dotted  line  will  of  course  cut 
off  the  two  side  pictures.  To  assist  the  eye 
in  combining  such  pairs  of  dissimilar  pic- 
tures, both  mirrors  and  lenses  have  been 
made  use  of,  and  the  instruments  in  which 
either  of  these  are  adapted  to  this  end  are 
called  stereoscopes. 

586.  Tbe  reflecting:  stereoscope. —  In 
the  reflecting  stereoscope  plane  mirrors  are 
used  to  change  the  apparent  position  of  the 
pictures,  so  that  they  are  both  seen  in  the 
same  direction,  aad  their  combination  by  the 
eye  is  thus  rendered  easy  and  almost  inevit- 
able. \iab,  ab  (fig.  470)  are  two  plane  mirrors 
inclined  to  one  another  at  an  angle  of  90° 
the  two  arrows,  x,  y  would  both  be  seen  by  the  eyes  situated  at  R  and  L 
in  the  position  marked  by  the  dotted  arrow.  If,  instead  of  the  arrows, 
we  now  substitute  such  a  pair  of  dissimilar  pictures  as  we  have  spoken  of 
above,  of  the  same  solid  object,  it  is  evident  that,  if  the  margins  of  the 
pictures  coincide,  other  corresponding  points  of  the  pictures  will  not. 
The  eyes,  however,  almost  without  effort,  soon  bring  such  points  into 


Fig:.  469. 


-^- 


^'        h     '^^ 


X 


L  R 

Fig.  470. 


H 


Fig.  471 


coincidence,  and  in  so  doing  make  them  appear  to  recede  or  advance, 
as  they  are  farthen  apart  or  nearer  together  than  any  two  corresponding 
points  (the  right-hand  corner,  for  instance)  of  the  margins,  when  the 
pictures  are  placed  side  by  side,  as  in  the  diagram  fig.  470.  It  will  be 
plain,  also,  on  considering  the  position  for  the  arrows  in  fig.  470,  that  to 
adapt  such  pictures  as  those  in  fig.  468  to  use  in  a  reflecting  stereoscope, 
one  of  them  must  be  reversed,  or  drawn  as  it  would  be  seen  through  the 
paper  if  held  up  to  the  light. 

587.  THe  refractingr  stereoscope.— Since  the  rays  passing  through  a 
convex  lens  are  bent  always  towards  the  thicker  part  of  the  lens,  any 


5i8  .       -  On  Light.  [587- 

segment  of  such  a  lens  may  be  readily  adapted  to  change  the  apparent 
position  of  any  object  seen  through  it.  Thus,  if  (fig.  471)  two  segments 
be  cut  from  a  double  convex  lens,  and  placed  with  their  edges  together, 
the  arrows  x^y,  would  both  be  seen  in  the  position  of  the  dotted  arrow 
by  the  eyes  at  R  and  L. 

If  we  substitute  for  the  arrows  two  dissimilar  pictures  of  the  same  solid 
object,  or  the  same  landscape,  we  shall  then,  if  a  a  diaphragm,  ab^  be  placed 
between  the  lenses  to  prevent  the  pictures  being  seen  crosswise  by  the 
eyes,  see  but  one  picture,  and  that  apparently  in  the  centre,  and  magnified. 
As  before,  if  the  margins  are  brought  by  the  power  of  the  lenses  to  coin- 
cide, other  corresponding  points  will  not  be  coincident  until  combined  by 
an  almost  insensible  effort  of  the  eyes.  Any  pair  of  corresponding  points 
which  are  farther  apart  than  any  other  pair  will  then  be  seen  farther  back 
in  the  picture,  just  as  any  point  in  the  background  of  a  landscape  would 
be  found  (if  we  came  tcr  compare  two  pictures  of  the  landscape,  one  drawn 
by  the  right  eye,  and  the  other  by  the  left)  to  be  represented  by  two 
points  farther  apart  from  one  another  than  two  others  which  represented 
a  point  in  the  foreground. 

To  any  one  curious  in  such  experiments,  it  will  be  instructive  to  notice 
that  there  is  also  a  second  point  on  this  side  of 
£  I,  the  paper,  at  which,    if  a  person  look   steadily, 

j\  /\         the  diagrams  in  fig.  472  will  combine,  and  form 

\  /    I  quite   a  different   stereoscopic   picture.      Instead 

\         /       I         of  a  solid  pyramid,  a  hollow  pyramidal  box  will 
\n/  I         then  be  seen.     The  point  may  easily  be  found  by 

/\  V       experiment.      Here   again   two   external   images 

/    \  I        will  also  be  seen.     If  we  wish  to  shut  these  out, 

/         \        I        and  see  only  their  central  stereoscopic  combina- 
\     1       tion,  we   must   use  a  diaphragm  of  paper  held 
\  1       parallel  to  the  plane  of  the  picture  with  a  square 
\l       hole  in  it.     This  paper  screen  must  be  so  adjusted 
S      that  it  may  conceal  the  right-hand  figure  from 
Fis-  472.  the  left  eye,  and  the  left-hand  figure   from  the 

right  eye,  while  the  central  stereoscopic  picture  may  be  seen  through  the 
hole.  It  will  be  plain  from  the  diagram  that  o  is  the  point  to  which  the 
eyes  must  be  directed,  and  at  which  they  will  imagine  the  point  to  be 
situated,  which  is  formed  by  the  combination  of  the  two  points  r  and  /. 
The  dotted  line  shows  the  position  of  the  screen.  A  stereoscope  with  or 
without  lenses  may  easily  be  constructed,  which  will  thus  give  us,  with 
the  ordinary  stereoscopic  slides,  a  reversed  picture,  for  instance,  if  the 
subject  be  a  landscape,  the  foreground  will  retire  and  the  background 
come  forward. 

When  the  two  retinas  view  simultaneously  two  different  colours,  the 
impression  produced  is  that  of  a  single  mixed  tint.  The  power,  however, 
of  combining  the  two  tints  into  a  single  one  varies  in  difterent  individuals, 
and  in  son^e  is  extremely  weak.  If  two  white  discs  at  the  base  of  the 
stereoscope  be  illuminated  by  two  pencils  of  complimentary  colours,  and 
if  each  coloured  disc  be  looked  at  with  one  eye,  a  single  white  one  is 


-589]  Accidental  Images.  519 

seen,  shewing  that  the  sensation  of  white  light  may  arise  from  two  com- 
plementary and  simultaneous  chromatic  impressions  on  each  of  the  two 
retinas. 

588.  Persistence  of  Impressions  on  tlie  retina. — When  an  ignited 
piece  of  charcoal  is  rapidly  rotated,  we  cannot  distinguish  it ;  the  appear- 
ance of  a  circle  of  fire  is  produced  ;  •  similarly,  rain,  in  falling  in  drops, 
appears  in  the  air  like  a  series  of  liquid  threads.  In  a  rapidly  rotating 
toothed  wheel  the  individual  teeth  cannot  be  seen.  But  if,  during  dark- 
ness, the  wheel  be  suddenly  illuminated,  as  by  the  electric  spark,  the 
individual  parts  may  be  clearly  made  out.  These  various  appearances  are 
due  to  the  fact  that  the  impression  of  these  images  on  the  retina  remains 
for  some  time  after  the  object  which  has  produced  them  has  disappeared 
or  become  displaced.  The  duration  of  the  persistence  varies  with  the 
sensitiveness  of  the  retina  and  the  intensity  of  light.  The  following  ex- 
periment is  a  further  illustration  of  this  property.  A  series  of  equal 
sectors  are  traced  on  a  disc  of  glass,  and  they  are  alternately  blackened  ; 
in  the  centre  there  is  a  pivot,  on  which  a  second  disc  is  fixed  of  the  same 
dimensions  as  the  first,  but  completely  blackened,  with  the  exception  of  a 
single  sector  ;  then  placing  the  apparatus  between  a  window  and  the  eye, 
the  second  disc  is  made  to  rotate.  If  the  movement  is  slow,  all  the 
transparent  sectors  are  seen,  but  only  one  at  a  time  ;  by  a  more  rapid 
rotation  we  see  simultaneously  two,  three,  or  a  greater  number. 

M.  Plateau  has  investigated  the  duration  of  the  impression  by  numerous 
similar  methods,  and  has  found  that  it  is  on  the  average  half  a  second. 
Among  many  curious  instances  of  these  phenomena,  the  following  is 
one  of  the  most  remarkable.  If,  after  having  looked  at  a  brightly  illumi- 
nated window,  the  eyes  are  suddenly  closed,  the  image  remains  for  a 
few  instants — that  is,  a  sashwork  is  seen  consisting  of  luminous  panes 
surrounded  by  dark  frames  :  after  a  few  seconds  the  colours  become  in- 
terchanged, the  same  framework  is  now  seen,  but  the  frames  are  now 
bright,  and  the  glasses  are  perfectly  black ;  this  new  appearance  may 
again  revert  to  its  original  appearance. 

The  impression  of  colours  remains  as  well  as  that  of  the  form  of  ob- 
jects ;  for  if  circles  divided  into  sectors  are  painted  in  dififererit  colours, 
they  become  confounded,  and  give  the  sensation  of  the  colour  which 
would  result  from  their  mixture.  Yellow  and  red  give  orange ;  blue  and 
red  violet ;  the  seven  colours  of  the  spectrum  give  white,  as  shown  in 
I'lewton's  disc  (fig.  421). 

A  great  number  of  pieces  of  apparatus  are  founded  on  the  persistence 
of  sensation  on  the  retina.  Such  are  the  thaumatropc,  Xh.^  phenakistoscope^ 
Faraday's  wheel,  the  kaleidopho7ie. 

589.  ikccidental  images. — A  coloured  object  being  placed  upon  a 
black  ground,  if  it  is  steadily  looked  at  for  some  time,  the  eye  is  soon 
tired,  and  the  intensity  of  the  colour  enfeebled  ;  if  now  the  eyes  are 
directed  towards  a  white  sheet,  or  to  the  ceiling,  an  image  will  be  seen 
of  the  same  shape  as  the  object,  but  of  the  complementary  colour  (536) ; 
that  is,  such  a  one  as  united  to  that  of  the  object  would  form  white.     For 


520  On  Light.  [589- 

a  green  object  the  image  will  be  red;  if  the  object  is  yellow,  the  image 
will  be  violet. 

Accidental  colours  are  of  longer  duration  in  proportion  as  the  object 
has  been  more  brilliantly  illuminated,  and  the  object  has  been  longer 
looked  at.  When  a  lighted  candle  has  been  looked  at  for  some  time, 
and  the  eyes  are  turned  towards  a  dark  part  of  the  room,  the  appearance 
of  the  flame  remains, -but  it  gradually  changes  colour;  it  is  first  yellow, 
then  it  passes  through  orange  to  red,  from  red  through  violet  to  greenish 
blue,  which  is  gradually  feebler  until  it  disappears.  If  the  eye  which  has 
been  looking  at  the  light  be  turned  towards  a  white  wall,  the  colours  fol- 
low almost  the  opposite  direction  :  there  is  first  a  dark  picture  on  a 
white  ground,  which  gradually  changes  into  blue,  is  then  successively 
green  and  yellow,  and  ultimately  cannot  be  distinguished  from  a  white 
ground. 

The  reason  of  this  phenomenon  is,  doubtless,  to  be  sought  in  the  fact 
that  the  subsequent  action  of  light  on  the  retina  is  not  of  equal  duration 
or  all  colours,  and  that  the  decrease  in  the  intensity  of  the  subsequent 
action  does  not  follow  the  same  law  for  all  colours. 

590.  Irradiation. — This  is  a  phenomenon  in  virtue  of  which  white 

objects  or  those  of  a  very  bright  colour,  when  seen  on 

■■■■■^H    a  dark  ground,   appear   larger   than   they   really   are. 

■  ^^^  ■  Thus  a  white  square  upon  a  black  ground  seems 
I     ^^H    I    larger   than   an   exactly    equal   black   square    upon   a 

■  iHI  I  white  ground  (fig.  473).  Irradiation  arises  from  the 
B  -  B  fact  that  the  impression  produced  on  the  retina  ex- 
^HUHT     tends  beyond  the  outline  of  the  image.     It  bears  the 

H  H       same  relation  to  the  space  occupied  by  the  image  that 

H^^^H       the  duration  of  the  impression  does  to  the  time  during 

||[||||||       which  the  image  is  seen. 

-I  The  effect  of  irradiation  is  very  perceptible  in  the 

apparent  magnitude  of  stars,  which  may  thus  appear 
much  larger  than  they  really  are  ;  also  in  the  appear- 
ance of  the  moon  when  two  or  three  days  old,  the  brightly  illuminated 
crescent  seeming  to  extend  beyond  the  darker  portion  of  the  disc,  and 
hold  it  in  its  grasp. 

Plateau,  who  has  investigated  this  subject,  finds  that  irradiation  differs 
very  much  in  different  people,  and  even  in  the  same  person  it  differs  on 
different  days.  He  has  also  found  that  irradiation  increases  with  the 
lustre  of  the  object,  and  the  length  of  time  during  which  it  is  viewed. 
It  manifests  itself  at  all  distances,  diverging  lenses  increase  it,  condensing 
lenses  diminish  it. 

Accidental  haloes  are  the  colours  which,  instead  of  succeeding  the  im- 
pression of  an  object  like  accidental  colours,  appear  round  the  object  it- 
self when  it  is  looked  at  fixedly.  The  impression  of  the  halo  is  the  oppo- 
site to  that  of  the  object ;  if  the  object  is  bright  the  halo  is  dark,  and  vice 
versa.  These  appearances  are  best  produced  in  the  following  manner. 
A  white  surface,  such  as  a  sheet  of  paper,  is  illuminated  by  coloured 
light,  and  a  narrow  opaque  body  held  so  as  to  cut  off  some  of  the  coloured 


-591]  The  Eye  is  not  AcJiromatic.  52 1 

rays.  In  this  manner  a  narrow  shadow  is  obtained  which  is  illuminated 
by  the  surrounding  white  daylight,  and  appears  complementary  to  the 
coloured  ground.  If  red  glass  is  used,  the  shadow  appears  green,  and  blue 
when  a  yellow  glass  is  used. 

The  contrast  of  colours  is  a  reciprocal  action  exerted  between  two 
adjacent  colours./  and  in  virtue  of  which  to  each  one  is  added  the 
complementary  colour  of  the  other.  This  contrast  was  observed 
by  M.  Chevreifl,  who  has  made  it  the  subject  of  study.  It  is  by  the 
reciprocal  influence  of  coloured  shadows  that  the  contrast  of  colour  is 
explained. 

M.  Chevreul  has  found  that  when  red  and  yellow  colours  are  adjacent 
red  acquires  a  violet  and  orange  a  yellow  tint.  If  the  experiment  is  made 
with  red  and  blue,  the  former  acquires  a  yellow,  and  the  latter  a  green 
tint  :  with  yellow  and  blue,  yellow  passes  to  orange,  and  blue  towards 
indigo  :  and  so  on  for  a  vast  number  of  combinations.  The  importance 
of  this  phenomenon  in  its  application  to  the  manufacture  of  cloths,  carpets, 
etc.,  may  be  readily  conceived. 

591.  The  eye  is  not  achromatic. — It  had  long  been  supposed  that  the 
human  eye  was  perfectly  achromatic,  but  this  is  clearly  impossible,  as  all 
the  refractions  are  made  the  same  way,  viz.  towards  the  axis ;  moreover, 
the  experiments  of  Wollaston,  of  Young,  of  Fraunhofer,  and  of  Miiller, 
have  shown  that  it  was  not  true  in  any  absolute  sense. 

Fraunhofer  showed  that  in  a  telescope  with  two  lenses,  a  very  fine  wire 
placed  inside  the  instrument  in  the  focus  of  the  object  glass  is  seen 
distinctly  through  the  eye-piece,  when  the  telescope  is  illuminated  with 
red  light ;  but  it  is  invisible  by  violet  light  even  when  the  eye-piece  is  in 
the  same  position.  In  order  to  see  the  wire  again,  the  distance  of  the 
lenses  must  be  diminished  to  a  far  greater  extent  than  would  corre- 
spond to  the  degree  of  refrangibility  of  violet  light  in  glass.  In  this  case, 
therefore,  the  effect  must  be  due  to  a  chromatic  aberration  in  the  eye. 

Miiller,  on  looking  at  a  white  disc  on  a  dark  ground,  found  that  the 
image  is  sharp  when  the  eye  is  accommodated  to  the  distance  of  the  disc, 
that  is,  when  the  image  forms  on  the  retina  ;  but  he  found  that  if  the 
image  is  formed  in  front  of  or  behind  the  retina,  the  disc  appears  sur- 
rounded by  a  very  narrow  blue  edge. 

If  a  finger  be  held  up  in  front  of  one  eye  (the  other  being  closed)  in  such 
a  manner  as  to  allow  the  light  to  enter  only  one-half  of  the  pupil,  and,  of 
course,  obliquely,  and  the  eye  be  then  directed  to  any  well-defined  line 
of  light,  such  as  a  slit  in  the  shutter  of  a  darkened  room,  or  a  strip  of 
white  paper  on  a  black  ground,  this  line  of  light  will  appear  as  a  complete 
spectrum. 

Miiller  concluded  from  these  experiments  that  the  eye  is  sensibly 
achromatic  as  long  as  the  image  is  received  at  the  focal  distance,  or 
when  it  is  accommodated  to  the  distance  of  the  object.  The  cause  of  this 
apparent  achromatism  cannot  be  exactly  stated.  It  has  generally  been 
attributed  to  the  tenuity  of  the  luminous  beams  which  pass  through  the 
pupillary  aperture,  and  that  these  unequally  refrangible  rays,  meeting 
the  surfaces  of  the  media  of  the  eye  almost  at  the  normal  incidence,  are 


522  On  Light.  [591- 

very  little  refracted,  from  which  it  follows  that  the  chromatic  aberration 
is  imperceptible  (547). 

Spherical  aberration,  as  we  have  already  seen,  is  corrected  by  the  iris 
(576).  The  iris  is  in  point  of  fact  a  diaphragm,  which  stops  the  marginal 
rays,  and  only  allows  those  to  pass  which  are  near  the  axis. 

592.  Sbort  sigrbt  and  long:  sig^bt;  myopy  and  presbytism. — The 
most  usual  affections  of  the  eye  are  myopy  and  presbytism^  or  short  sight 
and  to?tg  sight.  Short  sight  is  the  habitual  accommodation  of  the  eyes 
for  a  distance  less  than  that  of  ordinary  vision,  so  that  persons  affected  in 
this  way  only  see  very  near  objects  distinctly.  The  usual  cause  of  short 
sight  is  a  too  great  convexity  of  the  cornea  or  of  the  crystalline ;  the  eye 
being  then  too  convergent,  the  focus,  in  place  of  forming  on  the  retina,  is 
formed  in  front,  so  that  the  image  is  indistinct.  It  may  be  remedied  by 
means  of  diverging  glasses,  which  in  making  the  rays  deviate  from  their 
common  axis  throw  the  focus  farther  back,  and  cause  the  image  to  be 
formed  on  the  retina. 

The  habitual  contemplation  of  small  objects,  as  when  children  are  too 
much  accustomed,  in  reading  and  writing,  to  place  the  paper  close  to  their 
eyes,  or  working  with  a  microscope,  may  produce  short  sight.  It  is  com- 
mon in  the  case  of  young  people,  but  diminishes  with  age. 

Long  sight  is  the  contrary  of  short  sight :  the  eye  can  see  distant  objects 
very  well,  but  cannot  distinguish  those  which  are  very  near.  The  cause  of 
long  sight  is  that  the  eye  is  not  sufficiently  convergent,  and  hence  the  image 
of  objects  is  formed  beyond  the  retina  :  but  if  the  objects  are  removed 
farther  off,  the  image  approaches  the  retina,  and  when  they  are  at  a  suitable 
distance  is  exactly  formed  upon  it,  so  that  the  object  is  clearly  seen. 

Long  sight  is  corrected  by  means  of  converging  lenses.  These  glasses 
bring  the  rays  together  before  their  entrance  into  the  eye,  and,  therefore, 
if  the  converging  power  is  properly  chosen,  the  image  will  be  formed 
exactly  on  the  retina. 

It  is  not  many  years  since  double  convex  lenses  were  alone  used  for 
long-sighted  persons,  and  double  concave  for  short-sighted  persons.  Wol- 
laston  first  proposed  to  replace  these  glasses  by  concavo-convex  lenses, 
C  and  F  (fig.  398),  so  placed  that  their  curvature  is  in  the  same  direction 
as  that  of  the  eye.  By  means  of  these  glasses  a  much  wider  range  is 
attained,  and  hence  they  have  been  called  periscopic  glasses.  They  have 
the  disadvantage  of  reflecting  too  much. 

593.  Eye-grlasses.  Spectacles. — The  glasses  commonly  used  by  short 
or  long  sighted  persons  are  known  under  the  general  name  of  eye-glasses, 
or  spectacles.  Generally  speaking,  numbers  are  engraved  on  these  glasses 
which  express  their  focal  length  in  inches. 

The  spectacles  must  so  be  chosen  that  they  are  close  to  the  eye,  and 
that  they  make  the  distance  of  distinct  vision  10  or  12  inches. 

The  number  which  a  short  or  long  sighted  person  ought  to  use  may  be 
calculated,  knowing  the  distance  of  distinct  vision.     The  formula 

/=J^    .......         (I) 

■^      d-p  ^  ^ 

serves  for  long-sighted  persons,  where /being  the  number  which  ought   0 


-596]  Ophthalmoscope.  523 

be  taken,  p  is  the  distance  of  distitiA^vision  in  ordin?.ry  cases  (about  12 
inches),  and  d  the  distance  of  distinct  vision  for  the  person  affected  by 
long  sight. 

The  above  formula  is  obtained  from  the  equation  -—-.,=   ,,  by   sub- 

P  P  J 
stituting  dior  p'.  In  this  case  the  fonxiula  (6)  of  article  527  is  used,  and 
not  formula  (5),  because  the  image  seen  by  spectacles  being  on  the  same 
side  of  the  object  in  reference  to  the  lens,  the  sign  of  p'  ought  to  be  the 
opposite  of  that  of  p,  as  in  the  case  of  virtual  images  from  the  paragraph 
already  cited. 

For  short-sighted  persons,yis  calculated  by  the  formula     —  -^  =  — 

P     P  f 

(527),  which  belongs  to  concave  lenses,  and  which,  replacing /' by  d,  gives 

^=/'.-     •     •     •     •     ■     w 

To  calculate,  for  instance,  the  number  of  a  glass  which  a  person  ought 
to  use  in  whom  the  distance  of  distinct  vision  is  36,  knowing  that  the  dis- 
tance of  ordinary  distinct  vision  is  12  inches ;  making/  =  12  and  rt'  =  36 

in  the  above  formula  (i),  we  get /"=  ^^— -  "  =  18. 
^  36-12 

594.  Dlplopy Diplopy  is  an  affection  of  the  eye  which  causes  objects 

to  be  seen  double,  that  is,  that  two  images  are  seen  instead  of  one.  Usually 
the  two  images  are  almost  entirely  superposed,  and  one  of  them  is  much 
more  distinct  than  the  other.  Diplopy  may  be  caused  by  the  co-operation 
of  two  unequal  eyes,  but  it  may  also  affect  a  single  eye.  The  latter  case 
is,  doubtless,  due  to  some  defect  of  conformation  in  the  crystalline  or  other 
parts  of  the  eye  which  produces  a  bifurcation  of  the  luminous  ray,  and 
thus  two  images  are  formed  on  the  retina  instead  of  one.  A  single  eye 
may  also  be  affected  with  triplopy^  but  in  this  case  the  third  image  is 
exceedingly  weak. 

595.  Achromatopsy:  3>altonism. — Achrofnatopsy,  or  co/oicr disease,  is 
a  curious  affection  which  renders  us  incapable  of  distinguishing  colours,  or 
at  any  rate  certain  colours.  In  some  cases  the  insensibility  is  complete,  while 
in  others  some  colours  can  be  very  well  distinguished.  Persons  affected 
in  this  manner  can  distinguish  the  outlines  of  bodies  without  difficulty, 
and  they  can  also  discriminate  between  light  and  shade,  but  they  are 
unable  to  distinguish  the  different  tints. 

D'H ombres- Firmas  cites  an  instance  of  a  person  affected  with  achro- 
matopsy, who  had  painted  in  a  room  a  landscape  of  which  the  ground, 
trees,  houses,  and  men  were  all  painted  blue,  and  when  asked  why  he 
had  not  given  each  its  proper  colour,  he  replied  that  he  wished  to 
assimilate  the  colour  of  his  drawing  to  that  of  his  furniture ;  now  this 
was  red. 

Achromatopsy  is  also  sometimes  called  Daltonism,  because  Dalton, 
who  has  carefully  described  it,  was  so  affected. 

596.  Opbtbalmoscope. — This  instrument,  as  its  name  indicates,  is  de- 
signed for  the  examination  of  the  eye,  and  was  invented  in  1851  by  Prof. 


iH 


Oh  Li^/iL 


[986- 


HelmhoUi.  It  consists ;— i.  Of  n  concave  spherical  reflector  of  glass  or 
metal,  M  (t\>5:s»  474,  475\  in  the  middle  of  which  is  a  suiall  hole  alnnit  a 
sixth  of  an  inch  in  diameter.  The  focal  lonj;lh  of  the  ivtloctor  is  ln)ni  vS 
to  10  inches,     a.  Oi  a  converginj>~  achromatic  K  mh  is  held  in 

fn>nt  o(  the  eye  of  the  patient.     3.  Of  several  ue  ionver>;vni, 

otheJ'S  diveiyent,  any  one  of  which  can  be  fixed  iu  ,1  li.une  behind  the 
mirror  so  as  to  correct  any  given  imperfection  in  the  o))server's  si>»ht.  ll 
the  niirror  is  of  silvercd  j»lass»  it  is  not  necessary  that  it  be  pierceii  at  the 
centre ;  it  is  sntlicient  that  the  silverinj;  at  the  centre  be  removcii. 

To  ni.iko  uso  v>f  \hc  i>phthabnoscope,  the  patient  is  placed  in  a  darkened 
room,  and  a  Lunp  tuinished  with  a  sciX'cn  put  l)eside  him,  K.  The  screen 
serves  to  shade  the  light  from  his  head,  and  keep  it  in  darkness.     Vhc  oU- 


Fif .  474' 

server  A,  holdings:  in  one  hand  the  reflector,  employs  it  to  concentiaie  the 
light  of  the  lanvp  near  the  eye  B  of  the  patient,  and  with   his   other 
hand  holds  the  achromatic  lens  0  in  front  of  the  eye.     Hy  this  .ui.u\u:c 
ment  the  back  of  the  eye  is  lis;hted  up,  and  its  stntcture  can  bi^  rUnU 
discerned. 

Fig.  475  shoM's  how  the  image  of  the  back  of  the  e>*e  is  prodnced,  which 
the  observer  A  sees  on  looking  through  the  hole  in  the  reflector.     Let  ttfi 


Fif.  47S. 

be  the  part  of  the  retina  on  which  the  lij^jht  is  concentrated,  pencils  of  rays 
proceeding  from  ad  would  form  an  inverted  and  av^rial  imaj;e  of  afi  at  a  />'. 
These  pencils,  however,  on  leaving  the  e\"e,  pass  through  the  lens  <>,  and 
thus  the  image  n''l>"  is  in  fact  formed,  inverted,  but  distinct,  and  in  a 
position  tit  for  vision. 


598]  Phosphorescence,  525 

III':  j^rcat  quantity  of  li^lit  concentrated  by  the  ophthalmofcope  if  apt 
i<>  irniiiic  painfully  the  eye  of  the  patient.  There  arc,  therefore,  interpo»ed 
between  the  lamp  and  the  reflector  coloured  glaf»ef,  to  cut  off  the  irri- 
tating rayj»,  viz.,  the  red,  yellow,  and  violet  ray».  The  glawet  generally 
employed  arc  »taincd  green  or  cobalt  blue. 

liy  means  of  the  ophthalmoH<;ope  flelmholtz  ha»  found  that  in  an 
optical  point  of  view  no  eye  is  free  from  defectu. 


CHAFfEK  VII. 

SOURCES  OF  T.TCHT.     PHOSPHOR ESCEKC15. 

597.  VarlotM  •onroes  at  lifbt. — The  various  source*  of  light  arc  the 
Bun,  the  start,  heat,  chemical  combination,  phosphorescence,  electricity, 
and  meteoric  phenomena.  The  last  two  sources  will  be  treated  under 
the  articles  Electricity  and  Meteorology. 

'ITie  origin  of  the  light  emitted  by  the  sun  and  by  the  stars  is  unknbwn ; 
it  is  assumed  that  the  ignited  envelope  hjy  which  the  sun  is  surrounded  is 
gaseous,  because  the  light  of  the  sun,  like  that  emitted  from  all  gaseous 
bodies,  gives  no  trace  of  polarisation  in  the  polarising  telescope  (Chapter 
VIII.). 

As  regards  the  light  devebped  by  heat,  Pouillct  has  observed  that 
bodies  begin  to  be  luminous  in  the  dark  at  a  temperature  of  500*  to  600*  ; 
above  that  the  light  ia  brighter  in  proportion  as  the  temperature  is  higher. 

The  luminous  effects  witnessed  in  many  chemical  combinations  are 
flue  to  the  higli  temperatures  produced.  This  is  the  case  with  the  arti- 
ficial lights  used  for  illuminations;  for  as  we  have  already  seen,  luminous 
flames  are  nothing  more  than  gaseous  matters  containing  solids  heated 
to  the  point  of  incandescence. 

598.  Fhospboreseenoe :  its  soiirce*. — Phosphorescence  is  the  pro- 
perty which  a  large  nurnljer  of  substances  possess  of  emitting  light  when 
placed  under  certain  conditions. 

M.  liecquerel,  who  has  studied  this  subject  in  a  very  comprehensive 
manner,  and  has  arrived  at  some  extremely  remarkable  results,  refers  the 
phenomena  to  five  causes: — 

i.  Spontaneous  phosphorescence  in  certain  vegetables  and  animals ;  for 
instance,  it  is  very  intense  in  the  glow-worm  and  in  the  lampyre,  and  the 
brightness  of  their  light  appears  to  depend  on  their  will.  In  tropical 
climates  the  sea  is  often  covered  with  a  bright  phosphorescent  light  due 
to  some  extremely  sirt^ill  zoophytes.  These  animalcula;  emit  a  luminous 
matter  so  subtile  that  MM.  (^uoy  and  Gaimard,  during  a  voyage  under 
the  equator,  having  placed  two  in  a  tumbler  c;f  water,  the  liquid  imme- 
diately became  luminous  throughout  its  entire  mass. 

ii.  Phosphorescence  by  elevation  of  temperature.  This  is  best  seen  in 
certain  species  of  diamonds  and  in  fluorspar,  which,  when  heated  to  300^* 
or  400'^,  suddenly  becomes  luminous,  emitting  a  bluish  light. 


526  On  Light.  [598- 

iii.  Phosphorescence  by  mechanical  effects^  such  as  friction,  percussion, 
cleavage,  etc. :  for  example,  when  two  crystals  of  quartz  are  rubbed 
against  each  other  in  darkness,  or  when  a  lump  of  sugar  is  broken. 

iv.  Phosphorescence  by  electricity,  like  that  which  results  from  the 
friction  of  mercury  against  the  glass  in  a  barometric  tube,  and  especially 
from  the  electric  sparks  proceeding  either  from  an  ordinary  electrical 
machine,  or  from  a  Ruhmkorff's  coil. 

V.  Phosphorescence  by  isolation  or  exposure  to  the  sun.  A  large  number 
of  substances,  after  having  been  exposed  to  the  action  of  solar  light,  or  ot 
the  diffused  light  of  the  atmosphere,  emit  in  darkness  a  phosphorescence, 
the  colour  and  intensity  of  which  depend  on  the  nature  and  physical  con- 
dition of  these  substances.  This  kind  of  phosphorescence  has  been 
studied  by  M.  Becquerel,  an  abstract  of  whose  researches  is  given  in  the 
next  paragraph. 

599.  Pbospborescence  by  isolation. — This  was  first  observed  in  1604 
in  Bolognese  phosphorus  (sulphide  of  barium),  but  M.  Ed.  Becquerel  has 
also  discovered  it  in  a  great  number  of  substances.  The  sulphides  of 
calcium  and  strontium  are  those  which  present  it  in  the  highest  degree. 
When  well  prepared,  after  being  exposed  to  the  light,  they  are  luminous 
for  several  hours  in  darkness.  But  as  this  phosphorescence  takes  place 
in  vacuo  as  well  as  in  a  gaseous  medium,  it  cannot  be  attributed  to  a 
chemical  action,  but  rather  to  a  temporary  modification  which  the  body 
undergoes  from  the  action  of  light. 

After  the  substances  above  named,  the  best  phosphorescents  are  the 
following,  in  the  order  in  which  they  are  placed  :  a  large  number  of  dia- 
monds (especially  yellow),  and  most  specimens  of  fluorspar ;  then  arrago- 
nite,  calcareous  concretions,  chalk,  apatite,  heavy  spar,  dried  nitrate  of 
calcium,  and  dried  chloride  of  calcium,  cyanide  of  calcium,  a  large  num- 
ber of  strontium  or  barium  compounds,  magnesium  and  its  carbonate, 
etc.  Besides  these  a  large  number  of  organic  substances  also  become 
phosphorescent  by  insolation  ;  for  instance,  dry  paper,  silk,  cane-sugar, 
milk-sugar,  amber,  the  teeth,  etc. 

Becquerel  finds  that  the  different  spectral  rays  are  not  equally  well 
fitted  to  render  substances  phosphorescent.  The  maximum  effect  takes 
place  in  the  violet  rays,  or  even  a  little  beyond ;  while  the  light  emitted 
by  phosphorescent  bodies  generally  corresponds  to  rays  of  a  smaller  re- 
frangibility  than  those  of  the  light  received  by  them,  and  giving  rise  to 
the  action. 

The  tint  which  phosphorescent  bodies  assume  is  very  variable,  and 
even  in  the  same  body  it  changes  with  the  manner  in  which  it  is  prepared. 
In  strontium  compounds  green  and  blue  tints  predominate  ;  and  orange, 
yellow,  and  green  tints  in  the  sulphides  of  barium. 

The  duration  of  phosphorescence  varies  also  in  different  bodies.  In 
the  sulphides  of  calcium  and  strontium  phosphorescence  lasts  as  much  as 
thirty  hours  ;  with  other  substances  it  does  not  exceed  a  few  seconds,  or 
even  a  fraction  of  a  second. 

Phosphoroscope.  In  experimenting  with  bodies  whose  phosphorescence 
lasts  a  few  minutes  or  even  a  few  seconds,  it  is  simply  necessary  to  ex- 


i 


-599]  Phosphor oscope.  527 

pose  them  to  solar  or  diffused  light  for  a  short  time,  and  then  place  them 
in  darkness  :  their  luminosity  is  very  apparent,  especially  if  care  has  pre- 
viously been  taken  to  close  the  eyes  for  a  few  instants.  But  in  the  case 
of  bodies  whose  phosphorescence  lasts  only  a.  very  short  time,  this 
method  is  inadequate.  M.  Becquerel  has  invented  a  very  ingenious  ap- 
paratus, the  phosphoroscope^  by  which  bodies  can  be  viewed  immediately 
after  being  exposed  to  light  :  the  interval  which  separates  the  insolation 
and  observation  can  be  made  as  small  as  possible,  and  measured  with 
great  precision. 

This  apparatus,  which  is  constructed  by  M.  Duboscq,  consists  of  a 
closed  cylindrical  box,  AB  (fig.  476),  of  blackened  metal ;  on  the  ends 
there  are  two  apertures  opposite  each  other  which  have  the  form  of  a 
circular  sector.  One  only  of  these,  o,  is  seen  in  the  figure.  The  box 
is  fixed,  but  it  is  traversed  in  the  centre  by  a  movable  axis,  to  which  are 
fixed  two  circular  screens,  MM  and  PP,  of  blackened  metal  (fig.  477). 
Each  of  these  screens  is  perforated  by  four  apertures  of  the  same  shape 
as  those  in  the  box  ;  but  while  the  latter  correspond  to  each  other,  the 
apertures  of  the  screens  alternate,  so  that  the  open  parts  of  the  one  cor- 
respond to  the  closed  parts  of  the  other.  The  two  screens,  as  already 
mentioned,  are  placed  in  the  box,  and  fixed  to  the  axis,  which  by  means 
of  a  train  of  wheels,  worked  by  a  handle,  can  be  made  to  turn  with  any 
velocity. 

In  order  to  investigate  the  phosphorescence  of  any  body  by  means  of 
this  instrument,  the  body  is  placed  on  a  stirrup  interposed  between  the 
two  rotating  screens.  The  light  cannot  pass'  at  the  same  time  through 
the  opposite  apertures  of  the  sides  A  and  B,  because  one  of  the  closed 
parts  of  the  screen  MM,  or  of  the  screen  PP,  is  always  between  them. 
So  that  when  a  body,  a,  is  illuminated  by  light  from  the  other  side  of 
the  apparatus,  it  could  not  be  seen  by  an  observer  looking  at  the  aperture 
0,  for  then  it  would  be  masked  by  the  screen  PP.  Accordingly,  when  an 
observer  saw  the  body  a,  it  would  not  be  illuminated,  as  the  light  would 
be  intercepted  by  the  closed  parts  of  the  screen  MM.  The  body  a  would 
alternately  appear  and  disappear  ;  it  would  disappear  during  the  time  of 
its  being  illuminated,  and  appear  when  it  was  no  longer  so.  The  time 
which  elapses  between  the  appearance  and  disappearance  depends  on 
the  velocity  of  rotation  of  the  screens.  Suppose,  for  instance,  that  they 
made  150  turns  in  a  second  ;  as  one  revolution  of  the  screens  is  effected 
in  ji^y  of  a  second,  there  would  be  four  appearances  and  four  disappear- 
ances during  that  time.  Hence  the  length  of  time  elapsing  between  the 
time  of  illuminatior 
o-ooo8  of  a  second. 

Observations  with  the  phosphoroscope  are  made  in  a  dark  chamber, 
the  observer  being  on  that  side  on  which  is  the  wheelwork.  A  ray  of 
solar  or  of  electric  light  is  allowed  to  fall  upon  the  substance  «,  and  the 
screens  being  made  to  rotate  more  or  less  rapidly,  the  body  a  appears 
luminous  by  transparence  in  a  continuous  manner,  when  the  interval 
between  insolation  and  observation  is  less  than  the  duration  of  the  phos- 
phoresence  of  the  body.     By  experiments  of  this  kind,  Becquerel  has 


528 


On  Light. 


[600- 


found  that  substances  which  usually  are  not  phosphorescent  become  so 
in  the  phosphoroscope  ;  such,  for  instance,  is  Iceland  spar.  Uranium 
compounds  present  the  most  brilliant  appearance  in  this  apparatus  ;  they 
emit  a  very  bright  luminosity  when  the  observer  can  see  them  0*03  or 


Fig.  476. 

0*004  ot  a  second  after  insolation.  But  a  large  number  of  bodies  present 
no  effect  in  the  phosphoroscope  ;  for  instance,  quartz,  sulphur,  phos- 
phorus, metals,  and  liquids. 


CHAPTER  VIII. 

DOUBLE   REFRACTION.      INTERFERENCE.      POLARISATION. 

600.  The  undulatory  theory  of  ligrht. — It  has  been  already  stated 
(469)  that  the  phenomenon  of  light  is,  with  good  reason,  ascribed  to 
undulations  propagated  through  an  exceedingly  rare  medium  called  the 
luminiferous  ether,  which  is  supposed  to  pervade  all   space,  and  to  exist 


-600]  Undidatory  Theory  of  Light.  529 

between  the  molecules  of  the  ordinary  forms  of  matter.  In  a  word,  it  is 
held  that  light  is  due  to  the  undulations  of  the  ether,  just  as  sound  is 
due  to  undulations  propagated  through  the  air.  In  the  latter  case  the 
undulations  cause  the  drum  of>the  ear  to  vibrate  and  produce  the  sensa- 
tion of  sound.  In  the  former  case  the  undulations  cause  points  of  the 
retina  to  vibrate  and  'produce  the  sensation  of  Light.  The  two.  cases 
difler  in  this,  that  in  the  case  of  sound  there  is  independent  evidence  of 
the  existence  and  vibration  of  the  medium  (air)  which  propagates  the 
undulation  ;  whereas  in  the  case  of  light  the  existence  of  the  medium  and 
its  vibrations  are  assumed,  because  that  supposition  connects  and  explains 
in  the  most  complete  manner  a  long  series  of  very  various  phenomena. 
There  is,  however,  no  independent  evidence  of  the  existence  of  the  lumi- 
niferous  ether. 

The  analogy  between  the  phenomena  of  sound  and  light  is  very  close  ; 
thus,  the  intensity  of  a  sound  is  greater  as  the  amplitude  of  the  vibration 
of  each  particle  of  the  air  is  greater,  and  the  intensity  of  light  is  greater 
as  the  amplitude  of  the  vibration  of  each  particle  of  the  ether  is  greater. 
Again,  a  sound  is  more  acute  as  the  length  of  each  undulation  producing 
the  sound  is  less,  or,  what  comes  to  the  same  thing,  according  as  the 
number  of  vibrations  per  minute  is  greater.  In  like  manner,  the  colour 
of  light  is  different  according  to  the  length  of  the  undulation  producing 
the  light  :  a  red  light  is  due  to  a  comparatively  long  undulation,  and  coi^- 
responds  to  a  deep  sound,  while  a  violet  light  is  due  to  a  short  undula- 
tion, and  corresponds  to  an  acute  soimd. 

Although  the  length  of  the  undulations  cannot  be  observed  directly, 
yet  they  can  be  inferred  from  certain  phenomena  with  great  exactness. 
The  following  table  gives  the  length  of  the  undulations  corresponding  to 
the  light  at  the  principal  dark  lines  of  the  spectrum.  The  lengths  are 
given  in  decimals  of  an  inch^ 

Dark  Length  of 

Line  Undulation 

B  ........  .  0-0000271 

C  .         .         .         .         .         ..        .  .  0*0000258 

D .  0-0000244 

E .  0-0000207 

F  .         .         •         •         •         •         •  •  0-0000191 

G  .         .         ...         .         .  .  0-0000169 

H  .......  .  0-0000155 

It  will  be  remarked  that  the  limits  are  very  narrow  within  which  the 
lengths  of  the  undulations  of  the  ether  must  be  comprised,  if  they  are  to 
be  capable  of  producing  the  sensation  of  light.  In  this  respect  light  is  in 
marked  contrast  to  sound.  For  the  limits  are  very  wide  within  which 
the  lengths  of  the  undulations  of  the  air  may  be  comprised  when  they 
produce  the  sensation  of  sound  (230). 

The  undulatory  theory  readily  explains  the  colours  of  different  bodies. 
According  to  that  theory,  certain  bodies  have  the  property  of  exciting 
undulations  of  different  lengths,  and  thus  producing  light  of  given  colours. 

A  A 


530  On  Light,  [600- 

White  light  or  daylight  results  from  the  coexistence  of  undulations  of  all 
possible  lengths. 

The  colour  of  a  body  is  due  to  the  power  it  has  of  extinguishing  certain 
vibrations,  and  reflecting  others  ;  and  the  body  appears  of  the  colour 
produced  by  the  coexistence  of  the  reflected  vibrations.  A  body  appears 
white  when  it  reflects  all  different  vibrations  in  the  proportion  in  which 
they  are  present  in  the  spectrum  :  it  appears  black  when  it  reflects  light 
in  such  small  quantities  as  not  to  affect  the  eye.  A  red  body  is  one 
which  has  the  property  of  reflecting  in  predominant  strength  those 
vibrations  which  produce  the  sensation  of  red.  This  is  seen  in  the  fact 
that,  when  a  piece  of  red  paper  is  held  against  the  daylight,  and  the  re- 
flected light  is  caught  on  a  white  wall,  this  also  appears  red.  A  piece  of 
red  paper  in  the  red  part  of  the  spectrum  appears  of  a  brighter  red,  and 
a  piece  of  blue  paper  held  in  the  blue  part  appears  a  brighter  blue ; 
while  a  red  paper  placed  in  the  violet  or  blue  part,  appears  almost  black. 
In  the  last  case  the  red  paper  can  only  reflect  red  rays,  while  it  extin- 
guishes the  blue  rays,  and  as  the  blue  of  the  spectrum  is  almost  free  from 
red,  so  little  is  reflected  that  the  paper  appears  black. 

The  undulatory  theory  likewise  explains  the  colours  of  transparent 
bodies.  Thus,  a  vibrating  motion  on  reaching  a  body  sets  it  in  vibration. 
So  also  the  vibrations  of  the  luminiferous  ether  are  communicated  to  the 
ether  in  a  body,  and  setting  it  in  motion  produce  light  of  different  colours. 
When  this  motion  is  transmitted  through  any  body,  it  is  said  to  be  trans- 
parent or  translucent^  according  to  the  different  degrees  of  strength  with 
which  this  transmission  is  effected.-  In  the  opposite  case  it  is  said  to  be 
opaque. 

When  light  falls  upon  a  transparent  body,  the  body  appears  colourless 
if  all  the  vibrations  are  transmitted  in  the  proportion  in  which  they  exist 
in  the  spectrum.  But  if  some  of  the  vibrations  are  checked  or  extin- 
guished, the  emergent  light  will  be  of  the  colour  produced  by  the  coexist- 
ence of  the  unchecked  vibrations.  Thus,  when  a  piece  of  blue  glass  is 
held  before  the  eye,  the  vibrations  producing  red  and  yellow  are  extin- 
guished, and  the  colour  is  due  to  the  emergent  vibrations  which  produce 
blue  light. 

The  undulatory  theory  also  accounts  for  the  reflection  and  refraction 
of  light,  as  well  as  other  phenomena  which  are  yet  to  be  described.  The 
explanation  of  the  refraction  of  light  is  of  so  much  importance  that  we 
shall  devote  to  it  the  following  article. 

60 1.  Pbysical  explanation  of  single  refraction. — The  explanation  of 
this  phenomenon  by  means  of  the  undulatory  theory  of  light  presupposes 
that  of  the  mode  of  propagation  of  a  plane  wave.  Now,  if  a  disturbance 
originated  at  any  point  of  the  ether,  it  would  be  propagated  as  a  spherical 
wave  in  all  directions  round  that  point  with  a  uniform  velocity.  If, 
instead  of  a  single  point,  we  consider  the  front  of  a  plane  wave,  it  is 
evident  that  disturbances  originate  simultaneously  at  all  points  of  the 
front,  and  that  spherical  waves  proceed  from  each  point  with  the  same 
uniform  velocity.  Consequently  all  these  spheres  will  at  any  subsequent 
instant  be  touched  by  a  plane  parallel  to  the  original  plane.     The  dis- 


-602]  Explanation  of  SirigLe  Kef raction.  531 

turbances  propagated  from  the  points  in  the  first  position  of  the  wave 
will  mutually  destroy  each  other,  except  in  the  tangent  plane ;  consequently 
the  wave  advances  as  a  plane  wave,  its  successive  positions  being  the 
successive  positions  of  the  tangent  plane.  If  the  wave  moves  in  the 
medium  with  a  velocity  v^  it  will  describe  a  space  vt  in  a  time  t. 

Suppose  the  plane  wave,  AC  (fig.  478),  to  move  through  vacuum  and 


Fig.  478. 

to  meet  the  plane  surface,  AB,  of  an  ordinary  refracting  medium  at  an 
angle  CAB  or  I.  Suppose  the  velocity  of  propagation  in  vaaio  to  be  7/, 
and  in  the  medium  to  be  v'.  Now  the  wave  entering  the  medium  at  A 
will,  after  any  time  /,  be  moving  partly  within  and  partly  without  the 
medium.  Suppose  PR  to  be  the  part  outside  the  medium,  draw  PN  at 
right  angles  to  AC,  then  PN  equals  vt.  Now  in  the  same  time,  /,  a 
spherical  wave  propagated  irom  A,  will  have  a  radius  v't\  if,  then,  PO  is 
drawn,  touching  a  circle  whose  centre  is  A  and  whose  radius  AQ  equals 
7/7,  then  PQ  will  be  the  position  of  the  plane  wave  within  the  medium  at 
the  instant  under  consideration.  If  we  denote  the  angle  APQ  by  R  it  is 
plain  that 

Sin  I  :  sin  R::PN  :  AQ::^//  :  v'twv  :  v\ 

But  a  succession  of  parallel  plane  waves  will  give  rise  to  a  pencil  of 
parallel  rays  at  right  angles  to  the  waves  ;  consequently,  with  respect  to 
any  one  of  these  rays,  I  and  R  are  the  angles  of  incidence  and  retraction. 
Therefore  the  ratio  of  the  sines  of  those  angles  is  constant  and  equals 
V  :  v',  which  is  the  distinctive  law  of  single  refraction. 

Moreover,  if  /u  is  the  refractive  index  of  the  substance,  v  -^  v'  equal  //, 
that  is,  V  equals  v'  ju.  Now,  under  all  circumstances,  ^  is  greater  than  i, 
and  therefore  v  is  greater  than  v^\  a  result  which  coincides  with  that  ob- 
tained from  experiment  (476). 

DOUBLE  REFRACTION. 

602.  Double  refraction. — It  has  been  already  stated  (504),  that  a  large 
number  of  crystals  possess  the  property  of  double  refraction,  in  virtue  of 
which  a  single  incident  ray  in  passing  through  any  one  of  them  is  divided 
into  two,  or  undergoes  bifurcation,  whence  it  follows  that,  when  an 


071  Light, 


[602 


object  is  seen  through  one  of  these  crystals,  it  appears  double.  The  fact 
of  the  existence  of  double  refraction  in  Iceland  spar  was  first  stated  by 
Bartholin  in  1669,  but  the  law  of  double  refraction  was  first  enunciated 
exactly  by  Huyghens  in  his  treatise  on  light  written  in  1678,  and  published 
in  1690. 

Crystals  which  possess  this  peculiarity  are  said  to  be  double  refracting. 
It  is  found  to  a  greater  or  less  extent  in  all  crystals  which  do  not  belong 
to  the  cubical  system.  Bodies  which  crystallise  in  this  system,  and  those 
which,  like  glass,  are  destitute  of  crystallisation,  have  no  double  refraction. 
The  property  can,  however,  be  imparted  to  them  when  they  are  unequally 
compressed,  or  when  they  are  cooled  quickly  after  having  been  heated,  in 
which  state  glass  is  said  to  be  ufimmealed.  Of  all  substances,  that  which 
possesses  it  most  remarkably  is  Iceland  spar  or  carbonate  of  calcium. 
In  many  substances  the  power  of  double  refraction  can  hardly  be  proved 
to  exist  directly  by  the  bifurcation  of  an  incident  ray  ;  but  its  existence 
is  shown  indirectly  by  their  being  able  to  depolarise  light  (625). 

Fresnel  has  explained  double  refraction  by  assuming  that  the  ether  in 
double  refracting  bcdies  is  not  equally  elastic  in  all  directions  ;  from 
which  it  follows  that  the  vibrations,  in  certain  directions  at  right  angles 
to  each  other,  are  transmitted  with  unequal  velocities  ;  these  directions 
being  dependent  on  the  constitution  of  the  crystal.  This  hypothesis  is 
confirmed  by  the  property  which  glass  acquires  of  becoming  double  re- 
fracting by  being  unannealed  and  by  pressure. 

603.  Uniaxial  crystals. — In  all  double  refracting  crystals  there  is  one 
direction,  and  in  some  a  second  direction  possessing  the  following  pro- 
perty. When  a  point  is  looked  at  through  the  crystal  in  this  particular 
direction,  it  does  not  appear  double.  The  lines  fixing  these  directions 
are  called  optic  axes ;  and  sometimes,  though  not  very  properly,  axes  of 
double  refraction.  A  crystal  is  called  uniaxial  when  it  has  one  optic  axis, 
that  is  to  say,  when  there  is  one  direction  within  the  crystal  along  which 
a  ray  of  light  can  proceed  without  bifurcation.  When  a  crystal  has  tivo 
such  axes,  it  is  called  a  Max  ial  crystal. 

The  uniaxial  crystals  most  frequently  used  in  optical  instruments  are 
Iceland  spar,  quartz,  and  tourmaline.     Iceland  spar  crystallises  in  rhom- 

bohedra,  whose  faces  form  with  each  other 
angles  of  105°  5'  or  74°  55'.  It  has  eight 
solid  angles  (see  fig.  479).  Of  these  two, 
situated  at  the  extremities  of  one  of  the 
diagonals,  are  severally  contained  by  three 
obtuse  angles.  A  line  drawn  within  one 
of  these  two  angles  in  such  a  manner  as 
to  be  equally  incHned  to  the  three  edges 
Fig.  479.  containing  the  angle  is  called  the  axis  of 

the  crystal.    If  all  the  edges  of  the  crystal 
were  equal,  the  axis  of  the  crystal  would  coincide  with  the  diagonal,  ab. 

Brewster  has  shown  that  in  all  uniaxial  crystals  the  optic  axis  coincides 
with  the  axis  of  crystallisation. 

The  principal  plane  with  reference  to  a  point  of  any  face  of  a  crystal, 


-605]  Double  Refraction.  533 

whether  natural  or  artificial,  is  a  plane  drawn  through  that  point  at  right 
angles  to  the  face  and  parallel  to  the  optic  axis.  If  in  fig.  479  we  suppose 
the  edges  of  the  rhombohedron  to  be  equal,  the  diagonal  plane  abed 
contains  the  optic  axis  {ab)^  and  is  at  right  angles  to  the  faces  aedf  and 
chbg ;  consequently,  it  is  parallel  to  the  principal  plane  at  any  point  of 
either  of  those  two  faces.  For  this  reason  abed  is  often  called  the  principal 
plane  with  respect  to  those  faces. 

604.  Ordinary  and  extraordinary  ray.—  Of  the  two  rays  into  which 
an  incident  ray  is  divided  on  entering  a  uniaxial  crystal,  one  is  called  the 
ordinary  and  the  other  the  extraordifiary  ray.  The  ordinary  ray  follows 
the  laws  of  single  refraction,  that  is,  with  respect  to  that  ray  the  sine  of 
the  angle  of  incidence  bears  a  constant  ratio  to  the  sine  of  the  angle  of 
refraction,  and  the  plane  of  incidence  coincides  with  the  plane  of  refrac- 
tion. Except  in  particular  positions,  the  extraordinary  ray  follows  neither 
of  these  laws.  The  images  corresponding  to  the  ordinary  and  extraordi- 
nary rays  are  called  the  ordinary  and  extraordinary  images  respectively. 

If  a  transparent  specimen  of  Iceland  spar  be  placed  over  a  dot  of  ink, 
on  a  sheet  of  white  paper,  the  two  images  will  be  seen.  One  of  them,  the 
ordinary  image,  will  seem  slightly  nearer  to  the  eye  than  the  other,  the  extra- 
ordinary image.  Suppose  the  spectator  to  view  the  dot  in  a  direction  at 
right  angles  to  the  paper,  then,  if  the  crystal,  with  the  face  still  on  the 
paper,  be  turned  round,  the  ordinary  image  will  continue  fixed,  and  the 
extraordinary  image  will  describe  a  circle  round  it,  the  line  joining  them 
being  always  in  the  direction  of  the  shorter  diagonal  of  the  face  of  the 
crystal,  supposing  its  edges  to  be  of  equal  length.  In  this  case  it  is  found 
that  the  angle  between  the  ordinary  and  extraordinary  ray  is  6°  I2^ 

605.  The  laws  of  double  refraction  in  a  uniaxial  crystal. — These 
phenomena  are  found  to  obey  the  following  laws: — 

i.  Whatever  be  the  plane  of  incidence,  the  ordinary  ray  always  obeys 
the  two  general  laws  of  single  refraction  (504).  The  refractive  index  for 
the  ordinary  ray  is  called  the  ordinary  refractive  index.  < 

ii.  In  every  section  perpendicular  to  the  optic  axis  the  extraordinary 
ray  also  follows  the  laws  of  single  refraction.  Consequently  in  this  plane 
the  extraordinary  ray  has  a  constant  refractive  index,  which  is  called  the 
extraordinary  refractive  index. 

iii.  In  every  principal  section  the  extraordinary  ray  follows  the  second 
law  only  of  single  refraction,  that  is,  the  planes  of  incidence  and  refraction 
coincide,  but  the  ratio  of  the  sines  of  the  angles  of  incidence  and  refraction 
is  not  constant. 

iv.  The  velocities  of  light  along  the  rays  are  unequal.  It  can  be  shown 
that  the  difference  between  the  squares  of  the  reciprocals  of  the  velocities 
along  the  ordinary  and  extraordinary  rays  is  proportional  to  the  square  of 
the  sine  of  the  angle  between  the  latter  ray  and  the  axis  of  the  crystal. 

There  is  an  important  difference  between  the  velocity  of  the  ray  and 
the  velocity  of  the  corresponding  plane  wave.  If  the  velocities  of  the 
plane  waves  corresponding  to  the  ordinary  and  extraordinary  rays  are 
considered,  the  difference  between  the  squares  of  these  velocities  is  pro- 
portional to  the  square  of  the  sine  of  the  angle  between  the  axis  of  the 


534  On  Light  [605- 

crystal  and  the  normal  to  that  plane  wave  which  corresponds  to  the  ex- 
traordinary ray.     The  normal  and  the  ray  do  not  generally  coincide. 

Huyghens  gave  a  very  remarkable  geometrical  construction,  by  means 
of  which  the  directions  of  the  refracted  rays  can  be  determined  when  the 
directions  of  the  incident  ray  and  of  the  axis  are  known  relatively  to  the 
face  of  the  crystal.  This  construction  was-  not  generally  accepted  by 
physicists  until  Wollaston  and  subsequently  Malus  showed  its  truth  by 
numerous  exact  measurements. 

606.  Positive  and  neg-ative  uniaxial  crystal. — The  term  extra- 
ordinary refractive  index  has  been  defined  in  the  last  article.  For  the 
same  crystal  its  magnitude  always  differs  from  that  of  the  ordinary  re- 
fractive index  :  for  example,  in  Iceland  spar  the  ordinary  refractive  index 
is  I -654,  while  the  extraordinary  refractive  index  is  i'483.  In  this  case 
the  ordinary  index  exceeds  the  extraordinary  index.  When  this  is  the 
case,  the  crystal  is  said  to  be  negative.  On  the  other  hand,  when  the 
extraordinary  index  exceeds  the  ordinary  index,  the  crystal  is  said  to  be 
positive.  The  following  list  gives  the  names  of  some  of  the  principal 
uniaxial  crystals : — 

Negative  Uniaxial  Crystals. 
Iceland  spar  Emerald 

Spathose  Iron  Apatite 

Tourmaline  Pyromorphite 

Sapphire  Ferrocyanide  of  potassium 

Ruby  Nitrate  of  sodium 

Positive  Uniaxial  Crystals. 

Zircon  Ice 

Quartz  Titanite 

Apophyllite  Boracite 

607.  Double  refraction  in  biaxial  crystals. — A  large  number  of 
crystals,  including  all  those  belonging  to  the  trimetric,  the  inonoclittic, 
and  the  triclinic  systems,  possess  two  optic  axes ;  in  other  words,  in  each 
of  these  crystals  there  are  two  directions  along  which  a  ray  of  light  passes 
without  bifurcation.  A  line  bisecting  the  acute  angle  between  the  optic 
axes  is  called  the  medial  line  ;  one  that  bisects  the  obtuse  angle  is  called 
the  supplementary  line.  It  has  been  found  that  the  medial  and  supple- 
mentary lines  and  a  third  line  at  right  angles  to  both  are  closely  related 
to  the  fundamental  form  of  the  crystal  to  which  the  optic  axes  belong. 

The  acute  angle  between  the  optic  axes  is  different  in  different  crystals. 
The  following  table  gives  the  magnitude  of  this  angle  in  the  case  of 
certain  crystals : — 


Nitre     . 

.       5°  20' 

Anhydrite 

.     28° 

r 

Strontianite  . 

.      6  56 

Heavy  spar  . 

•     37 

42 

Arragonite     . 

.     18  18 

Mica     . 

•     45 

0 

Brazilian  topaz 

.    49  50 

Kyanite  - 

.     81 

48 

Sugar    . 

.     50    0 

Epidote 

.     84 

19 

Selenite 

.    60    0 

Sulphate  of  iron 

.     90 

0 

-  608]  Interference  of  L  ight.  535 

When  a  ray  of  light  enters  a  biaxial  crystal,  and  passes  in  any  direction 
not  coinciding  with  an  optic  axis,  it  undergoes  bifurcation  ;  in  this  case 
however,  neither  ray  conforms  to  the  laws  of  single  refraction,  but  both 
are  extraordinary  rays.  To  this  general  statement  the  following  exception 
must  be  made.  In  a  section  of  a  crystal  at  right  angles  to  the  medial 
line  one  ray  follows  the  law  of  ordinary  refraction,  and  in  a  section  at 
right  angles  to  the  supplementary  line  the  other  ray  follows  the  laws  of 
ordinary  refraction. 

INTERFERENCE  AND   DIFFRACTION. 

608.  Interference  of  ligrht.— The  name  interference  is  given  to  the 
mutual  action  which  two  luminous  rays  exert  upon  each  other  when  they 
are  emitted  from  two  neighbouring  sources,  and  meet  each  other  under  a 
very  small  angle.  This  action  may  be  observed  by  means  of  the  following 
experiment.  In  the  shutter  of  a  dark  room  two  very  small  apertures  are 
made,  of  the  same  diameter,  at  a  very  small  distance  from  each  other. 
The  apertures  are  closed  by  pieces  of  coloured  glass — red,  for  example — 
by  which  two  pencils  of  homogeneous  light  are  introduced.  These  two 
pencils  form  two  divergent  luminous  cones,  which  meet  at  a  certain  dis- 
tance ;  they  are  received  on  a  white  screen  a  little  beyond  the  place  at 
which  they  meet,  and  in  the  segment  common  to  the  two  discs  which 
form  upon  this  screen  some  very  well-defined  alternations  of  red  and 
black  bands  are  seen.  If  one  of  the  two  apertures  be  closed,  the  fringes 
disappear,  and  are  replaced  by  an  almost  uniform  red  tint.  From  the 
fact  that  the  dark  fringes  disappear  when  one  of  the  beams  is  intercepted, 
it  is  concluded  that  they  arise  from  the  interference  of  the  two  pencils 
which  cross  obliquely. 

This  experiment  was  first  made  by  Grimaldi,  but  was  modified  by 
Young.  Grimaldi  had  drawn  from  it  the  conclusion  that  light  added  to 
light  produced  darkness.  The  full  importance  of  this  principle  remained 
for  a  long  time  unrecognised,  until  these  enquiries  were  resumed  by  Young 
and  Fresnel,  of  whom  the  latter,  by  a  modification  of  Grimaldi's  experi- 
ment, rendered  it  an  exper-imentum  cruets  of  the  truth  of  the  undulatory 
hypothesis. 

In  Grimaldi's  experiment  diffraction  (609)  takes  place  ;  for  the  luminous 
rays  pass  by  the  edge  of  the  aperture.  In  Fresnel's  experiment  the  two 
pencils  interfere  without  the  possibility  of  diffraction. 

Two  plane  mirrors,  AB  and  BC  (fig.  480),  of  metal,  are  arranged  close 
to  each  other,  so  as  to  form  a  very  obtuse  angle,  ABC,  which  must  be 
very  little  less  than  180°.  A  pencil  of  red  light,  which  passes  into  the 
dark  chamber,  is  brought,  by  means  of  a  lens,  L,  to  a  focus  F.  On 
diverging  from  F  the  rays  fall  partly  on  AB,  and  partly  on  BC.  If  BA 
is  produced  to  P  and  FPF^  is  drawn  at  right  angles  to  AP,  and  if  PFj  is 
made  equal  to  PF,  then  the  rays  which  fall  on  AB  will,  after  reflection, 
proceed  as  if  they  diverged  from  F^.  If  a  similar  construction  is  made 
for  the  rays  falling  on  BC,  they  will  proceed  after  reflection  as  if  they 
diverged  from  F2.     A  little  consideration  will  show  that  Fj  and  Fj  are 


536 


On  Light, 


[608 


very  near  each  other.  Suppose  the  reflected  rays  to  fall  on  a  screen  SS^ 
placed  nearly  at  right  angles  to  their  directions.  Every  point  of  the 
screen  -which  receives  light  from  both  pencils  is  illuminated  by  two  rays, 
viz.  one  from  F^,  the  other  from  F.^ ;  thus  the  point  H  is  illuminated  by 
two  rays,  as  also  are  K  and  I.     Now  the  combined  action  of  these  two 


^^^-^;::^ 


pencils  is  to  form  a  series  of  parallel  bands  alternately  hght  and  dark  on 
the  screen  at  right  angles  to  the  plane  of  the  paper.  This  is  the  funda- 
mental phenomenon  of  interference,  and  that  it  results  from  the  joint 
action  of  the  two  pencils  is  plain,  since,  if  the  light  which  falls  upon  either 
of  the  mirrors  is  cut  off,  the  dark  bands  disappear. 

This  remarkable  fact  is  explained  in  the  most  satisfactory  manner  by 
the  undulatory  theory  of  light.  The  explanation  exactly  resembles  that 
already  given  of  the  formation  of  nodes  and  loops  by  the  combined  action 
of  two  aerial  waves  (253)  ;  the  only  difference  being  that  in  that  case 
the  vibrating  particles  were  supposed  to  be  particles  of  air,  whereas,  in 
the  present  case,  the  vibrating  particles  are  supposed  to  be  those  of  the 
luminiferous  ether.  Consider  any  point  K  on  the  screen,  and  first  let  us 
suppose  the  distances  of  K  from  F^  and  F2  to  be  equal.  Then  the  un- 
dulations which  reach  K  will  always  be  in  th-e  same  phase,  and  the 
particle  of  ether  at  K  will  vibrate  as  if  the  light  came  from  one  source  : 
the  amplitude  of  the  vibration,  however,  will  be  increased  in  exactly  the 
same  manner  as  happens  at  a  loop  or  ventral  point;  consequently  at  K 
the  intensity  of  the  light  will  be  increased.^  And  the  same  will  be  true 
for  all  points  on  the  screen,  such  that  the  difference  between  their  dis- 
tarrces  from  the  two  images  ec^uals  the  length  of  o?i€,  two,  three,  etc., 
undulations.  If,  on  the  other  hand,  the  distances  of  K  from  Fj  and  F'o 
differ  by  the  length  of  half  an  undulatnon,  then  the  two  waves  would 
reach  K  in  exactly  opposite  phases.  Consequently,  whatever  velocity 
would  be  communicated  at  any  instant  to  a  particle  of  ether  by  the  one 
undulation,  an  exactly  equal   and  opposite  velocity  would  be   commu- 


-609] 


Diffraction  and  Fi'inges. 


537 


nicated  by  the  other  undulation,  and  the  particle  would  be  permanently 
at  rest,  or  there  would  be  darkness  at  that  point;  this  result  being  pro- 
duced in  a  manner  precisely  resembling  the  formation  of  a  nodal  point 
already  explained.  The  same  will  be  true  for  all  positions  of  K,  such 
that  the  differences  between  its  distances  from  F^  and  F<j  equal  three 
halves,  or  five  halves,  or  seven  halves,  etc.,  of  an  undulation.  Accord- 
ingly^ there  will  be  on  the  screen  a  succession  of  alternations  of  light  and 
dark  points,  or  rather  lines — for  what  is  true  of  points  in  the  plane  of  the 
paper  (fig.  480)  will  be  equally  true  of  other  points  on  the  screen  which 
is  supposed  to  be  at  right  angles  to  the  plane  of  the  paper.  Between  the 
light  and  dark  lines  the  intensity  of  the  light  will  vary,  increasing  gra- 
dually from  darkness  to  its  greatest  intensity,  and  then  decreasing  to  the 
second  dark  line,  and  so  on. 

If  instead  of  red  light  any  other  coloured  light  were  used,  for  example 
violet  light,  an  exactly  similar  phenomenon  would  be  produced,  but  the 
distance  from  one  dark  line  to  another  would  be  different.  If  white  light 
were  used,  each  separate  colour  tends  to  produce  a  different  set  of  dark 
lines.  Now  these  sets  being  superimposed.on  each  other,  and  not  coin- 
ciding, the  dark  lines  due  to  one  colour  are  illuminated  by  other  colours, 
and  instead  of  dark  lines  a  succession  of  coloured  bands  is  produced. 
The  number  of  coloured  bands  produced  by  white  light  is  much  smaller 
than  the  number  of  dark  lines  produced  by  a  homogeneous  light ;  since 
at  a  small  distance  from  the  middle  band  the  various  colours  are  com- 
pletely blended,  and  a  uniform  white  light  produced. 

609.  Diffraction  and  fringes. — Diffraction  is  a  modification  which 
light  undergoes  when  it  passes  the  edge  of  a  body,  or  when  it  traverses 
a  small  aperture ;  a  modification  in  virtue  of  which  the  luminous  rays 
appear  to  become  bent,  and  to  penetrate  into  the  shadow. 

This  phenomenon  may  be  observed  in  the  following  manner  :  A  beam 
of  solar  light  is  allowed  to  pass  through  a  very  small  aperture  in  the 
shutter  of  a  dark  room,  where  it  is  received  on  a  condensing  lens,  L  (fig. 
481),  with  a  short  focal  length.      A  red  glass  is  placed  in  the  aperture 


^;""""" """""^^^3 


Fig.  481. 

so  as  only  to  allow  red  light  to  pass.  An  opaque  screen,  <?,  with  a  sharp 
edge,  a  razor  for  instance,  is  placed  behind  the  lens  beyond  its  focus,  and 
intercepts  one  portion  of  the  luminous  cone,  while  the  other  is  projected 
on  the  screen  b,  of  which  B  represents  a  front  view.  The  following 
phenomena  are  now  seen :  Within  the  geometrical  shadow,  the  limit  of 
which  is  represented  by  the  line  ab,  a  faint  light  is  seen,  which  gradually 
fades  in  proportion  as  it  is  farther  from  the  limits  of  the  shadow.  In 
this  part  of  the  screen  which,  being  above  the  line  ab,  might  be  expected 

A  A  3 


538  On  Light.  [609- 

to  be  uniformly  illuminated  a  series  of  alternate  dark  and  light  bands  or 
fringes  are  seen  parallel  to  the  line  of  shadow,  which  gradually  become 
more  indistinct  and  ultimately  disappear.  The  limits  between  the  light 
and  dark  fringes  are  not  quite  sharp  lines ;  there  are  parts  of  maximum 
and  minimum  intensity  which  gradually  fade  off  into  each  other. 

All  the  colours  of  the  spectrum  give  rise  to  the  same  phenomenon,  but 
the  fringes  are  broader  in  proportion  as  the  light  is  less  refrangible. 

Thus,  with  red  light  they  are  broader  than  with  green,  and  with  green 
than  with  violet.  Hence,  with  white  light,  which  is  composed  of 
different  colours,  the  dark  spaces  of  one  tint  overlap  the  light  spaces  of 
another,  and  thus  a  series  of  prismatic  colours  will  be  produced. 

If,  instead  of  placing  the  edge  of  an  opaque  body  between  the  light 
and  the  screen,  a  very  narrow  body  be  interposed,  such  as  a  hair  or  a 
fine  metallic  wire,  the  phenomena  will  be  different.  Outside  the  space 
corresponding  to  the  geometrical  shadow,  there  is  a  series  of  fringes,  as 
in  the  former  case.  But  within  the  shadow  also  there  is  a  series  of 
alternate  light  and  dark  bands.  They  are  called  interior  fringes,  and 
are  much  narrower  and  more  numerous  than  the  external  fringes. 

When  a  small  opaque  circular  disc  is  interposed,  its  shadow  on  the 
screen  shows  in  the  middle  a  bright  spot  surrounded  by  a  series  of 
coloured  concentric  rings ;  the  bright  spot  is  of  various  colours  according 
to  the  relative  positions  of  the  disc  and  screen.  The  haloes  some- 
times seen  round  the  sun  and  moon  belong  to  this  class  of  pheno- 
mena. They  are  due,  as  P^raunhofer  has  shown,  to  the  diffraction  of 
light  by  small  globules  of  fog  in  the  atmosphere.  Fraunhofer  has  even 
given  a  method  of  estimating  the  mean  diameter  of  these  globules  from 
the  dimensions  of  the  haloes.  A  beautiful  phenomenon  of  the  same  kind 
is  produced  by  looking  at  a  flame  through  lycopodium  powder  strewed  on 
glass. 

6io.  Gratingrs* — Phenomena  of  diffraction  of  another  class  are  pro- 
duced by  allowing  the  pencil  of  light  from  the  luminous  point  to 
traverse  an  aperture  in  an  opaque  screen.  The  diffracted  light  may  be 
received  on  a  sheet  of  white  paper,  but  the  images  are  much  better  seen 
through  a  small  telescope  placed  behind  the  aperture.  If  the  aperture  is 
very  small,  the  telescope  may  be  dispensed  with,  and  the  figure  may  be 
viewed  by  placing  the  aperture  before  the  eye. 

.Some  of  the  simpler  apertures,  such  as  straight  lines,  triangles,  squares, 
or  circles,  may  be  cut  out  of  tinfoil  pasted  on  glass.  Gratings  may  be 
obtained  either  by  a  series  of  fine  equidistant  wires,  or  by  careful  ruling 
on  a  piece  of  smoked  glass  ;  and  apertures  of  any  form  may  be  produced 
with  great  accuracy  by  taking  on  glass  a  collodion  picture  of  a  sheet  of 
paper  on  which  the  required  forms  are  drawn  in  black. 

Looking  through  any  of  these  apertures,  we  see  the  luminous  point 
suVrounded  with  coloured  spectra  of  very  various  forms,  and  of  great 
beauty.  The  beautiful  colours  seen  on  looking  through  a  bird's  feather 
at  a  distant  source  of  light,  and  the  colours  of  striated  surfaces,  such  as 
mother-of-pearl,  are  due  to  a  similar  cause. 


-610] 


Gratings. 


539 


The  whole  of  these  phenomena  are  in  exact  accordance  with  the  undu- 
latory  theory,  but  the  explanation  is  in  many  cases  difficult. 

The  case  oi gratmgs  is  more  simple  and  important  than  the  others,  and 
therefore  shall  be  considered  in  detail. 

If  a  series  of  fine  equidistant  lines  ruled  on  glass,  or  a  series  of  fine 


0 


■  p 


ig.  482. 

equidistant  wires,  be  placed  before  the  eye  or  before  a  telescope,  and  a 
distant  point  or  line  of  Hght  be  viewed  through  the  grating  thus  formed, 
we  see  on  each  side  of  the  bright  point  or  line  a  series  of  equidistant 
spectra,  all  having  their  violet  ends  directed  inwards. 

To  explain  these  appearances,  let  us  suppose  the  telescope  removed, 
and  the  spectra  received  on  a  distant  screen. 

In  figure  482  let  O  represent  the  luminous  point,  AB  the  grating,  and 
CD  the  distant  screen. 

We  conceive  of  the  effect  on  the  screen  of  the  light  transmitted 
through  the  grating  in  the  following  manner.  The  ether  in  the  trans- 
parent intervals  of  the  grating  becomes  simultaneously  disturbed  and 
kept  in  vibration  by  the  light  from  O.  The  disturbance  of  each  point 
in  those  intervals  becomes  the  origin  of  a  spherical  wave,  as  in  art.  589, 
and  the  effect  produced  at  any  point  of  the  screen  is  the  sum  of  the  effects 
due  to  the  action  of  the  waves  thus  proceeding  from  all  the  transparent 
intervals.  Now,  at  the  point  <?,  which  is  equidistant  from  all  parts  oi" 
the  grating,  all  these  waves  will  arrive  in  the  same  phase,  and  will,  there- 
fore, reinforce  each  other,  and  give  a  bright  point. 

At  other  points,  pp^  on  each  side  of  0,  whose  distance  from  successive 
intervals  of  the  grating  differ  by  one  wave  length,  or  any  whole  number 
of  wave  lengths,  the  vibrations  will  also  arrive  in  the  same  phase,  and 
produce  brightness.  But  at  intermediate  points  the  vibrations  will  arrive 
from  different  points  of  the  grating  in  all  phases,  and  will,  therefore, 
neutralise  each  other  and  give  rise  to  darkness. 

The  fact  that  the  spectra  on  each  side  of  the  central  one  are  coloured 
arises  from  the  wave  lengths  being  different  for  different  colours  ;  and 


540  On  Light  [610- 

the  measurement  of  tTie  distances  between  the  spectra  corresponding  to 
different  colours  affords  the  most  accurate  method  of  determining  these 
wave  lengths. 

6ii.  Biffraction  spectra. — The  spectra  produced  by  means  of  a 
grating  are  "known  as  intei'/a-ence  or  diffraction  spectra.  Very  accurate 
gratings  can  now  be  easily  produced  by  means  of  photography,  at  a  cheap 
rate,  and  their  use  for  scientific  purposes  is  extending. 

For  objective  representation  the  image  of  a  slit  in  a  dark  shutter, 
through  which  the  sunlight  enters,  is  focussed  by  means  of  a  convex  lens 
on  a  screen  at  a  distance,  and  then  a  grating  is  placed  in  the  path  of  the 
rays. 

There  are  many  points  of  difference  between  these  spectra  and  those 
produced  by  the  prism,  and  for  scientific  work  the  former  are  preferable. 

A  diffraction  spectrum  is  the  purer  the  greater  the  number  of  fines  in 
the  grating,  provided  they  are  equi-distant.  The  spectra  are  less  bright 
than  prismatic  spectra ;  and  to  obtain  the  maximum  brightness  the 
opaque  intervals  should  be  as  opaque  and  the  transparent  ones  as  trans- 
parent as  possible. 

On  the  other  hand,  in  diffraction  spectra,  the  colours  are  uniformly 
distributed  in  their  true  order  and  extent,  while  in  prismatic  spectra,  the 
red  rays  are  concentrated,  and  the  violet  ones  dispersed.  In  diffraction 
spectra  the  centre  is  the  brightest  part. 

Diffraction  spectra  have  moreovei- the  advantage  of  giving  a  far  larger 
number  of  dark  lines,  and  of  giving  them  in  their  exact  relative  positions. 
Thus,  in  a  particular  region  in  whidh  Angstrom  had  mapped  ii8  lines, 
Draper,  by  means  of  a  diffraction  spectrum  was  able  to  photograph  at  least 
293.  Diffraction  spectra  also  extend  further  in  the  direction  of  the  ultra 
violet,  and  give  more  dark  lines  in  that  region. 

612.  Colours  of  thin  plates.  Newton's  rings. — All  transparent 
bodies,  solids,  liquids,  or  gases,  when  in  sufficiently  fine  laminas,  appear 


Fig.  483. 

colotiTcd  with  very  bright  tints,  especially  by  refl-ection.  Crystals  which 
cleave  easily,  and  can  be  attained  in  very  thin  plates,  such  as  mica  and 
selenite,  show  this  phenomenon,  which  is  also  well  seen  in  soap-bubbles 
and  in  the  layers  of  air  in  cracks  in  glass  and  in  crystals.  A  drop  of  oil 
spread  rapidly  over  a  large  sheet  of  water  exhibits  all  the  colours  of  the 
spectra  in  a  con-^tant  order.  A  soap-bubble  appears  white  at  first,  but  in 
proportion  as  it  is  blown  out,  brilfiant  iridescent  colours  appear,  espe- 
cially at  the  top,  where  it  is  thinnest.  These  colours  are  arranged  in 
horizontal  zones  around  the  summit,  which  appears  black  when  there 
is  not  thickness  enough  to  reflect  light,  and  the  bubble  then  suddenly 
bursts. 


-613]  New  toils  Rings.  541 

Newton,  who  first  studied  the  phenomena  of  the  coloured  rings  in  soap- 
bubbles,  wishing  to  investigate  the  relation  between  the  thickness  of  the 
thin  plate,  the  colour  of  the  rings,  and  their  extent,  produced  them  by- 
means  of  a  layer  of  air  interposed  between  two  glasses,  one  plane  and  the 
other  convex,  and  with  a  very  long  focus  (fig.  483).  The  two  surfaces 
being  cleaned  and  exposed  to  ordinary  light  in  front  of  a  window,  so  as 
to  reflect  light,  there  is  seen  at  the  point  of  contact  a  black  spot  sur- 
rounded by  six  or  seven  coloured  rings,  the  tints  of  which  become  gradu- 
ally less  strong.  If  the  glasses  are  viewed  by  transmitted  light,  the  centre 
of  the  rings  is  white,  and  each  of  the  colours  is  exactly  complementary  of 
that  of  the  rings  by  reflection. 

With  homogeneous  light,  red  for  example,  the  rings  are  successively 
black  and  red  ;  the  diameters  of  corresponding  rings  are  less  as  the  colour 
is  more  refrangible,  but  with  white  light  the  rings  are  of  the  different 
colours  of  the  spectrum,  which  arises  from  the  fact  that,  as  the  rings  of 
the  different  simple  colours  have  different  diameters,  they  are  not  exactly 
superposed,  but  are  more  or  less  separated. 

If  the  focal  length  of  the  lens  is  from  three  to  four  yards,  the  rings 
can  be  seen. with  the  naked  eye  ;  but  if  the  length  is  less,  the  rings  must 
be  looked  at  with  a  lens. 

6 1 3.  Sxplanation  of  Wewton's  ringrs. — Newton's  rings,  and  all  pheno- 
mena of  thin  plates,  are  simple  cases  of  interference. 

In  fig.  484,  let  MNOP  represent  a  thin  plate  of  a  transparent  body,  on 
which  a  pencil  of  parallel  rays  of  homogeneous  light  ab,  impinges  ;  this 
will  be  partially  reflected  in  the  direction  be,  and 
partially  refracted  towards  d.  But  the  refracted 
ray  will  undergo  a  second  reflection  at  the  sur- 
face, OP  ;  the  reflected  ray  will  emerge  at  e  in 
the  same  direction  as  the  pencil  of  light  reflected 
at  the  first  surface ;  and  consequently  the  two 
pencils  be  and  ef  will  destroy  or  augment  each 
other's  effect  according  as  they  are  in  the  same 
or  different  phases.  We  shall  thus  have  an 
effect  produced  similar  to  that  of  the  fringes. 

It  is  usual  to  speak  of  the  successive  rings  as  Jii  U/ 
the  first,  second,  third,  etc.     By  the  Jirst  ring  is  Fig.  484. 
understood  that  of  least  diameter.     Newton  de- 
termined by  calculation  the  thickness  of  the  layer  of  air  at  the  points 
where  the  successive  rings  were  formed,  and  found  that  the  thicknesses 
corresponding  to  the  successive  da7'k  rings  are  proportional  to  the  num- 
bers o,  2,  4,  6 ,  while  for  the  bright  rings  the  thicknesses  were 

proportional  to  i,  3,  5 He  found  that  for  the  first  bright  ring  the 

thickness  was  jy/ooo  ^^  ^'^  inch,  when  the  light  used  was  the  brightest 
part  of  the  spectrum,  that  is  the  part  on  the  confines  of  the  orange  and 
yellow  rays.  He  further  found  that  for  rings  of  the  same  order  the 
diameter  is  greater  as  the  refrangibility  of  the  light  producing  it  is  less. 


542  On  Light.  [614- 


POLARISATION   OF   LIGHT. 

614.  Polarisation  by  double  reflraction. — It  has  been  already  seen 
that,  when  a  ray  of  Hght  passes  through  a  crystal  of  Iceland  spar,  it 
becomes  divided  into  two  rays  of  equal  intensity^  viz.  the  ordinary  ray, 
and  the  extraordinary  ray.  These  rays  are  found  to  possess  other  pecu- 
liarities, which  are  expressed  by  saying  they  are  polarised^  namely,  the 
ordinary  ray  in  a  principle  plane,  and  the  extraordinary  ray  in  a  plane  at 
right  angles  to  a  principal  plane.  The  phenomena  which  are  thus  desig- 
nated may  be  described  as  follows  : — Suppose  a  ray  of  light  which  has 
undergone  ordinary  refraction  in  a  crystal  of  Iceland  spar  to  be  allowed 
to  pass  through  a  second  crystal,  it  will  generally  be  divided  into  two 
rays,  namely,  one  ordinary,  and  the  other  extraordinary,  but  of  unequal 
intensities.  If  the  second  crystal  be  turned  round  until  the  two  principal 
planes  coincide,  that  is,  until  the  crystals  are  in  similar  or  in  opposite 
positions,  then  the  extraordinary  ray  disappears,  and  the  ordinary  ray  is 
at  its  greatest  intensity  ;  if  the  second  crystal  is  turned  further  round,  the 
extraordinary  ray  reappears,  and  increases  in  intensity  as  the  angle  in- 
creases, while  the  ordinary  ray  diminishes  in  intensity  until  the  principal 
planes  are  at  right  angles  to  each  other,  when  the  extraordinary  ray  is 
at  its  greatest  intensity,  and  the  ordinary  ray  vanishes.  These  are  the 
phenomena  produced  when  the  ray  which  experienced  ordinary  refraction 
in  the  first  crystal  passes  through  the  second.  If  the  ray  which  has  ex- 
perienced extraordinary  refraction  in  the  first  crystal  is  allowed  to  pass 
through  the  second  crystal,  the  piienomena  are  similar  to  those  above 
described,  but  when  the  principal  planes  coincide,  an  extraordinary  ray 
alone  emerges  from  the  second  crystal,  and  when  the  planes  are  at  right 
angles,  an  ordinary  ray  alone  emerges. 

These  phenomena  may  also  be  thus  described  : — Let  O  and  E  denote 
the  ordinary  and  extraordinary  rays  produced  by  the  first  crystal.  When 
O  enters  the  second  crystal,  it  generally  gives  rise  to  two  rays,  an  ordinary 
(O^),  and  an  extraordinary  {Oe)^  of  unequal  intensities.  When  E  enters 
the  second  crystal,  it  Hkewise  gives  rise  to  two  rays,  viz.  an  ordinary  (E^), 
and  an  extraordinary  (E^),  of  unequal  intensities  ;  the  intensities  varying 
with  the  angle  between  the  principal  planes  of  the  crystals.  When  the 
principal  planes  coincide,  only  two  rays,  viz.  Oo  and  E^  emerge  from 
the  second  crystal,  and  when  the  planes  are  at  right  angles,  only  two  rays 
viz.  Oe  and  E<9,  emerge  from  the  second  crystal.  Since  O  gives  rise  to 
an  ordinary  ray  when  the  principal  planes  are  parallel,  and  JE  gives  rise 
to  an  ordinary  ray  when  they  are  at  right  angles,  it  is  manifest  that  O  is 
related  to  the  principal  plane  in  the  same  manner  that  E  is  related  to  a 
plane  at  right  angles  to  a  principal  plane. 

This  phenomenon,  which  is  produced  by  all  double  refracting  crystals, 
was  observed  by  Huyghens  in  Iceland  spar,  and  in  consequence  of  a 
suggestion  of  Newton's  was  afterwards  c?i\\Q<\ polarisation.  It  remained, 
however,  an  isolated  fact  until  the  discovery  of  polarisation  by  reflection 


-616] 


Polarisation  of  L  igh t. 


543 


recalled  the  attention  of  physicists  to  the  subject.     The  latter  discover)^^ 
was  made  by  Malus  in  1808. 

615.  Polarisation  by  reflection. — When  a  ray  of  light,  ab  (fig.  485), 
falls  on  a  polished  unsilvered  glass  surface,  ^/^'/z/,  inclined  to  it  at  an  angle 
of  35°  25',  it  is  reflected,  and  the  reflected  ray 
is  polarised  in  the  plane  of  reflection.  If  it 
were  transmitted  through  a  crystal  of  Ice- 
land spar,  it  would  be  transmitted  without 
bifurcation,  and  undergo  an  ordinary  refrac- 
tion, when  the  principal  plane  coincides  with 
the  plane  of  reflection  ;  it  would  also  be 
transmitted  without  bifurcation  but  undergo 
extraordinary  refraction,  when  the  principal 
plane  is  at  right  angles  to  the  plane  of 
reflection  :  in  other  positions  of  the  crystal 
it  would  give  rise  to  an  ordinary  and  an 
extraordinary  ray  of  different  intensities,  ac- 
cording to  the  angle  between  the  plane  of 
reflection  and  the  principal  plane  of  the 
crystal.  The  peculiar  property  which  the 
light  has  acquired  by  reflection  at  the 
surface /^///  can  also  be  exhibited  as  follows  : — Let  the  polarised  ray  be 
be  received  at  c,  on  a  second  surface  of  unsilvered  glass,  at  the  same 
angle,  viz.  35°  25^  If  the  surfaces  are  parallel,  the  ray  is  reflected  : 
but  if  the  second  plate  is  caused  to  turn  round  cb,  the  intensity  of  the 
reflected  ray  continually  diminishes,  and  when  the  glass  surfaces  are  at 
right  angles  to  each  other,  no  light  is  reflected.  By  continuing  to  turn 
the  upper  mirror,  the  intensity  of  the  reflected  ray  gradually  increases,  and 
attains  a  maximum  value  when  the  surfaces  are  again  parallel. 

The  above  statement  will  serve  to  describe  the  phenomenon  of  polari- 
sation by  reflection  so  far  as  the  principles  are  concerned  ;  the  apparatus 
best  adapted  for  exhibiting  the  phenomenon  will  be  described  farther  on. 

616.  Angrle  of  Polarisation. — T\vq  polarising  angle  of  a  substance  is 
the  angle  which  the  incident  ray  must  make  with  the  normal  to  a  plane 
polished  surface  of  that  substance  in  order  that  the  polarisation  be  com- 
plete. For  glass  this  angle  is  54°  35',  and  if  in  the  preceding  experiment 
the  lower  mirror  were  inclined  at  any  other  angle  than  this,  the  light 
would  not  be  completely  polarised  in  any  position  ;  this  would  be  shown 
by  its  being  partially  reflected  from  the  upper  surface  in  all  positions. 
Such  light  is  said  to  be  pa7'tially  polarised.  The  polarising  angle  for 
water  is  52°  45^ ;  for  quartz,  57°  32'  ;  for  diamond,  68°  ;  and  it  is  56°  30^  for 
obsidian,  a  kind  of  volcanic  glass  which  is  often  used  in  these  experiments. 

Light  which  is  reflected  from  the  surface  of  water,  from  a  slate  roof, 
from  a  polished  table,  is  all  more  or  less  polarised.  The  ordinary  light  of 
the  atmosphere  is  frequently  polarised,  especially  in  the  earlier  and  later 
periods  of  the  day,  when  the  solar  rays  fall  obliquely  on  the  atmosphere. 
Almost  all  reflecting  surfaces  may  be  used  as  polarising  mirrors.  Metallic 
surfaces  form,  however,  an  important  exception. 


544  On  Light  [616- 

Brewster  has  discovered  the  following  remarkably  simple  law  in  refer- 
ence to  the  polarising  angle  : — 

The  polarisi7ig  angle  of  a  substance  is  that  angle  of  incidence  for  which 
the  reflected  polarised  ray  is  at  right  angles  to  the  refracted  ray. 

Thus,  in  fig.  486,  if  si  is  the  incident,  ir  the  refracted,  and 
if  the  reflected  ray,  the  polarisation  is 
most  complete  when  //  is  at  right  angles 
to  ir. 

The  plane  of  polarisation  is  the  plane 
of  reflection  in  which  the  light  becomes 
polarised  ;  it  coincides  with  the  plane  of 
incidence,  and,  therefore,  contains  the 
polarising  angle. 

617.  Polarisation  by  singrle  refrac- 
tion.— When    an    unpolarised    luminous 
ray  falls  upon  a  glass  plate  placed  at  the 
^'^-  489-  polarising  angle,   one   part    is   reflected  ; 

the  other  part,  in  passing  through  the  glass,  becomes  refracted,  and  the 
transmitted  light  is  now  found  to  be  partially  polarised.  If  the  light 
which  has  passed  through  one  plate,  and  whose  polarisation  is  very  feeble, 
be  transmitted  through  a  second  plate  parallel  to  the  first,  the  effects  be- 
come more  marked,  and  by  ten  or  twelve  plates  are  tolerably  complete. 
A  bundle  of  such  plates,  for  which  the  best  material  is  the  glass  used  for 
covering  microscopic  objects,  fitted  in  a  tube  at  the  polarising  angle,  is 
frequently  used  for  examining  or  producing  polarised  light. 

If  a  ray  of  light  fall  at  any  angle  on  a  transparent  medium,  the  same 
holds  good  with  a  slight  modification.  In  fact,  part  of  the  light  is  reflected 
and  part  refracted,  and  both  are  found  to  be  partially  polarised,  ^^/m/ 
quantities  in  each  being  polaj^ised^  and  their  piaiies  of  polarisation  being 
at  right  angles  to  each  other.  It  is,  of  course,  to  be  understood  that  the 
polarised  portion  of  the  reflected  light  is  polarised  in  the  plane  of  reflec- 
tion, which  is  likewise  the  plane  of  refraction. 

618.  Polarising-  instruments. — Every  instrument  for  investigating 
the  properties  of  polarised  light  consists  essentially  of  two  parts,  one  for 
polarising  the  light,  the  other  for  ascertaining  or  exhibiting  the  fact  of 
light  having  undergone  polarisation.  The  former  part  is  called  the  polar- 
iser,  the  latter  the  analyser.  Thus  in  art.  614  the  crystal  producing  the 
first  refraction  is  the  polariser,  that  producing  the  second  refraction  is  the 
analyser.  In  art.  615,  the  mirror  at  which  the  first  reflection  takes  place 
is  the  polariser,  that  at  which  the  second  reflection  takes  place  is  the 
analyser.  Some  of  the  most  convenient  means  of  producing  polarised 
light  will  now  be  described,  and  it  will  be  remarked  that  any  instrument 
that  can  be  used  as  a  polariser  can  also  be  used  as  an  analyser.  The  ex- 
perimeter  has  therefore  considerable  liberty  of  selection. 

619.  KTorrembergr's  apparatus. — The  most  simple  but  complete  in- 
strument for  polarising  light  is  that  invented  by  Norremberg.  It  may 
be  used  for  repeating  most  of  the  experiments  on  polarised  light. 

It  consists  of  two  brass  rods  b  and  d  (fig.  487),  which  support  an  un- 


619] 


Norremberg  s  Apparatus. 


545 


silvered  mirror,  ;2,  of  ordinary  glass,  movable  about  a  horizontal  axis.  A 
small  graduated  circle  indicates  the  angle  of  inclination  of  the  mirror. 
Between  the  feet  of  the  two  columns  there  is  a  silvered  glass,/,  which  is 
fixed  and  horizontal.  At  the  upper  end  of  the  columns  there  is  a  gra- 
duated plate,  /,  in  which  a  circular  disc,  o,  rotates.  This  disc,  in  which  there 
is  a  square  aperture,  supports  a  mirror  of  black  glass,  m,  which  is  inclined 
to  the  vertical  at  the  polarising  angle.  An  annular  disc,  k^  can  be  fixed 
at  different  heights  on  the  columns  by  means  of  a  screw,  A  second  ring, 
«,  may  be  moved  around  the  axis.  It  supports  a  black  screen,  in  the 
centre  of  which  there  is  a  circular  aperture. 


Fig.  487. 


When  the  mirror  n  makes  with  the  vertical  an  angle  of  35°  25',  which 
is  the  complement  of  the  polarising  angle  for  glass,  the  luminous  rays,  S;/, 
which  meet  the  mirror  at  this  angle,  become  polarised,  and  are  reflected 
in  the  direction  np  towards  the  mirror  p^  which  sends  them  in  the  direc- 
tion pur.  After  having  passed  through  the  glass,  ?/,  the  polarised  ray 
falls  upon  the  blackened  glass  m  under  an  angle  of  35°  25',  because  the 
mirror  makes  exactly  the  same  angle  with  the  vertical.  But  if  the  disc,  o, 
to  which  the  mirror,  w,  is  fixed,  be  turned  horizontally,  the  intensity  of 


546  On  Light.  [619- 

the  light  reflected  from  the  upper  mirror  gradually  diminishes,  and  totally 
disappears  when  it  has  been  moved  through  90°.  The  position  is  that 
represented  in  the  diagram :  the  plane  of  incidence  on  the  upper  mirror 
is  then  perpendicular  to  the  plane  of  incidence,  S;//,  on  the  mirror  n. 
When  the  upper  mirror  is  again  turned,  the  intensity  of  the  light  increases 
until  it  has  passed  through  180°,  when  it  again  reaches  a  maximum. 
The  mirrors  in  and  //  are  then  parallel.  The  same  phenomena  are  re- 
peated as  the  mirror  ni  continues  to  be  turned  in  the  same  direction, 
until  it  again  comes  into  its  original  position  ;  the  intensity  of  the  re- 
flected light  being  greatest  when  the  mirrors  are  parallel,  and  being 
reduced  to  zero  when  they  are  at  right  angles.  If  the  mirror  m  is  at  a 
greater  or  less  angle  than  35°  25',  a  certain  quantity  of  light  is  reflected 
in  all  positions  of  the  plane  of  incidence. 

620.  Tourmaline. — The  primary  form  of  this  crystal  is  a  regular  hex- 
agonal prism.  Tourmaline,  as  already  stated,  is  a  negative  uniaxial  crystal, 
and  its  optic  axis  coincides  with  the  axis  of  the  prism.  For  optical  pur- 
poses a  plate  is  cut  from  it  parallel  to  the  axis.  When  a  ray  of  light 
passes  through  such  a  plate,  an  ordinary  ray  and  an  extraordinary  ray  are 
produced,  polarised  in  planes  at  right  angles  to  each  other,  viz.  the  former 
in  a  plane  at  right  angles  to  the  plate  parallel  to  the  axis,  and  the  latter 
in  a  plane  at  right  angles  to  the  axis.  The  crystal  possesses,  however, 
the  remarkable  property  of  rapidly  absorbing  the  ordinary  ray ;  conse- 
quently, when  a  plate  of  a  certain  thickness  is  used,  the  extraordinary  ray 
alone  emerges — in  other  words,  a  beam  of  common  light  emerges  from  the 
plate  of  tourmaline  polarised  in  a  plane  at  right  angles  to  the  axis  of  the 
crystal.  If  the  light  thus  transmitted  be  viewed  through  another  similar 
plate  held  in  a  parallel  position,  little  change  will  be  observed,  excepting 
that  the  intensity  of  the  transmitted  light  will  be  about  equal  to  that  which 
passes  through  a  plate  of  double  the  thickness ;  but  if  the  second  tour- 
maline be  slowly  turned,  the  light  will  become  feebler,  and  will  ultimately 
disappear  when  the  axes  of  the  two  plates  are  at  right  angles. 

The  objections  to  the  use  of  the  tourmaline  are  that  it  is  not  very 
transparent,  and  that  plates  of  considerable  thickness  must  be  used  if  the 
polarisation  is  to  be  complete.  For  unless  the  ordinary  ray  is  completely 
absorbed,  the  emergent  light  will  be  only  partially  polarised. 

Mr.  Hcrepath  discovered  that  sulphate  of  iodoquinine  has  the  property 
of  polarising  light  in  a  remarkable  degree.  Unfortunately,  it  is  a  very 
fragile  salt  and  difficult  to  obtain  in  large  crystals. 

621.  Double  refracting:  prisms  of  Iceland  spar. — When  a  ray  of 
light  passes  throagh  an  ordinary  rhombohedron  of  Iceland  spar,  the  or- 
dinary and  extraordinary  rays  emerge  parallel  to  the  original  ray,  conse- 
quently the  separation  of  the  rays  is  proportional  to  the  thickness  of 
the  prism.  But  if  the  crystal  is  cut  so  that  its  faces  are  inclined  to  each 
other,  the  deviations  of  the  ordinary  and  extraordinary  rays  will  be  dif- 
ferent, they  will  not  emerge  parallel,  and  their  separation  will  be  greater 
as  their  distance  from  the  prism  increases.  ,The  light,  however,  in  pass- 
ing through   the  prism   becomes    decomposed,   and   the  rays  will  be 


623] 


NicoVs  Prism. 


SAf 


Fig.  489. 


coloured.  It  is  therefore  necessary  to  achromatise  the  prism,  which  is' 
done  by  combining  it  with  a  prism  of  glass  with  its  refracting  angle 
turned  in  the  contrary  direction  (fig.  489).  In  order  to 
obtain  the  greatest  amount  of  divergence,  the  refracting 
edges  of  the  prism  should  be  cut  parallel  to  the  optic 
axis,  and  this  is  always  done. 

Let  us  suppose  that  a  ray  of  polarised  light  passes  along 
the  axis  of  the  cylinder  (fig.  489),  and  let  us  suppose  that 
the  cylinder  is  caused  to  turn  slowly  round  its  axis ;  then 
the  resulting  phenomena  are  exactly  like  those  already 
described  (614).  Generally  there  will  be  an  ordinary  and  extraordinary 
ray  produced,  whose  relative  intensities  will  vary  as  the  tube  is  turned. 
But  in  two  opposite  positions  the  ordinary  ray  alone  will  emerge,  and  in 
two  others  at  right  angles  to  the  former  the  extraordinary  ray  will  alone 
emerge.  When  the  ordinary  ray  alone  emerges,  the  principal  plane  of  the 
crystal— that  is,  a  plane  at  right  angles  to  its  face,  and  parallel  to  its 
refracting  edge— coincides  with  the  original  plane  of  polarisation  of  the 
ray.  Consequently,  by  means  of  the  prism,  it  can  be  ascertained  both 
that  the  ray  is  polarised,  and  hkewise  the  plane  in  which  it  is  polarised. 

622.  M'icors  prism. — The  Nicol's  prism  is  one  of  the  most  valuable 
means  of  polarising  light,  for  it  is  perfectly  colourless,  it  polarises  light 
completely,  and  it  transmits  only  one  beam  of  polarised  light,  the  other 
being  entirely  suppressed. 

It  is  constructed  out  of  a  rhombohedron  of  Iceland  spar,  about  an  inch 
in  height  and  ^  of  an  inch  in  breadth.  This  is  bisected  in  the  plane 
which  passes  through  the  obtuse  angles  as  shown  in  fig.  491— that  is, 
along  the  plane  abed  (fig.  479).  The  two  halves  are  then  again  joined  in 
the  same  order  by  means  of  Canada  balsam. 

The  principle  of  the  Nicol's  prism  is  this :   the  refractive  index  of 


:>^ 


Fig.  490. 


Fig.  491 


Canada  balsam  1*549  is  less  than  the  ordinary  index  of  Iceland  spar 
1-654,  but  greater  than  its  extraordinary  index  i'483.  Hence,  when 
a  luminous  ray,  SC,  fig.  491,  enters  the  prism,  the  ordinary  ray  under- 
goes total  reflection  on  the  surface  ab,  and  takes  the  direction  CdO,  by 
which  it  is  refracted  out  of  the  crystal ;  while  the  extraordinary  ray,  Ce, 
emerges  alone.  Since  the  Nicol's  prism  allows  only  the  extraordinary 
ray  to  pass,  it  may  be  used,  like  a  tourmaline,  as  an  analyser  or  as  a 
polariser. 

623.  Physical  theory  of  polarised  Ugrht. — The  explanation  of  the 
dark  bands  produced  by  the  interference  of  light  is  stated  in  art.  608  to 


548  On  Light.  [623- 

resemble   exactly   that  of  the  formation   of  nodes  and  loops  given  in 
art.  260. 

It  might  hence  be  supposed  that  the  vibrations  producing  light  are 
similar  to  those  producing  sound.  But  this  is  by  no  means  the  case. 
In  fact,  if  art.  614  be  examined,  it  will  be  found  that  no  assumption  is 
there  made  as  to  the  direction  in  v^^hich  the  vibrating  particles  move,  and 
accordingly  that  explanation  is  equally  true  whether  the  particles  vibrate 
in  the  direction  AB,  BA,  or  at  right  angles  to  AB.  As  a  matter  of  fact, 
the  former  is  the  case  with  the  vibrations  producing  sound,  the  latter 
with  the  vibrations  producing  light.  In  other  words,  the  vibrations  pro- 
ducing sound  take  place  in  the  direction  of  propagation,  the  vibrations 
producing  light  are  transversal  to  the  direction  of  propagation. 

This  assumption  as  to  the  direction  of  the  vibration  of  the  particles  of 
ether  producing  light  is  rendered  necessary,  and  is  justified  by  the  phe- 
nomena of  polarisation. 

When  a  ray  of  light  is  polarised,  all  the  particles  of  ether  in  that  ray 
vibrate  in  straight  lines  parallel  to  a  certain  direction  in  the  front  of  the 
wave  corresponding  to  the  ray. 

When  a  ray  of  light  enters  a  double  refracting  medium,  such  as  Ice- 
land spar,  it  becomes  divided  into  two,  as  we  have  already  seen.  Now 
it  can  be  shown  to  be  in  strict  accordance  with  mechanical  principles 
that,  if  a  medium  possesses  unequal  elasticity  in  different  directions,  a 
plane  wave  produced  by  transversal  vibrations  entering  that  medium  will 
give  rise  to  two  plane  waves  moving  with  different  velocities  within  the 
medium,  and  the  vibi-ations  of  the  particles  in  front  of  these  waves  will 
be  in  directions  parallel  respectively  to  two  lines  at  right  angles  to  each 
other.  If,  as  is  assumed  in  the  undulatory  theory  of  light,  the  ether  exists 
in  a  double  refracting  crystal  in  such  a  state  of  unequal  elasticity,  then 
the  two  plane  waves  will  be  formed  as  above  described,  and  these  having 
different  velocities,  will  give  rise  to  two  rays  of  unequal  refrangibility 
(compare  art.  601).  This  is  the  physical  account  of  the  phenomenon  of 
double  refraction.  It  will  be  remarked  that  the  vibra^^ions  corresponding 
to  the  two  rays  are  transversal,  rectilinear,  and  in  directions  perpendicular 
to  each  other  in  the  rays  respectively.  Accordingly  the  same  theory 
accounts  for  the  fact  that  the  two  rays  are  both  polarised,  and  in  planes 
at  right  angles  to  each  other. 

It  is  a  point  still  unsettled  whether,  when  a  ray  of  light  is  polarised 
with  respect  to  a  given  plane,  the  vibrations  take  place  in  directions 
within  or  perpendicular  to  that  plane.  Fresnel  was  of  the  latter  opinion. 
It  is,  however,  convenient  in  some  cases  to  regard  the  plane  of  polarisa- 
tion as  that  plane  in  which  the  vibrations  take  place. 

COLOURS   PRODUCED   BY  THE   INTERFERENCE  OF   POLARISED   LIGHT. 

624.  Ziaws  of  the  interference  of  polarised  rays. — After  the  dis- 
covery of  polarisation,  Fresnel  and  Arago  tried  whether  polarised  rays 
presented  the  same  phenomena  of  interference  as  ordinary  rays.  They 
were  thus  led  to  the  discovery  of  the  following  laws  in  reference  to  the 


-625]  Colours  produced  by  Intcrfererice  of  Polarised  Light.  549 

interference  of  polarised  light,   and,  at  the  same  time,  of  the  brilliant 
phenomena  of  colouration,  which  will  be  presently  described  : — 

I.  When  two  rays  polarised  in  the  same  plane  interfere  with  each 
other,  they  will  produce  by  their  interference  fringes  of  the  very  same 
kind  as  if  they  were  common  light. 

II.  When  two  rays  of  light  are  polarised  at  right  angles  to  each  other, 
they  produce  no  coloured  fringes  in  the  same  circumstances  under  which 
two  rays  of  common  light  would  produce  them.  When  the  rays  are  po- 
larised in  planes  inclined  to  each  other  at  any  other  angles,  they  produce 
fringes  of  intermediate  brightness,  and  if  the  angle  is  made  to  change,  the 
fringes  gradually  decrease  in  brightness  from  0°  to  90°,  and  are  totally 
obliterated  at  the  latter  angle. 

III.  Two  rays  originally  polarised  in  planes  at  right  angles  to  each 
other  may  be  subsequently  brought  into  the  same  plane  of  polarisation 
without  acquiring  the  power  of  forming  fringes  by  their  interference. 

IV.  Two  rays  polarised  at  right  angles  to  each  other,  and  afterwards 
brought  into  the  same  plane  of  polarisation,  produce  fringes  by  their 
interference  like  rays  of  common  light,  provided  they  originated  in  a 
pencil  the  whole  of  which  was  originally  polarised  in  any  one  plane. 

V.  In  the  phenomena  of  interference  produced  by  rays  that  have  suf- 
fered double  refraction,  a  difference  of  half  an  undulation  must  be  allowed, 
as  one  of  the  pencils  is  retarded  by  that  quantity  from  some  unknown 
cause. 

625.  Sffect  produced  by  causing-  a  pencil  of  polarised  rays  to 
traverse  a  double  refracting-  crystal. — The  following  important  ex- 
periment may  be  made  most  conveniently  by  Norremberg's  apparatus 
(fig.  487).  At  g  (fig.  488)  there  is  a  NicoFs  prism.  A  plate  of  a  double 
refracting  crystal  cut  parallel  to  its  axis  is  placed  on  the  disc  at  ^.  In 
the  first  place,  however,  suppose  the  plate  of  the  crystal  to  be  removed. 
Then,  since  the  Nicol's  prism  allows  only  the  extraordinary  ray  to  pass 
when  it  is  turned  so  that  its  principal  plane  coincides  with  the  plane  of 
reflection,  no  light  will  be  transmitted  (622).  Place  the  plate  of  doubly 
refracting  crystal,  which  is  supposed  to  be  of  moderate  thickness,  in  the 
path  of  the  reflected  ray  at  e.  Light  is  now  transmitted  through  the 
Nicol's  prism.  On  turning  the  plate  the  intensity  of  the  transmitted 
light  varies  ;  it  reaches  its  maximum  when  the  principal  plane  of  the 
plate  is  inclined  at  an  angle  of  45°  to  the  plane  of  reflection,  and  dis- 
appears when  these  planes  either  coincide  with  or  are  at  right  angles  to 
eaqh  other.  The  light  in  this  case  is  white.  The  interposed  plate  may 
be  called  the  depolarising  plate.  The  same  or  equivalent  phenomena 
are  produced  when  any  other  analyser  is  used.  Thus,  assume  the  double 
refracting  prism  to  be  used.  Suppose  the  depolarising  plate  to  be  re- 
moved. Then,  generally,  two  rays  are  transmitted  ;  but  if  the  principal 
plane  of  the  analyser  is  turned  into  the  plane  of  primitive  polarisation, 
the  ordinary  ray  only  is  transmitted,  and  then,  when  turned  through  90°, 
the  extraordinary  ray  only  is  transmitted.  Let  the  analyser  be  turned 
into  the  former  position,  then,  when  the  depolarising  plate  is  interposed, 
both  ordinary  and  extraordinary  rays  are  seen,  and  when  the  depolarising 


550  On  Light.  [625^ 

plate  is  slowly  turned  round,  the  ordinary  and  extraordinary  rays  are 
seen  to  vary  in  intensity,  the  latter  vanishing  when  the  principal  plane  of 
the  polarising  plate  either  coincides  with  or  is  at  right  angles  to  the  plane 
of  primitive  polarisation. 

626.  S£fect  produced  wben  the  plate  of  crystal  is  very  thin. —  In 
order  to  exhibit  this,  take  a  thin  film  of  selenite  or  mica  between  the 
twentieth  and  sixtieth  of  an  inch  thick,  and  interpose  it  as  in  the  last 
article.  If  the  thickness  of  the  film  is  uniform,  the  light  now  transmitted 
through  the  analyser  will  be  no  longer  white,  but  of  a  uniform  tint  ;  the 
colour  of  the  tint  being  different  for  different  thicknesses — for  instance, 
red,  or  green,  or  blue,  or  yellow,  according  to  the  thickness ;  the  intensity 
of  the  colour  depending  on  the  inclination  of  the  principal  plane  of  the 
film  to  the  plane  of  reflection,  being  greatest  when  the  angle  of  inclina- 
tion is  45°.  Let  us  now  suppose  the  crystalline  film  to  be  fixed  in  that 
position  in  which  the  light  is  brightest,  and  suppose  its  colour  to  be  red. 
Let  the  analyser  (the  Nicol's  prism)  be  turned  round,  the  colour  will  grow 
fainter,  and  when  it  has  been  turned  through  45°,  the  colour  disappears, 
and  no  light  is  transmitted;  on  turning  it  farther,  the  complementary 
colour,  green,  makes  its  appearance,  and  increases  in  intensity  until  the 
analyser  has  been  turned  through  90°;  after  which  the  intensity  dimi- 
nishes until  an  angle  of  135°  is  attained,  when  the  light  again  vanishes, 
and,  on  increasing  the  angle,  it  changes  again  into  red.  Whatever  be  the 
colour  proper  to  the  plate,  the  same  series  of  phenomena  will  be  observed, 
the  colour  passing  into  its  complementary  when  the  analyser  is  turned. 
That  the  colours  are  really  complementary  is  proved  by  using  a  double 
refracting  prism  as  analyser.  In  this  case  two  rays  are  transmitted,  each 
of  which  goes  through  the  same  changes  of  colour  and  intensity  as  the 
single  ray  described  above,  but  whatever  be  the  colour  and  intensity  of 
the  one  ray  in  a  given  position,  the  other  ray  will  have  the  same  when 
the  analyser  has  been  turned  through  an  angle  of  90°.  Consequently, 
these  two  rays  give  simultaneously  the  appearances  which  are  succes- 
sively presented  in  the  above  case  by  the  same  ray  at  an  interval  of  90°. 
If  now  the  two  rays  are  allowed  to  overlap,  they  produce  white  light  ; 
thereby  proving  their  colours  to  be  complementary. 

Instead  of  using  plates  of  different  thickness  to  produce  different  tints, 
the  same  plate  may  be  employed  inclined  at  different  angles  to  the  polar- 
ised ray.  This  causes  the  ray  to  traverse  the  film  obliquely,  and,  in  fact, 
amounts  to  an  alteration  in  its  thickness. 

With  the  same  substance,  but  with  plates  of  increasing  thickness,  the 
tints  follow  the  laws  of  the  colours  of  Newton's  rings  (612).  The  thick- 
ness of  the  depolarising  plate  must,  however,  be  different  from  that  of  the 
layer  of  air  in  the  case  of  Newton's  rings  to  produce  corresponding 
colours.  Thus  corresponding  colours  are  produced  by  a  plate  of  mica 
and  a  layer  of  air  when  the  thickness  of  the  former  is  about  400  times 
that  of  the  latter.  In  the  case  of  selenite  the  thickness  is  about  230 
times,  and  in  the  case  of  Iceland  spar  about  13  times,  that  of  the  cor- 
responding layer  of  air. 


-627]  Theory  of  Depolarisation.  551 

627.  Tbeory  of  the  pbenoxnena  of  depolarisation. — The  phenomena 
described  in  the  last  articles  admit  of  complete  explanation  by  the  undu- 
latory  theory,  but  not  without  the  aid  of  abstruse  mathematical  calcula- 
tions. What  follows  will  show  the  nature  of  the  explanation.  Let  us 
suppose,  for  convenience,  that  in  the  case  of  a  polarised  ray  the  particles 
of  ether  vibrate  in  the  plane  of  polarisation  (see  art.  610),  and  that  the 
analyser  is  a  double  refracting  prism,  with  its  principal  plane  in  the  plane 
of  primitive  polarisation  ;  then  the  vibrations  being  wholly  in  that  plane 
have  no  resolved  part  in  a  plane  at  right  angles  to  it,  and,  consequently, 
no  extraordinary  ray  passes  through  the  analyser  ;  in  other  words,  only 
an  ordinary  ray  passes.  Now  take  the  depolarising  plate  cut  parallel  to 
the  axis,  and  let  it  be  interposed  in  such  a  manner  that  its  principal  plane 
makes  any  angle,  {^^)  with  the  plane  of  primitive  polarisation.  The  effect 
of  this  will  be  to  cause  the  vibrations  of  the  primitive  ray  to  be  resolved 
in  the  principal  plane,  and  at  right  angles  to  the  principal  plane,  thereby 
giving  rise  to  an  ordinary  ray  (O),  and  an  extraordinary  ray  (E),  which, 
however,  do  not  become  separated  on  account  of  the  thinness  of  the  de- 
polarising plate.  They  will  not  form  a  single  plane  polarised  ray  on 
leaving  the  plate,  since  they  are  unequally  retarded  in  passing  through  it, 
and  consequently  leave  it  in  different  phases.  Since  neither  of  the  planes 
of  polarisation  of  O  and  E  coincides  with  the  principal  plane  of  the 
analyser,  the  vibrations  composing  them  will  again  be  resolved  by  the 
analyser  into  vibrations  in  and  at  right  angles  to  the  principal  plane — viz. 
O  gives  rise  to  O^  and  Oe  and  E  gives  rise  to  E^  and  Y.e.  But  the 
vibrations  composing  Oo  and  Y.o  being  in  the  same  plane  give  rise  to  a 
single  ordinary  ray,  I^,  and  in  like  manner  Oe  and  E^  give  rise  to  a  single 
extraordinary  ray,  \e.  Thus  the  interposition  of  the  depolarising  plate 
restores  the  extraordinary  ray. 

Suppose  the  angle  0  to  be  either  0°  or  90".  In  either  case  the  vibra- 
tions are  transmitted  through  the  depolarising  plate  without  resolution, 
consequently  they  remain  wholly  in  the  plane  of  primitive  polarisation, 
and  on  entering  the  analyser  cannot  give  rise  to  an  extraordinary  ray. 

If  the  Nicol's  prism  is  used  as  an  analyser,  the  ordinary  ray  is  sup- 
pressed by  mechanical  means.  Consequently  only  \e  will  pass  through 
the  prism,  and  that  for  all  values  of  d  except  0°  and  90°. 

A  little  consideration  will  show  that  the  joint  intensities  of  all  the  rays 
existing  at  any  stage  of  the  above  transformations  must  continue  constant, 
but  that  the  intensities  of  the  individual  rays  will  depend  on  the  magnitude 
of  f^,  and  when  this  circumstance  is  examined  in  detail,  it  explains  the 
fact  that  \e  increases  in  intensity  as  0  increases  from  0°  to  45°,  and  then 
decreases  in  intensity  as  0  increases  from  45°  to  90°. 

In  regard  to  the  colour  of  the  rays,  it  is  to  be  observed  that  the  formulas 
for  the  intensities  of  \o  and  \e  contain  a  term  depending  on  the  length  of 
the  wave  and  the  thickness  of  the  plate.  Consequently,  when  white  light 
is  used,  the  relative  intensities  of  its  component  colours  are  changed,  and, 
therefore,  \o  and  \e  will  each  have  a  prevailing  tint,  which  will  be  different 
for  different  thicknesses  of  the  plate.  The  tints  will,  however,  be  comple- 
mentary, since,  the  joint  intensities  of  \o  and  \e  being  the  same  as  that  of 


552  On  LighU  [627- 

the  original  ray,  they  will,  when  superimposed,  restore  all  the  components 
of  that  ray  in  their  original  intensities,  and  therefore  produce  white  light. 
628.  Coloured  ring:s  produced  by  polarised  lig-bt  in  traversing 
double  refractingr  films — In  the  experiments  with  Norremberg's  appa- 
ratus which  have  just  been  described  (619),  a  pencil  of  parallel  rays 


Fig.  492.  *< 

traverses  the  film  of  crystal  perpendicularly  to  its  faces,  and  as  all  parts 
of  the  film  act  in  the  same  manner,  there  is  everywhere  the  same  tint. 
But  when  the  incident  rays  traverse  the  plate  under  differeMt  obliquities, 
which  comes  to  the  same  thing  as  if  they  traversed  plates  differing  in 
thickness,  coloured  rings  are  formed  similar  to  Newton's  rings. 

The  best  method  of  observing  these  new  phenomena  is  by  means  of 
the  tourmaline  pincette.  This  is  a  small  instrument  consisting  of  two 
tourmalines,  cut  parallel  to  the  axis,  each  of  them  being  fitted  in  a  copper 
disc.  These  two  discs,  which  are  perforated  in  the  centre,  and  blackened, 
are  mounted  in  two  rings  of  silvered  copper,  which  is  coiled,  as  shown  in 
the  figure,  so  as  to  form  a  spring,  and  press  together  the  tourmalines. 
The  tourmalines  turn  with  the  disc,  and  may  be  so  arranged  that  their 
axes  are  either  perpendicular  or  parallel. 

The  crystal  to  be  experimented  upon  being  fixed  in  the  centre  of  a  cork 
disc,  is  placed  between  the  two  tourmalines,  and  the  pincette  is  held  before 
the  eye  so  as  to  view  diffused  light.  The  tourmaline  farthest  from  the  eye 
acts  as  polariser,  and  the  other  as  analyser.  If  the  crystal  thus  viewed  is 
uniaxial,  and  cut  perpendicularly  to  the  axis,  and  a  homogeneous  light — 
red,  for  instance — is  looked  at,  a  series  of  alternately  dark  and  red  rings 
are  seen.  With  another  simple  colour  similar  rings  are  obtained,  but 
their  diameter  decreases  with  the  refrangibility  of  the  colour.  On  the 
other  hand,  the  diameters  of  the  rings  diminish  when  the  thickness  of  the 
plates  increases,  and  beyond  a  certain  thickness  no  more  rings  are  pro- 
duced. If,  instead  of  illuminating  the  rings  by  homogeneous  light,  white 
light  be  used,  as  the  rings  of  the  different  colours  produced  have  not  the 
same  diameter,  they  are  partially  superposed,  and  produce  very  brilliant 
variegated  colours 

The  position  of  the  crystal  has  no  influence  on  the  rings,  but  this  is  not 
the  case  with  the  relative  position  of  the  two  tourmalines.  P"or  instance, 
in  experimenting  on  Iceland  spar  cut  perpendicular  to  the  axis,  and  from 
I  to  20  millimetres  in  thickness,  when  the  axes  of  the  tourmalines  are 
perpendicular,  a  beautiful  series  of  rings  is  seen  brilliantly  coloured,  and 
traversed  by  a  black  cross,  as  shown  in  fig.  i,  Plate  II.  If  the  axes  of 
the  tourmalines  are  parallel,  the  rings  have  tints  complementary  to  those 
they  had  at  first,  and  there  is  a  white  cross  (fig.  1 1^  Plate  II.),  instead  of  a 
black  one. 


V' 


-629]        Coloured  Rings  produced  hi  Biaxial  Crystals.         553 

In  order  to  understand  the  formation  of  these  rings  when  polarised 
light  traverses  double  refracting  films,  it  must  first  be  premised  that  these 
films  are  traversed  by  a  converging  conical  pencil,  whose  summit  is  the 
eye  of  the  observer.  Hence  it  follows  that  the  virtual  thickness  of  the 
film  which  the  rays  traverse  increases  with  their  divergence  ;  but  for  rays 
of  the  same  obliquity  this  thickness  is  the  same  ;  hence  there  result  dif- 
ferent degrees  of  retardation  of  the  ordinary  with  respect  to  the  extra- 
ordinary ray  at  different  points  of  the  plate,  and  consequently  different 
colours  are  produced  at  different  distances  from  the  axis,  but  the  same 
colours  will  be  produced  at  the  same  distance  from  the  axis,  and  conse- 
quently the  colours  are  arranged  in  circles  round  the  axis.  The  arms  of 
the  black  cross  are  parallel  to  the  optic  axis  of  each  of  the  tourmalines, 
and  are  due  to  an  absorption  of  the  polarised  light  in  these  directions. 
When  the  tourmalines  are  parallel  the  vibrations  are  transmitted,  and 
hence  the  white  cross. 

Analogous  effects  are  produced  with  all  uniaxial  crystals  ;  for  instance, 
tourmahne,  emerald,  sapphire,  beryl,  mica,  pyromorphite,  and  ferrocya- 
nide  of  potassium. 

629.  Rings  in  biaxial  crystals. — In  biaxial  crystals,  coloured  rings 
are  also  produced,  but  their  form  is  more  complicated.  The  coloured 
bands,  instead  of  being  circular  and  concentric,  have  the  form  of  curves, 
with  two  centres,  the  centre  of  each  system  corresponding  to  an  axis 
of  the  crystal.  Figs.  4,  5,  and  ^,  Plate  II.,  represent  the  curves  seen 
when  a  plate  of  either  Cerussite,  topaz,  or  nitre,  cut  perpendicularly  to 
the  axis,  is  placed  between  the  two  tourmalines,  the  plane  containing 
the  axes  of  the  crystal  being  in  the  plane  of  primitive  polarisation. 
When  the  axes  of  the  two  tourmalines  are  at  right  angles  to  each 
other,  fig.  4,  Plate  II.  is  obtained.  On  turning  the  crystal  without 
altering  the  tourmahnes,  fig.  5,  Plate  II.  is  seen,  which  changes  into  fig. 
6,  Plate  II.  when  the  crystal  has  been  turned  through  45°.  If  the  axes  of 
the  tourmalines  are  parallel,  the  same  coloured  curves  are  obtained,  but 
the  colours  are  complementary,  and  the  black  cross  changes  into  white. 
The  angle  of  the  optic  axis  in  the  case  of  nitre  is  only  5"  20',  and  hence 
the  whole  system  can  be  seen  at  once.  But  when  the  angle  exceeds  20^ 
to  25°,  the  two  systems  of  curves  cannot  be  simultaneously  seen.  There 
is  then  only  one  dark  bar  instead  of  the  cross,  and  the  bands  are  not 
oval,  but  circular.  Fig.  3,  Plate  II.  represents  the  phenomenon  as  seen 
with  arragonite. 

Herschel,  who  has  carefully  measured  the  rings  produced  by  biaxial 
crystals,  refers  them  to  the  kind  of  curve  known  in  geometry  as  the  lemnis- 
cate,  in  strict  accordance  with  the  results  of  the  undulatory  theory  of  light. 

The  observation  of  the  system  of  rings  which  plates  of  crystals  give 
in  polarised  light  presents  a  means  of  distinguishing  between  optical 
uniaxial  and  optical  biaxial  crystals,  even  in  cases  in  which  no  conclu- 
sion can  be  drawn  as  to  the  system  in  which  a  mineral  crystallises 
from  mere  morphological  reasons.  In  this  way,  the  optical  investiga- 
tion becomes  a  valuable  aid  in  mineralogy,  as,  for  example,  in  the  case  of 

r.  B 


554  On  Light.  [629- 

mica,  of  which  there  are  two  mineralogical  species,  the  uniaxial  and  the 
biaxial. 

All  the  phenomena  which  have  been  described  are  only  obtained  by 
means  of  polarised  light.  Hence  a  double  refracting  film,  with  either  a 
Nicol's  prism  or  a  tourmaline  as  analyser,  may  be  used  to  distinguish  be- 
tween polarised  and  unpolarised  light— that  is,  as  a  polariscope. 

630.  Colours  produced  by  compressed  or  by  unannealed  ^lass. 

Ordinary  glass  is  not  endowed  with  the  power  of  double  refraction.     It 

Fig-  493-  Fig-  494-  Fig.  495. 


n 


Fig.  496. 


o 


Fig.  497. 


Fig.  498. 


acquires  this  property,  however,  if  by  any  cause  its  elasticity  becomes 
more  modified  in  one  direction  than  in  another.  In  order  to  effect  this, 
it  may  be  strongly  compressed  in  a  given  direction,  or  it  may  be  curved, 
or  tempered— that  is  to  say,  cooled  after  having  been  heated.  If  the 
glass  is  then  traversed  by  a  beam  of  polarised  light,  effects  of  colour  are 
obtained  which  are  entirely  analogous  to  those  described  in  the  case 
of  doubly  refracting  crystals.  They  are,  however,  susceptible  of  far 
greater  variety,  according  as  the  plates  of  glass  have  a  circular,  square, 
rectangular,  or  triangular  shape,  and  according  to  the  degree  of  tension 
of  their  particles. 

When  the  polariser  is  a  mirror  of  black  glass,  on  which  the  light  of  the 
sky  is  incident,  and  the  analyser  is  a  Nicol's  prism,  through  which  the 
glass  plates  traversed  by  polarised  light  are  viewed,  figs.  493,  494,  496, 
represent  the  appearances  presented  successively,  when  a  square  plate 
of  compressed  glass  is  turned  in  its  own  plane ;  figs.  495  and  498  re- 
present the  appearances  produced  by  a  circular  plate  under  the  same 
circumstances ;  and  fig.  497,  that  produced  when  one  rectangular  plate  is 
superposed  on  another.  This  figure  also  varies  when  the  system  of  plates 
is  turned. 

Compressed  and  curved  glasses  present  phenomena  of  the  same  kind, 
which  also  vary  under  the  same  conditions. 


-632]     Origin  of  Elliptical  and  Circular  Polarisation.        555 


ELLIPTICAT.,   CIRCULAR,   AND    ROTATORY   POLARISATION. 

631.  Definition    of  elliptical    and  circular  polarisation. — In  the 

cases  hitherto  considered  the  particles  of  ether  composing  a  polarised  ray- 
vibrate  in  parallel  straight  lines ;  to  distinguish  this  case  from  those  we 
are  now  to  consider  such  light  is  frequently  called  plane  polarised  light. 
It  sometimes  happens  thaf  the  particles  of  ether  describe  ellipses  round 
their  positions  of  rest,  the  planes  of  the  ellipses  being  perpendicular  to  the 
direction  of  the  ray.  If  the  axes  of  these  ellipses  are  equal  and  parallel, 
the  ray  is  said  to  be  elliptically  polarised.  In  this  case  the  particles  which , 
when  at  rest,  occupied  a  straight  line,  are,  when  in  motion,  arranged  in  a 
helix  round  the  line  of  their  original  position  as  an  axis,  the  helix  chang- 
ing from  instant  to  instant.  If  the  axes  of  the  ellipses  are  equal,  they 
become  circles,  and  the  light  is  said  to  be  circularly  polarised.  If  the 
minor  axes  become  zero,  the  ellipses  coincide  with  their  major  axes,  and 
the  light  becomes  plane  polarised.  Consequently,  plane  polarised  light 
and  circularly  polarised  light  are  particular  cases  of  elliptically  polarised 
light. 

632.  Tbeory  oftbe  origrin  of  elliptical  and  circular  polarisation. — 
Let  us  in  the  first  place  consider  a  simple  pendulum  (51)  vibrating  in 
any  plane,  the  arc  of  vibration  being  small.  Suppose  that,  when  in 
its  lowest  position,  it  received  a  blow  in  a  direction  at  right  angles  to 
the  direction  of  its  motion,  such  as  would  make  it  vibrate  in  an  arc  at 
right  angles  to  its  arc  of  primitive  vibration,  it  follows  from  the  law  of 
the  composition  of  velocities  (48)  that  the  joint  effect  will  be  to  make  it 
vibrate  in  an  arc  inclined  at  a  certain  angle  to  the  arc  of  primitive  vibra- 
tion, the  magnitude  of  the  angle  depending  on  the  magnitude  of  the  blow. 
If  the  blow  communicated  a  velocity  equal  to  that  with  which  the  body 
is  already  moving,  the  angle  would  be  45°.  Next,  suppose  the  blow  to 
communicate  an  equal  velocity,  but  to  be  struck  when  the  body  is  at  its 
highest  point,  this  will  cause  the  particle  to  describe  a  circle,  and  to 
move  as  a  conical  pendulum  (53)  If  the  blow  is  struck  under  any 
other  circumstances,  the  particle  will  describe  an  ellipse.  Now  as  the' 
two  blows  would  produce  separately  two  simple  vibrations  in  direc- 
tions at  right  angles  to  each  other,  we  may  state  the  result  arrived  at 
as  follows : — If  two  rectilinear  vibrations  are  superinduced  on  the 
same  particle  in  directions  at  right  angles  to  each  other,  then  :  i.  If 
they  are  in  the  same  or  opposite  phases,  they  make  the  point  describe  a 
rectilinear  vibration  in  a  direction  inclined  at  a  certain  angle  to  either  of 
the  original  vibrations.  2.  But  if  their  phases  differ  by  90°  or  a  quarter 
of  a  vibration,  the  particle  will  describe  a  circle,  provided  the  vibrations 
are  equal.  3.  Under  other  circumstances  the  particle  will  describe  an 
ellipse. 

To  apply  this  to  the  case  of  polarised  light.  Suppose  two  rays  of  light 
polarised  in  perpendicular  planes  to  coincide,  each  would  separately 
cause  the  same  particles  to  vibrate  in  perpendicular  directions.  Conse- 
quently— I.  If  the  vibrations  are  in  the  same  or  opposite  phases,  the 


556  On  Light.  [632- 

light  resulting  from  the  two  rays  is  plane  polarised.  2.  If  the  rays  are 
of  equal  intensity,  and  their  phases  differ  by  90°,  the  resulting  light  is 
circularly  polarised.  3.  Under  other  circumstances  the  light  is  ellipti- 
cally  polarised. 

As  an  example,  if  reference  is  made  to  arts.  638  and  639,  it  will  be 
seen  that  the  rays  denoted  by  O  and  E  are  superimposed  in  the  manner 
above  described.  Consequently,  the  light  which  leaves  the  depolarising 
plate  is  elliptically  polarised.  If,  however,  the  principal  plane  of  the 
depolarising  plate  is  turned  so  as  to  make  an  angle  of  45°  with  the  plane 
of  primitive  polarisation,  O  and  E  have  equal  intensities  ;  and,  if  further, 
the  plate  is  made  of  a  certain  thickness,  so  that  the  phases  of  O  and  E 
may  differ  by  90°,  or  by  a  quarter  of  a  vibration,  the  light  which  emerges 
from  the  plate  is  circularly  polarised.  This  method  may  be  employed  to 
produce  circularly  polarised  light. 

Circular  or  elliptical  polarisation  may  be  either  right-handed  or  left- 
haiided^  or  what  is  sometimes  called  dextrogyrate  and  IcEvogyrate.  If  the 
observer  looks  along  the  ray  in  the  direction  of  propagation,  from  polar- 
iser  to  analyser,  then,  if  the  particles  move  in  the  same  direction  as  the 
hands  of  a  watch,  with  its  face  to  the  observer,  the  polarisation  is  right- 
handed. 

633.  Fresnel's  rbomb. — This  is  a  means  of  obtaining  circularly 
polarised  light.  We  have  already  seen  (632)  that,  to  obtain  a  ray  of 
circularly  polarised  light,  it  is  sufficient  to  de- 
compose a  ray  of  plane  polarised  light  in  such  a 
manner  as  to  produce  two  rays  of  light  of  equal 
intensity  polarised  in  planes  at  right  angles  to 
each  other,  and  differing  in  their  paths  by  a 
quarter  of  an  undulation.  Fresnel  effected  this 
by  means  of  a  rhomb,  which  has  received  his 
name.  It  is  made  of  glass  ;  its  acute  angle  is 
54°,  and  its  obtuse  126°.  If  a  ray,  a,  fig.  499,  of 
plane  polarised  light  falls  perpendicularly  on 
the  face  AB,  it  will  undergo  two  total  internal 
reflections  at  an  angle  of  about  54°,  one  at  E, 
Pl^  and  the  other  at  F,  and  will  emerge  perpendicu- 

larly. 
If  the  plane  ABCD  be  inclined  at  an  angle  of  45°  to  the  plane  of 
polarisation,  the  polarised  ray  will  be  divided  into  two  coincident  rays, 
with  their  planes  of  polarisation  at  right  angles  to  each  other,  and  it  ap- 
pears that  one  of  them  Idses  exactly  a  quarter  of  an  undulation,  so  that 
on  emerging  from  the  rhomb  the  ray  is  circularly  polarised.  If  the  ray 
emerging  as  above  from  Fresnel's  rhomb  is  examined,  it  will  be  found  to 
differ  from  plane  polarised  light  in  this,  that,  when  it  passes  through  a 
double  refracting  prism,  the  ordinary  and  extraordinary  rays  are  of  equal 
intensity  in  all  positions  of  the  prism.  Moreover,  it  differs  from  ordinary 
light  in  this,  that  if  it  passed  through  a  second  rhomb  placed  parallel  to 
the  first,  a  second  quarter  of  an  undulation  will  be  lost,  so  that  the  parts 
of  the  original  plane  polarised  ray  will  differ  by  half  an  undulation,  and 


-636]    Elliptical  Polarisation.     Rotatory  Polarisation.        557 

the  emergent  ray  will  be  plane  polarised  ;  moreover,  the  plane  of  polari- 
sation will  be  inclined  at  an  angle  of  45°  to  ABCU,  but  on  the  other  side 
from  the  plane  of  primitive  polarisation. 

634.  Slliptical  polarisation. — Our  limits  will  not  allow  us  to  enter 
into  this  subject,  but  we  may  state  that,  in  addition  to  the  method  already 
mentioned  (633),  elliptically  polarised  light  is  generally  obtained  when- 
ever plane  polarised  light  suffers  reflection.  Polarised  light  reflected  from 
metals  becomes  elliptically  polarised,  the  degree  of  ellipticity  depending 
on  the  direction  of  the  incident  ray,  and  of  its  plane  of  polarisation,  as 
well  as  on  the  reflecting  substance.  When  reflected  from  silver,  the  po- 
larisation is  almost  circular,  and  from  galena  almost  plane.  If  elliptically 
polarised  light  be  analysed  by  the  NicoFs  prism,  it  never  vanishes,  though 
at  alternate  positions  it  becomes  fainter  ;  it  is  thus  distinguished  from 
plane  and  from  circular  polarised  light.  If  analysed  by  Iceland  spar 
neither  image  disappears,  but  they  undergo  changes  in  intensity. 

Light  can  also  be  polarised  elliptically  in  Fresnel's  rhomb.  If  the 
angle  between  the  planes  of  primitive  polarisation  and  of  incidence  be 
any  other  than  45°,  the  emergent  ray  is  elliptically  polarised. 

635.  Rotatory  polarisation. — Rock  crystal  or  quartz  possesses  a 
remarkable  property  which  was  long  regarded  as  peculiar  to  itself 
among  all  crystals,  though  it  has  been  since  found  to  be  shared  by 
tartaric  acid  and  its  salts,  together  with  some  other  crystalline  bodies. 
This  property  is  called  rotatory  polarisation,  and  may  be  described  as 
follows  : — Let  a  ray  of  homogeneous  light  be  polarised  and  let  the 
analyser,  say  a  Nicol's  prism,  be  turned  till  the  light  does  not  pass 
through  it.  Take  a  thin  section  of  a  quartz  crystal  cut  at  right  angles 
to  its  axis,  and  place  it  between  the  polariser  and  the  analyser  with  its 
plane  at  right  angles  to  the  rays.  The  light  will  now  pass  through  the 
analyser.  The  phenomenon  is  not  the  same  as  that  previously  described 
(625),  for,  if  the  rock  crystal  is  turned  round  its  axis,  no  effect  is  pro- 
duced, and  if  the  analyser  is  turned,  the  ray  is  found  to  \iQ^  plane  polarised 
in  a  plane  inclined  at  a  certain  angle  to  the  plane  of  primitive  polarisa- 
tion. If  the  light  is  red,  and  the  plate  i  millimetre  thick,  this  angle  is 
about  17°.  In  some  specimens  of  quartz  the  plane  of  polarisation  is 
turned  to  the  right  hand,  in  others  to  the  left  hand.  Specimens  of  the 
former  kind  are  said  to  be  right-handed,  those  of  the  latter  kind  left- 
handed.  This  difference  corresponds  to  a  difference  in  crystallographic 
structure.  The  property  possessed  by  rock  crystal  of  turning  the  plane 
of  polarisation  through  a  certain  angle  was  thoroughly  investigated  by 
M.  Biot,  who,  amongst  other  results,  arrived  at  this  : — For  a  given  colour 
the  angle  through  which  the  plane  of  polarisation  is  turned  is  proportional 
to  the  thickness  of  the  quartz. 

636.  Pbysical  explanation  of  rotatory  polarisation. — The  explana- 
tion of  the  phenomenon  described  in  the  last  article  is  as  follows  : — When 
a  ray  of  polarised  light  passes  along  the  axis  of  the  quartz  crystal,  it  is 
divided  into  two  rays  of  circular ly  polarised  light  of  equal  intensity,  which 
pass  through  the  crystal  with  different  velocities.  In  one  the  circular 
polarisation  is  right-handed,  in  the  other  left-handed  (632).     The  existence 


558  On  Light.  [636- 

of  these  rays  was  proved  by  Fresnel,  who  succeeded  in  separating  them. 
On  emerging  from  the  crystal,  they  are  compounded  into  a  plane  polarised 
ray,  but  since  they  move  with  unequal  velocities  within  the  crystal,  they 
emerge  in  different  phases,  and  consequently  the  plane  of  polarisation 
will  not  coincide  with  the  plane  of  primitive  polarisation.  This  can  be 
readily  shown  by  reasoning  similar  to  that  employed  in  art.  632.  The 
same  reasoning  will  also  show  that  the  plane  of  polarisation  will  be 
turned  to  the  right  or  left,  according  as  the  right-handed  or  left-handed 
ray  moves  with  the  greater  velocity.  Moreover,  the  amount  of  the  rotation 
will  depend  on  the  amount  of  the  retardation  of  the  ray  whose  velocity  is 
least— that  is  to  say,  it  will  depend  on  the  thickness  of  the  plate  of  quartz. 
In  this  manner  the  phenomena  of  rotatory  polarisation  can  be  completely 
accounted  for.  , 

637.  Coloration  produced  by  rotatory  polarisation. — The  rotation 
is  different  with  different  colours  ;  its  magnitude  depends  on  the  re- 
frangibility,  and  is  greatest  with  the  most  refrangible  rays.  In  the  case 
of  red  light  a  plate  i  millimetre  in  thickness  will  rotate  the  plane  17°, 
while  a  plate  of  the  same  thickness  will  rotate  it  44°  in  the  case  of  violet 
light.  Hence  with  white  light  there  will,  in  each  position  of  the  analysing 
Nicol's  prism,  be  a  greater  or  less  quantity  of  each  colour  transmitted. 
In  the  case  of  a  right-handed  crystal,  when  the  Nicol's  prism  is  turned  to 
the  right,  the  colours  will  successively  appear  from  the  less  refrangible  to 
the  more  so — that  is,  in  the  order  of  the  spectrum, 
from  red  to  violet  ;  with  a  left-handed  crystal  in 
the  reverse  order.  Obviously  in  turning  the  Nicol's 
prism  to  the  left,  the  reverse  of  these  results  will 
take  place. 

When  a  quartz  plate  cut  perpendicularly  to  the 
»g-  soo.  ^^.g  ^^^  traversed  by  a  ray  of  polarised  light  is 

looked  at  through  a  doubly  refracting  prism,  two  brilliantly  coloured  images 
are  seen,  of  which  the  tints  are  complementary ;  for  their  images  are  partially 
superposed,  and  in  this  position  there  is  a  white  light  (fig.  500).  When  the 
prism  is  turned  from  left  to  right,  the  two  images  change  colours,  and  as- 
sume successively  all  the  colours  of  the  spectrum. 

This  will  be  understood  from  what  has  been  said  about  the  different 
rotation  for  different  colours.  Quartz  rotates  the  plane  of  polarisation  for 
red  1 7°  for  each  millimetre,  and  for  violet  44°  ;  hence  from  the  great 
difference  of  these  two  angles,  when  the  polarised  light  which  has  traversed 
the  quartz  plate  emerges,  the  various  simple  colours  which  it  contains  are 
polarised  in  different  planes.  Consequently,  when  the  rays  thus  trans- 
mitted by  the  quartz  pass  through  a  double  refracting  prism,  they  are 
each  decomposed  into  two  others  polarised  at  right  angles  to  each  other  : 
the  various  simple  colours  are  not  divided  in  the  same  proportion  be- 
tween the  ordinary  and  extraordinary  rays  furnished  by  the  prism  ;  the 
two  images  are,  therefore,  coloured  ;  but,  since  those  which  are  wanting  in 
the  one  occur  in  the  other,  the  colours  of  the  images  are  perfectly  com- 
plementary. 

These  phenomena  of  coloration  maybe  well  seen  by  means  of  Norrem- 


-638] 


Rotatory  Power  of  Liquids. 


559 


berg's  apparatus  (fig.  488).  A  quartz  plate,  s,  cut  at  right  angles  to  the  axis 
and  fixed  in  a  cork  disc,  is  placed  on  a  screen,  e  ;  the  mirror, ;/  (fig.  488),  - 
being  then  so  inclined  that  a  ray  of  polarised  light  passes  through  the 
quartz,  the  latter  is  viewed  through  a  refracting  prism,  ^  ;  when  this  tube 
is  turned,  the  cemplementary  images  furnished  by  the  passage  of  polarised 
light  through  the  quartz  are  seen. 

638.  Rotatory  power  of  liquids. — Biot  has  found  that  a  great  num- 
ber of  liquids  and  solutions  possess  the  property  ot  rotatory  polarisation. 


Fig.  501. 

He  has  further  observed  that  the  deviation  of  the  plane  of  polarisation 
can  reveal  differences  in  the  composition  of  bodies  where  none  is  ex- 
hibited by  chemical  analysis.  For  instance,  uncrystallisable  grape-sugar 
deflects  the  plane  of  polarisation  to  the  left,  while  cane-sugar  deflects  it 
to  the  right,  although  the  chemical  composition  of  the  two  sugars  is  the 
same. 

The  rotatory  power  of  liquids  is  far  less  than  that  of  quartz.  In  con- 
centrated syrup  of  cane-sugar,  which  possesses  the  rotatory  power  in  the 
highest  degree,  the  power  is  ^^\h  that  of  quartz,  so  that  it  is  necessary  to 
operate  upon  columns  of  liquids  of  considerable  length — 8  inches  for 
example. 

Fig.  501  represents  the  apparatus  devised  by  Biot  for  measuring  the 
rotatory  power  of  liquids.  On  a  metal  groove,^,  fixed  to  a  support,  r,  is 
a  brass  tube  20  centimetres  long,  in  which  is  contained  the  liquid  expe- 
rimented upon.     This  tube,  which  is  tinned  inside,  is  closed  at  each  end  by 


560  On  Light.  [638- 

j^lass  plates  fastened  by  screw  collars.  At  7n  is  a  mirror  of  black  glass,  in- 
clined at  the  polarising  angle  to  the  axis  of  the  tubes  bd  and  rt,  so  that  the 
ray  reflected  by  the  mirror  ;;z,  in  the  direction  bda,  is  polarised.  In  the 
centre  of  the  graduated  circle  h,  inside  the  tube  <7,  and  at  right  angles  to 
the  axis  bda,  is  a  double  refracting  achromatic  prism,  which  can  be  turned 
about  the  axis  of  the  apparatus  by  means  of  a  button  n.  The  latter  is 
fixed  to  a  limb  c,  on  which  is  a  vernier,  to  indicate  the  number  of  degrees 
turned  through.  Lastly,  from  the  position  of  the  mirror  ?«,  the  plane  of 
polarisation,  St?<f,  of  the  reflected  ray  is  vertical,  and  the  zero  of  the 
graduation  of  the  circle,  /z,  is  on  this  plane. 

Before  placing  the  tube  d  in  the  groove  g,  the  extraordinary  image  fur- 
nished by  the  double  refracting  prism  disappears  whenever  the  limb  c  cor- 
responds to  the  zero  of  the  graduation,  because  then  the  double  refracting 
prism  is  so  turned  that  its  principal  section  coincides  with  the  plane  of 
polarisation  (623).  This  is  the  case  also  when  the  tube  d  is  full  of  water 
or  any  other  inactive  liquid,  like  alcohol,  ether,  etc.,  which  shows  that  the 
plane  of  polarisation  has  not  been  turned.  But  if  the  tube  be  filled  with 
a  solution  of  cane-sugar  or  any  other  active  liquid,  the  extraordinary  image 
reappears,  and  to  extinguish  it  the  limb  must  be  turned  to  a  certain  extent 
either  to  the  right  or  to  the  left  of  zero,  according  as  the  liquid  is  right- 
handed  or  left-handed,  showing  that  the  polarising  plane  has  been  turned 
by  the  same  angle.  With  solution  of  cane-sugar  the  rotation  takes  place 
to  the  right  ;  and  if  with  the  same  solution  tubes  of  different  lengths  are 
taken,  the  rotation  is  found  to  increase  proportionally  to  the  length,  in  con- 
formity with  art.  635  ;  further,  with  the  same  tube,  but  with  solutions  of 
various  strengths,  the  rotation  increases  with  the  quantity  of  sugar  dis- 
solved, so  that  the  quantitative  analysis  of  a  solution  may  be  made  by 
means  of  its  angle  of  deviation. 

In  this  experiment  homogeneous  light  must  be  used  ;  for  as  the  various 
tints  of  the  spectra  have  different  rotatory  powers,  white  light  is  decom- 
posed in  traversing  an  active  liquid,  and  the  extraordinary  image  does  not 
disappear  completely  in  any  position  of  the  double  refracting  prism — it 
simply  changes  the  tint.  The  transition  tint  (639)  may,  however,  be  ob- 
served. To  avoid  this  inconvenience,  a  piece  of  red  glass  is  placed  in  the 
tube  between  the  eye  and  the  double  refracting  prism,  which  only  allows 
red  light  to  pass.  The  extraordinary  image  disappears  in  that  case,  when- 
ever the  principal  section  of  the  prism  coincides  with  the  plane  of  polari- 
sation of  the  red  ray. 

639.  Soleil's  saccliarlzueter. — M.  Soleil  has  constructed  an  apparatus, 
based  upon  the  rotatory  power  of  liquids,  for  analysing  saccharine  sub- 
stances, to  which  the  name  saccharinieter  is  applied. 

Figure  502  represents  the  saccharinieter  fixed  horizontally  on  its  foot, 
and  fig.  503  gives  a  longitudinal  section,  with  the  modifications  which  have 
been  introduced  by  M.  Duboscq. 

The  principle  of  this  instrument  is  not  the  amphtude  of  the  rotation  of 
the  plane  of  polarisation,  as  in  Biot's  apparatus,  but  that  of  compensation  ; 
that  is  to  say,  a  second  active  substance  is  used  acting  in  the  opposite 
direction  to  that  analysed,  and  whose  thickness  can  be  altered  until  the 


639] 


Soldi 's  Saccharimeter. 


561 


contrary  actions  of  the  two  substances  completely  neutralise  each  other. 
Instead  of  measuring  the  deviation  of  the  plane  of  polarisation,  the  thick- 
ness is  measured  which  the  plate  of  quartz  must  have  in  order  to  obtain 
perfect  compensation. 

The  apparatus  consists  of  three  parts — a  tube  containing  the  liquid  to 
be  analysed,  a  polar iser,  and  an  analyser. 

The  tube  m,  containing  the  liquid,  is  made  of  copper,  tinned  on  the  in- 
side, and  closed  at  both  ends  by  two  glass  plates.  It  rests  on  a  support, 
k^  terminated  at  both  ends  by  tubes,  r  and  a,  in  which  are  the  crystals 
used  as  analysers  and  polarisers,  and  which  are  represented  in  section 
(fig-  5Q3). 


Fig.  502, 

In  front  of  the  aperture,  S  (hg.  503),  is  placed  an  ordinary  moderator 
lamp.  The  light  emitted  by  this  lamp  in  the  direction  of  the  axis  first 
meets  a  double  refracting  prism,  r,  which  serves  as  polariser  (621).  The 
ordinary  image  alone  meets  the  eye,  the  extraordinary  image  being  pro- 
jected out  of  the  field  of  vision  in  consequence  of  the  amplitude  of  the 
angle  which  the  ordinary  makes  with  the  extraordinary  ray.  The  double 
refracting  prism  is  in  such  a  position  that  the  plane  of  polarisation  is 
vertical,  and  passes  through  the  axis  of  the  apparatus. 

Emerging  from  the  double  refracting  prism,  the  polarised  ray  meets  a 
plate  of  quartz  with  double  rotation  ;  that  is,  this  plate  rotates  the  plane 
both  to  the  right  and  to  the  left.  This  is  effected  by  constructing  the  plate 
of  two  quartz  plates  of  opposite  rotation  placed  one  on  the  other,  as  shown 
in  figure  506,  so  that  the  line  of  separation  is  vertical  and  in  the  same 
plane  as  the  axis  of  the  apparatus.     These  plates,  cut  perpendicularly  to 


56: 


On  Light. 


[639- 


the  axis,  have  a  thickness  of  375  milHmetres,  corresponding  to  a  rotation 
of  90°,  and  give  a  rose-violet  tint,  called  the  tint  of  passage  or  transition- 
tint.  As  the  quartz,  whether  right-handed  or  left-handed,  turns  always 
to  the  same  extent  for  the  same  thickness,  it  follows  that  the  two  quartz 
plates,  a  and  ^,  turn  the  plane  of  polarisation  equally,  one  to  the  right  and 


fig-  503- 


Fig.  506. 


the  other  to  the  left.  Hence,  looked  at  through  a  double  refracting  prism, 
they  present  exactly  the  same  tint. 

Having  traversed  the  quartz,  q^  the  polarised  ray  passes  into  the  liquid 
in  the  tube  ;«,  and  then  meets  a  single  plate  of  quartz,  /,  of  any  thickness, 
the  use  of  which  will  be  seen  presently.  The  compensator,  «,  which  de- 
stroys the  rotation  of  the  column  of  liquid  ?«,  consists  of  two  quartz  plates, 
with  the  same  rotation  either  to  the  right  and  the  left,  but  opposite  to  that 
of  the  plate  /.  These  two  quartz  plates,  a  section  of  which  is  represented 
in  fig.  504,  are  obtained  by  cutting  obliquely  a  quartz  plate  with  parallel 
sides,  so  as  to  form  two  prisms  of  the  same  angle,  N,  N';  superposing,  then, 
these  two  prisms,  as  shown  in  the  figure,  a  single  plate  is  obtained  with 
parallel  faces,  which  can  be  varied  at  will.  This  is  effected  by  fixing  each 
prism  to  a  slide,  so  as  to  move  it  in  either  direction  without  disturbing  the 
parallelism.  This  motion  is  effected  by  means  of  a  double  rackwork  and 
pinion  motion  turned  by  a  milled  head,  b  (figs.  502,  503). 

When  these  plates  move  in  the  direction  indicated  by  the  arrows 
(fig.  504),  it  is  clear  that  the  sum  of  their  thicknesses  increases,  and  that 
it  diminishes  when  the  plates  are  moved  in  the  contrary  direction.  A 
scale  and  a  vernier  follow  the  plates  in  their  motion,  and  measure  the 
thickness  of  the  compensator.  This  scale,  represented  with  its  vernier 
in  figure  505,  has  two  divisions,  with  a  common  zero,  one  from  left  to 
right  for  right-handed  liquids,  and  another  from  right  to  left  for  left- 
handed. 

When  the  vernier  is  at  zero  of  the  scale,  the  sum  of  the  thicknesses  of 
the  plates  NN'  is  exactly  equal  to  that  of  the  plate  /,  and  as  the  rotation  of 
the  latter  is  opposed  to  that  of  the  compensator,  the  effect  is  zero.  But 
by  moving  the  plates  of  the  compensator  in  one  or  the  other  direction 


-639]  Soleil's  SaccJiarimetcr.  563 

either  the  compensator  or  the  quartz,  /,  preponderates,   and  there  is  a 
rotation  from  left  to  right. 

Behind  the  compensator  is  a  double  refracting  prism,  c  (fig.  503),  serv- 
ing as  analyser  to  observe  the  polarised  ray  which  has  traversed  the 
liquid  and  the  various  quartz  plates.  In  order  to  understand  more  easily 
the  object  of  the  prism,  r,  we  will  neglect  for  a  moment  the  crystals  and 
the  lenses  on  the  left  of  the  drawing.  If  at  first  the  zero  of  the  vernier,  o^ 
coincides  with  that  of  the  scale,  and  if  the  liquid  in  the  tube  is  inactive, 
the  actions  of  the  compensator,  and  of  the  plate  /,  neutralise  each  other  ; 
and  the  liquid  having  no  action,  the  two  halves  of  the  plate  q,  seen  through 
the  prism  6,  give  exactly  the  same  tint  as  has  been  observed  above.  But 
if  the  tube  filled  with  inactive  liquid  be  replaced  by  one  full  of  solution  of 
sugar,  the  rotatory  power  of  this  solution  is  added  to  that  of  one  of  the 
halves  {a  or  b)  of  the  plate  q  (viz.  that  half  which  tends  to  turn  the  plane 
of  polarisation  in  the  same  direction  as  the  solution),  and  subtracted  from 
that  of  the  other.  Hence  the  two  halves  of  the  plate  q  no  longer  show 
the  same  tint ;  the  half  a,  for  instance,  is  red,  while  the  half  b  is  blue. 
The  prisms  of  the  compensator  are  then  moved,  by  t'urning  the  milled  head 
b^  either  to  the  right  or  to  the  left,  until  the  difference  of  action  of  the 
compensator  and  of  the  plate  /  compensates  the  rotatory  power  of  the 
solution,  which  takes  place  when  the  two  halves  of  the  plate  Q,  with 
double  rotation,  revert  to  their  original  tmt. 

The  direction  of  the  deviation  and  the  thickness  of  the  compensator 
are  measured  by  the  relative  displacement  of  the  scale  <?,  and  of  the 
vernier  r.  Ten  of  the  divisions  on  the  scale  correspond. to  a  difference  of 
I  millimetre  in  the  thickness  of  the  compensator ;  and  as  the  vernier 
gives  itself  tenths  of  these  divisions,  it  therefore  measures  differences  of 
ji^  Jn  the  thickness  of  the  compensator. 

When  once  the  tints  of  the  two  halves  of  the  plate  are  exactly  the  same, 
and  therefore  the  same  as  before  interposing  the  solution  of  sugar,  the 
division  on  the  scale  corresponding  to  the  vernier  is  read  off,  and  the 
corresponding  number  gives  the  strength  of  the  solution.  This  depends  on 
the  experimental  fact  that  16-47 1  grains  of  pure  and  well-dried  sugar-candy 
being  dissolved  in  water,  and  the  solution  diluted  to  the  volume  of  100 
cubic  centimetres,  and  observed  in  a  tube  of  20  centimetres  in  length,  the 
deviation  produced  is  the  same  as  that  effected  by  a  quartz  plate  a 
millimetre  thick.  In  making  the  analysis  of  raw  sugar,  a  weight  of 
16-471  grains  of  sugar  is  taken,  dissolved  in  water,  and  the  solution  made 
up  to  100  cubic  centimetres,  with  which  a  tube  20  centimetres  in  length  is 
filled,  and  the  number  indicated  by  the  vernier  read  off,  when  the  primitive 
tint  has  been  obtained.  This  number  being  42,  for  example,  it  is  con- 
cluded that  the  amount  of  crystallisable  sugar  in  the  solution  is  42  per 
cent,  of  that  which  the  solution  of  sugar-candy  contained,  and,  therefore, 
16-471  grains  x  j*^^^  or  6-918  grains.  This  result  is  only  valid  when  the 
sugar  is  not  mixed  with  uncrystallisable  sugar  or  some  other  left-handed 
substance.  In  that  case  the  crystallisable  sugar,  which  is  right-handed, 
must  be,  by  means  of  hydrochloric  acid,  converted  into  uncrystallisable 


564  On  Light.  [639- 

sugar,  which  is  left-handed  ;  and  a  new  determination  is  made,  which, 
together  with  the  first,  gives  the  quantity  of  crystallisable  sugar. 

The  arrangement  of  crystals  and  lenses,  o,g,f,  and  a^  placed  behind 
the  prism  c,  forms  what  M.  Soleil  calls  the  producer  of  sensible  tints. 
For  the  most  delicate  tint,  that  by  which  a  very  feeble  difference  in  the 
coloration  of  the  two  halves  of  the  rotation  plate  can  be  distinguished,  is 
not  the  same  for  all  eyes  ;  for  most  people  it  is  of  a  violet  blue  tint,  like 
flax-blossom,  and  it  is  important  either  to  produce  this  tint  or  some  other 
equally  sensible  to  the  eye  of  the  observer.  This  is  effected  by  placing 
in  front  of  the  prism  ^,  at  first  a  quartz  plate,  o,  cut  perpendicular  to  the 
axis,  then  a  small  Galilean  telescope  consisting  of  a  double  convex  glass, 
g^  and  a  double  concave  glass, y^  which  can  be  approximated  or  removed 
from  each  other  according  to  the  distance  of  distinct  vision  of  each  ob- 
server. Lastly,  there  is  a  double  refracting  prism,  r,  acting  as  polariser 
in  reference  to  the  quartz,  and  the  prism  a  as  analyser;  and  hence,  when 
the  latter  is  turned  either  right  or  left,  the  light  which  has  traversed  the 
prism  (T,  and  the  plate  o,  changes  its  tint,  and  finally  gives  that  which  is 
the  most-delicate  for  the  experimenter. 

640.  Analysis  of  diabetic  urine. — In  the  disease  diabetes^  the  urine 
contains  a  large  quantity  of  fermentescible  sugar,  called  diabetic  sugar, 
which  in  the  natural  condition  of  the  urine  turns  the  plane  of  polarisation 
to  the  right.  To  estimate  the  quantity  of  this  sugar,  the  urine  is  first 
clarified  by  heating  it  with  acetate  of  lead  and  filtering ;  the  tube  is  filled 
with  the  clear  liquid  thus  obtained ;  and  the  milled  head,  b^  turned,  until 
by  means  of  the  double  rotating  plate  the  same  tint  is  obtained  as  before 
the  interposition  of  the  urine.  Experiment  has  shown  that  100  parts  of 
the  saccharimetric  scale  represent  the  displacement  which  the  quartz 
compensators  must  have  when  there  are  225-6  grains  of  sugar  in  a  litre  ; 
hence  each  division  of  the  scale  represents  2  256  of  sugar.  Accordingly, 
to  obtain  the  quantity  of  sugar  in  a  given  urine,  the  number  indicated  by 
the  vernier  at  the  moment  at  which  the  primitive  tint  reappears  must  be 
multiphed  by  2-256. 

641.  Polarisation  of  beat. — The  rays  of  heat,  like  those  of  light,  may 
become  polarised  by  reflection  and  by  refraction.  The  experiments  on 
this  subject  are  difficult  of  execution  ;  they  were  first  made  by  Malus  and 
Berard,  in  1810;  after  the  death  of  Malus  they  were  continued  by  the 
latter  philosopher. 

In  his  experiments,  the  calorific  rays  reflected  from  one  mirror  were 
received  upon  a  second,  just  as  in  Norremberg's  apparatus;  from  the  second 
they  fell  upon  a  small  metallic  reflector,  which  concentrated  them  upon 
the  bulb  of  a  differential  thermometer.  Berard  observed  that  heat  was 
not  reflected  when  the  plane  of  reflection  of  the  second  mirror  was  at 
right  angles  to  that  of  the  first.  As  this  phenomenon  is  the  same  as  that 
presented  by  light  under  the  same  circumstances,  Berard  concluded  that 
heat  became  polarised  in  being  reflected. 

The  double  refraction  of  heat  may  be  shown  by  concentrating  the  sun's 
rays  by  means  of  a  heliostat  on  a  prism  of  Iceland  spar,  and  investigating 
the  resultant  pencil  by  means  of  a  thermopile,  which  must  have  a  sharp 


-641]  Polarisation  of  Heat.  565 

narrow  edge.  In  this  case  also  there  is  an  ordinary  and  an  extraordinary 
ray,  which  follows  the  same  laws  as  those  of  light.  In  the  optic  axis  of 
the  calcspar,  heat  is  not  doubly  refractive.  A  Nicol's  prism  can  be  used 
for  the  polarisation  of  heat  as  well  as  for  that  of  light  :  a  polarised  ray 
does  not  traverse  the  second  Nicol  if  the  plane  of  its  principal  section  is 
perpendicular  to  the  vibrations  of  the  ray.  The  phenomena  of  the  polar- 
isation of  heat  may  also  be  studied  by  means  of  plates  of  tourmaline 
and  of  mica.  The  angle  of  polarisation  is  virtually  the  same  for  heat  as 
for  light.  In  all  these  experiments  the  prisms  must  be  very  near  each 
other. 

The  diffraction,  and  therefore  the  interference,  of  rays  of  heat  has 
recently  been  established  by  the  experiments  of  Knoblauch  and  others. 
And  Forbes,  who  has  repeated  Fresnel's  experiment  with  a  rhombohedron 
of  rock  salt,  has  found  that  heat  by  two  total  internal  reflections  is  circu- 
larly polarised  just  as  is  the  case  with  light. 


566  On  Magtietism.  [642- 


BOOK  VIII. 

ON    MAGNETISM. 


CHAPTER    I. 
PROPERTIES   OF   MAGNETS. 

642.  Katural  and  artificial  magnets. — Magnets  2iX<s.  substances  which 
have  the  property  of  attracting  iron,  and  the  term  magnetism  is  appHed 
to  the  cause  of  this  attraction,  and  to  the  resulting  phenomena. 

This  property  was  known  to  the  ancients  ;  it  exists  in  the  highest 
degree  in  an  ore  of  iron  which  is  known  in  chemistry  as  the  magnetic 
oxide  of  iron.     Its  composition  is  represented  by  the  formula  Feg  O^. 

This  magnetic  oxide  of  iron,  or  lodestone,  as  it  is  called,  was  first  found 
at  Magnesia,  in  Asia  Minor,  the  name  magnet  being  derived  from  this 
circumstance.  The  name  lodestone,  which  is  applied  to  this  natural 
magnet,  was  given  on  account  of  its  being  used  when  suspended  as  a 
guiding  or  leading  stone,  from  the  Saxon  Icedan,  to  lead ;  so  also  the  word 
lodestar.  Lodestone  is  very  abundant  in  nature  :  it  is  met  with  in  the 
older  geological  formations,  especially  in  Sweden  and  Norway,  where  it 
is  worked  as  an  iron  ore,  and  furnishes  the  best  quality  of  iron. 

When  a  bar  or  needle  of  steel  is  rubbed  with  a  magnet,  it  acquires 
magnetic  properties.  Such  bars  are  called  artificial  inagnets ;  they  are 
more  powerful  than  natural  magnets,  and  as  they  are  also  more  con- 
venient, they  will  be  exclusively  referred  to  in  describing  the  phenomena 
of  magnetism  ;  the  best  modes  of  preparing  them  will  be  explained  in  a 
subsequent  article. 

643.  Poles  and  neutral  line. — When  a  small  particle  of  soft  iron  is 
suspended  by  a  thread,  and  a  magnet  is  approached  to  it,  the  iron  is 
attracted  towards  the  magnet,  and  some  force  is  required  for  its  removal. 
The  force  of  the  attraction  varies  in  different  parts  of  the  magnet  :  it  is 
strongest  at  the  two  ends,  and  is  totally  wanting  in  the  middle. 

This  variation  may  also  be  seen  very  clearly  when  a  magnetic  bar  is 
placed  in  iron  filings  ;  these  become  arranged  round  the  ends  of  the  bar 
in  feathery  tufts,  which  decrease  towards  the  middle  of  the  bar,  where 
there  are  none.  That  part  of  the  surface  of  the  bar  where  there  is  no 
visible  magnetic  force  is  called  the  neuti'al  line  ;  and  the  points  near  the 
ends  of  the  bar  where  the  attraction  is  greatest  are  called  the  poles. 
Every  magnet,  whether  natural  or  artificial,  has  two  poles  and  a  neutral 
line :  sometimes,  however,  in  magnetising  bars  and  needles,  poles  are 


i 


644] 


Properties  of  Magnets. 


567 


produced  lying  between  the  extreme  points.  Such  magnets  are  abnormal, 
and  these  points  are  called  intermediate  or  consequent  potes.  The  shortest 
line  joining  the  two  poles  is  termed  the  axis  of  the  magnet  ;  in  a  horse- 
shoe magnet  the  axis  is  in  the  direction  of  the  keeper.  The  plane  at 
right  angles  to  the  axis  of  a  bar  magnet  and  passing  through  the  neutral 
line  is  sometimes  called  the  equator  of  the  magnet. 

We  shall  presently  see  that  a  freely  suspended  magnet  always  sets 
with  one  pole  pointing  towards  the  north,  and  the  other  towards  the 


Fig.  507. 


south.  The  end  pointing  towards  the  north  is  called  in  this  country  the 
north  pote,  and  the  other  end  is  the  south  pote.  The  end  of  the  magnetic 
needle  pointing  to  the  north  is  also  sometimes  called  the  marked  end  of 
the  needle.  Sometimes  also  the  end  pointing  to  the  north  is  called  the 
red  pole,  and  that  to  the  south,  the  blue  pole  ,  the  corresponding  terms 
red  and  blue  magnetisms  are  also  used. 

644.  Mutual  action  of  two  poles.— The  two  poles  of  a  magnet  appear 
identical  when  they  are  brought  in 
contact  with  iron  filings,  but  this 
identity  is  only  apparent,  for  when  a 
small  magnetic  needle,  ab  (fig.  508),  is 
suspended  by  a  fine  thread,  and  the 
north  pole,  A,  of  another  needle  is 
brought  near  its  north  pole,  a,  a  repul- 
sion takes  place.  If,  on  the  contrary, 
A  is  brought  near  the  south  pole,  b,  of 
the  movable  needle,  the  latter  is 
strongly  attracted.  Hence  these  two 
poles,  a  and  b,  are  not  identical,  for 
one  is  repelled  and  the  other  attracted 
by  the  same  pole  of  the  magnet,  A. 
It  may  be  shown  in  the  same  manner 
that  the  two  poles  of  the  latter  are  also 
different,  by  successively  presenting 
them  to  the  same  pole,  a,  of  the  movable  needle.  In  one  case  there  is 
repulsion,  in  the  other  attraction.  Hence  the  following  law  may  be 
enunciated  : 

Poles  of  the  same  name  repel ^  and  poles  of  contrary  name  attract  one 
another. 

The  opposite  actions  of  the  north  and  south  poles  may  be  shown  by 
the  following  experiment  : — A  piece  of  iron,  a  key  for  example,  is  sup- 
ported by  a  magnetised   bar.     A  second  magnetised  bar  of  the  same 


Fig.   508. 


'568  On  Magnetism.  [644- 

dimensions  is  then  moved  along  the  first,  so  that  their  poles  are  contrary 
(fig.  509).  The  key  remains  suspended  so  long  as  the  two  poles  are  at 
some  distance,  but  when  they  are  sufficiently  near,  the  key  drops,  just  as 
if  the  bar  which  supported  it  had  lost  its  magnetism.     This,  however,  is 


■>.N>^^ 


Fig.  509. 

not  the  case,  for  the  key  would  be  again  supported  if  the  first  magnet  were 
presented  to  it  after  the  removal  of  the  second  bar. 

The  attraction  which  a  magnet  exerts  upon  iron  is  reciprocal,  which  is 
indeed  a  general  principle  of  all  attractions.  It  is  easily  verified  by  pre- 
senting a  mass  of  iron  to  a  movable  magnet,  when  the  latter  is  attracted. 

645.  Hypotbesis  of  two  magrnetic  fluids. — In  order  to  explain  the 
phenomena  of  magnetism,  the  existence  of  two  hypothetical  magnetic 
flicids  has  been  assumed,  each  of  which  acts  repulsively  on  itself,  but 
attracts  the  other  fluid.  The  fluid  predominating  at  the  north  pole  of  the 
magnet  is  called  the  north  fluid  or  red  magnetism,  and  that  at  the  south 
pole,  the  south  fluid  or  blue  magnetism.  The  term  '  fluid '  is  apt  to  puzzle 
beginners,  from  its  ambiguity.  Ordinarily  the  idea  of  a  liquid  is  associated 
with  the  term  a  fluid  ;  hence  the  use  of  this  term  to  explain  the  phenomena 
of  magnetism  and  electricity  has  produced  a  widely  prevailing  impression 
of  the  material  nature  of  these  two  forces.  The  word  fluid,  it  must  be 
remembered,  embraces  gases  as  well  as  liquids,  and  here  it  must  be 
pictured  to  the  mind  as  representing  an  invisible,  elastic,  gaseous  atmo- 
sphere or  shell  surrounding  the  particles  of  all  magnetic  substances. 

It  is  assumed  that,  before  magnetisation,  these  fluids  are  combined 
round  each  molecule,  and  mutually  neutralise  each  other ;  they  can  be 
separated  by  the  influence  of  a  force  greater  than  that  of  their  mutual 
attraction,  and  can  arrange  themselves  round  the  molecules  to  which  they 
are  attached,  but  cannot  be  removed  from  them. 

The  hypothesis  of  the  two  fluids  is  very  convenient  in  explaining  mag- 
netic phenomena,  and  will  be  adhered  to  in  what  follows.  But  it  must  not 
be  regarded  as  anything  more  than  an  hypothesis,  and  it  will  afterwards  be 
shown  (826)  that  magnetic  phenomena  appear  to  result  from  electrical  cur- 
rents, circulating  in  magnetic  bodies ;  a  mode  of  view  which  connects  the 
theory  of  magnetism  with  that  of  electricity. 

646.  Precise  definition  of  poles. — By  the  aid  of  the  preceding  hypo- 
thesis we  are  enabled  to  obtain  a  clearer  idea  of  the  distribution  of  the 
magnetism  in  a  magnetised  bar,  and  to  account  for  the  circumstance  that 
there  is  no  free  magnetism  in  the  middle  of  the  bar,  and  that  it  is  strongest 
at  the  poles.     If  AB  (fig.  5 10)  represent  a  magnet,  then  the  alternate  black 


-646]  Definition  of  Poles.  569 

and  white  spaces  may  be  taken  to  represent  the  position  of  the  magnetic 
fluids  in  a  series  of  particles  after  magnetisation  ;  in  accordance  with  what 
has  been  said,  the  white  spaces,  representing  the  south  fluid,  all  point  in 
one  direction,  and  the  north  fluid  in  the  opposite  direction.     The  last  half 


Fig.  510. 

of  the  terminal  molecule  at  one  end  would  have  north  polarity,  and  at  the 
other  south  polarity.  Let  N  represent  the  north  pole  of  a  magnetic  needle 
placed  near  the  magnet  AB ;  then  the  south  fluid,  j,  in  the  terminal  mole- 
cule would  tend  to  attract  N,  and  the  north  fluid  n  would  tend  to  repel  it ; 
but  as  the  molecule  of  south  fluid  s  is  nearer  N  than  the  molecule  of  north 
fluid  «,  the  attraction  between  j  and  N  would  be  greater  than  the  repulsion 
between  n  and  N.  Similarly  the  attraction  between  s'  and  N  would  be 
greater  than  the  repulsion  between  n'  and  N,and  so  on  with  the  following 
s"  and  n'\  etc.  And  all  these  forces  would  give  a  resultant  tending  to 
attract  N,  whose  point  of  application  would  have  a  certain  fixed  position, 
which  would  be  the  south  pole  of  AB.  In  like  manner  it  might  be  shown 
that  the  resultant  of  the  forces  acting  at  the  other  end  of  the  bar  would 
form  a  north  pole,  and  would  hence  repel  the  north  pole  of  the  needle,  but 
would  attract  its  south  pole. 

That  such  a  series  of  polarised  particles  really  acts  like  an  ordinary 
magnet  may  be  shown  by  partly  filling  a  glass  tube  with  steel  filings,  and 
passing  the  pole  of  a  strong  magnet  several  times  along  the  outside  in 
one  constant  direction,  taking  care  not  to  shake  the  tube.  The  individual 
filings  will  thus  be  magnetised,  and  the  whole  column  of  them  presented 
to  a  magnetic  needle  will  attract  and  repel  its  poles  just  like  an  ordinary 
bar  magnet,  exhibiting  a  north  pole  at  one  end,  a  south  pole  at  the  other, 
and  no  polarity  in  the  middle  ;  but  on  shaking  the  tube,  or  turning  out  the 
filings,  and  putting  them  in  again  so  as  to  destroy  the  regularity,  every 
trace  of  polarity  will  disappear.  It  appears  hence  that  the  polarity  at  each 
end  of  a  magnet  is  caused  by  the  fact  that  the  resultant  action  on  a  mag- 
netic body  is  strongest  near  the  ends,  and  does  not  arise  from  any  accu- 
mulation of  magnetic  fluids  at  the  ends. 

The  same  point  may  be  illustrated  by  the  following  experiment,  which 
is  due  to  Grove.  In  a  glass  tube  with  flat  glass  ends  is  placed  water  in 
which  is  difl"used  magnetic  oxide  of  iron.  Round  the  outside  of  the  tube 
is  coiled  some  insulated  wire.  On  looking  at  a  light  through  the  tube  the 
liquid  appears  dark  and  muddy,  but  on  passing  a  current  of  electricity 
through  the  wire  it  becomes  clearer  (829),  This  is  due  to  the  fact  that 
by  the  magnetising  action  of  the  current,  the  particles  becoming  mag- 
netised, set  with  their  longest  dimension  parallel  to  the  axis  of  the  tube, 
in  which  position  they  obstruct  the  passage  of  light  to  a  less  extent. 


570  On  Magnetism.  [647- 

647.  Experiments  with  broken  niag:nets. — That  the  two  magnetis- 
ing fluids  are  present  in  all  parts  of  the  bar,  and  are  not  simply  accumulated 
at  the  ends,  is  also  evident  from  the  following  experiment.  A  steel 
knitting-needle  is  magnetised  by  friction  with  one  of  the  poles  of  a 
magnet,  and  then,  the  existence  of  the  two  poles  and  of  the  neutral  line 
having  been  ascertained  by  means  of  iron  filings,  it  is  broken  in  the 
middle.  But  now,  on  presenting  successively  the  two  halves  to  a  magnet, 
each  will  be  found  to  possess  two  opposite  poles  and  a  neutral  line,  and 
in  fact  is. a  perfect  magnet.  If  these  new  magnets  are  broken  in  turn  in 
two  halves,  each  will  be  a  complete  magnet  with  its  two  poles  and  neutral 
hne,  and  so  on,  as  far  as  the  division  can  be  continued.  It  is,  therefore, 
concluded  by  analogy  that  the  smallest  parts  of  a  magnet,  the  ultimate 
molecules,  contain  the  two  magnetisms. 

648.  Magrnetic  induction. — When  a  magnetic  substance  is  placed  in 
contact  with  a  magnet,  the  two  fluids  of  the  former  become  separated  ; 
and  so  long  as  the  contact  remains,  it  is  a' complete  magnet,  having  its 
two  poles  and  its  neutral  line.  For  instance,  if  a  small  cylinder  of  soft 
iron  ab  (fig  511),  be  placed  in  contact  with  one  of  the  poles  of  a  magnet, 
the  cyhnder  can  in  turn  support  a  second  cyhnder  ;  this  in  turn  a  third 


J^-> 


Fi-.  5". 


and  so  on,  to  as  many  as  seven  or  eight,  according  to  the  power  of  the 
magnet.  Each  of  these  little  cylinders  is  a  magnet ;  if  it  be  the  north  pole 
of  the  magnet  to  which  the  cylinders  are  attached,  the  part  a  will  have 
south,  and  b  north  magnetism  ;  b  will  in  like  manner  develope  in  the  nearest 
end  of  the  next  cylinder  south  magnetism,  and  so  on.  But  these  cyhnders 
are  only  magnets  so  long  as  the  influence  of  a  magnetised  bar  continues. 
For,  if  the  first  cyhnder  be  removed  from  the  magnet,  the  other  cyhnders 
immediately  drop,  and  retain  no  trace  of  magnetism.  The  separation  of 
the  two  magnetisms  is  only  momentary,  which  proves  that  the  magnet 
yields  nothing  to  the  iron.  Hence  we  may  have  tejuporary  magnets  as 
well  as  permanent  magnets  :  the  former  of  iron  and  nickel,  the  latter  of 
steel  and  cobalt  (643). 

This  action,  in  virtue  of  which  a  magnet  can  develope  magnetism  in 
iron,  is  called  magnetic  mdnction  or  influence,  and  it  can  take  place 
without  actual  contact  between  the  magnet  and  the  iron,  as  is  seen  in  the 
following  experiment.  A  bar  of  soft  iron  is  held  with  one  end  near  a 
magnetic  needle.  If  now  the  north  pole  of  a  magnet  be  approached  to  the 
iron  without  touching  it,  the  needle  will  be  attracted  or  repelled,  accord- 
ing as  its  south  or  north  pole  is  near  the  bar.     For  the  north  pole  of  the 


-650]  Difference  between  Magnets  and  Magnetic  Substances.  571 

magnet  will  develope  south  magnetism  in  the  end  of  the  bar  nearest  it, 
and  therefore  north  magnetism  at  the  other  end,  which  would  thus 
attract  the  south,  but  repel  the  north^end  of  the  needle.  Obviously,  if  the 
other  end  of  the  magnet  were  brought  near  the  iron,  the  opposite  effects 
would  be  produced  on  the  needle ;  or  if  the  opposite  pole  of  a  second 
magnet  of  equal  strength  simultaneously  be  brought  near  the  iron,  the 
needle  would  be  unaffected,  as  one  magnet  would  outdo  the  work  of  the 
other. 

Among  other  things,  magnetic  induction  explains  the  formation  of  the 
tufts  of  iron  filings  which  become  attached  to  the  poles  of  magnets.  The 
parts  in  contact  with  the  magnet  are  converted  into  magnets  ;  these  act 
inductively  on  the  adjacent  parts,  these  again  on  the  following  ones,  and 
so  on  producing  a  filamentary  arrangement  of  the  filings. 

649.  Coercive  force. — We  have  seen  from  the  above  experiments  that 
soft  iron  becomes  instantaneously  magnetised  under  the  influence  of  a 
magnet,  but  that  this  magnetism  is  not  permanent,  and  ceases  when  the 
magnet  is  removed.  Steel  likewise  becomes  magnetised  by  contact  with 
a  magnet,  but  the  operation  is  effected  with  difficulty,  and  the  more  so  as 
the  steel  is  more  highly  tempered.  Placed  in  contact  with  a  magnet,  a 
steel  bar  acquires  magnetic  properties  very  slowly,  and  to  make  the 
magnetism  complete,  the  steel  must  be  rubbed  with  one  of  the  poles. 
But  this  magnetism,  once  evoked  in  steel,  is  permanent,,  and  does  not 
disappear  when  the  inducing  force  is  removed. 

These  different  effects  in  soft  iron  and  steel  are  ascribed  to  a  coercive 
force,  which,  in  a  magnetic  substance,  offers  a  resistance  to  the  separation 
of  the  two  magnetisms,  but  which  also  prevents  their  recom.bination  when 
once  separated.  In  steel  this  coercive  force  is  very  great,  in  soft  iron  it  js 
very  small  or  almost  absent.  By  oxidation,  pressure,  or  torsion,  a  certain 
amount  of  coercive  force  may  be  imparted  to  soft  iron  :  and  by  heat, 
hammering,  etc.,  the  coercive  force  may  be  lessened,  as  will  be  afterwards 
seen. 

650.  Difference  between  magrnets  and  magnetic  substances. — 
Mag7ietic  substances  are  substances  which,  like  iron,  steel,  nickel,  are 
attracted  by  the  magnet.  They  contain  the  two  fluids,  but  in  a  state  of 
neutralisation.  Compounds  containing  iron  are  usually  magnetic,  and 
the  more  so  in  proportion  as  they  contain  a  larger  quantity  of  iron. 
Some,  however,  like  iron  pyrites,  are  not  attracted  by  the  magnet. 

A  magnetic  substance  is  readily  distinguished  from  a  magnet.  The 
former  has  no  poles ;  if  successively  presented  to  the  two  ends  of  a  mag- 
netic needle,  ab  (fig.  508),  it  will  attract  both  ends  equally,  while  a  mag- 
net would  attract  the  one,  but  repel  the  other.  Magnetic  substances 
also  have  no  action  on  each  other,  while  magnets  attract  or  repel  each 
other,  according  as  unhke  or  like  poles  are  presented. 

Iron  is  not  the  only  substance  which  possesses  magnetic  properties ; 
nickel  has  considerable  magnetic  power,  but  far  less  than  that  of  iron ; 
cobalt  is  less  magnetic  than  nickel;  while  to  even  a  slighter  extent 
chromium  and  manganese  are  magnetic.  Further,  we  shall  see  that 
powerful  magnets  exert  a  peculiar  influence  on  all  substances. 


572  On  Magnetism.  [651- 


w- 


A' 


^^^ 


i^'^r 

On  Magnetism. 

v>' 

CHAPTER   II. 

TERRESTRIAL  MAGNETISM.      COMPASSES 

1  651.  Directive  action  of  the  eartb  on  magrnets. — When  a   mag- 

netised needle  is  suspended  by  a  thread,  as  represented  in  fig.  508,  or 
■^    when   placed   on   a   pivot   on   which   it   can   move  freely    (fig.    512),  it 
ultimately  sets  in  a  position  which  is  more  or  less  north  and  south.     If 

removed  from  this  position  it  always  re- 
.' '     turns  to  it  after  a  certain  number  of  oscil- 
lations. 

Analogous    observations    have    been 

made  in  different  parts  of  the  globe,  from 

which  the  earth  has  been  compared  to  an 

S,.-'  )  .  immense   magnet,  whose  poles  are  very 

near  the  terrestrial  poles,  and  whose 
neutral  line  virtually  coincides  with  the 
equator. 

The  polarity  in  the  northern  hemis- 
phere is  called  the  northern  or  boreal 
polarity  and  that  in  the  southern  hemis- 
phere the  southern  or  austral  polarity. 
In  French  works  the  end  of  the  needle  pointing  north  is  called  the  austral 
or  southern  pole,  and  that  pointing  to  the  south,  the  boreal  or  northern 
pole  ;  a  designation  based  on  this  hypothesis  of  a  terrestrial  magnet,  and 
on  the  law  that  unlike  magnetisms  attract  each  other.  In  practice  it  will 
be  found  more  convenient  to  use  the  English  names,  and  call  that  end  of 
the  magnet  which  points  to  the  north  the  north  pole,  and  that  which 
points  to  the  south  the  south  pole.  To  avoid  ambiguity  that  end  of  the 
needle  pointing  north  is  in  England  sometimes  spoken  of  as  the  marked 
end  of  the  needle. 

652.  Terrestrial  magnetic  couple. — From  what  has  been  stated,  it  is 
clear  that  the  magnetic  action  of  the  earth  on  a  magnetised  needle  may 
be  compared  to  a  couple.,  that  is,  to  a  system  of  two  equal  forces,  parallel, 
but  acting  in  contrary  directions. 

For  let  ab  (fig.  513)  be  a  movable  magnetic  needle  making  an  angle 
with  the  magnetic  meridian  MM'  (653).  The  earth's  north  pole  acts 
attractively  on  the  marked  pole,  a,  and  repulsively  on  the  other  pole,  b, 
and  two  contrary  forces  are  produced,  an,  and  bn' ,  which  are  equal  and 
parallel  :  for  the  terrestrial  pole  is  so  distant,  and  the  needle  so  small,  as 
to  justify  the  assumption  that  the  two  directions  an,  and  bn',  are  parallel, 
and  that  the  two  poles  are  equidistant  from  the  earth's  north  pole.  But 
the  earth's  south  pole  acts  similarly  on  the  poles  of  the  needle,  and  pro- 
duces two  other  forces,  as  and  bs',  which  are  also  equal  and  parallel,  but 
the  two  forces  an  and  as  may  be  reduced  to  a  single  resultant  rtN  (33) 
and  the  forces  bn'  and  bs'  to  a  resultant  b^  ;  these  two  forces  ^zN  and  /^S 
are  equal,  parallel,  and  act  in  opposite  directions,  and  they  constitute  the 


-653]  Magnetic  Elements.     Declination.  573 

terrestrial  inagtietic  couple  ;  it  is  this  couple  which  makes  the  needle  set 
ultimately  in  the  magnetic  meridian,  a  position  in  which  the  two  forces 
N  and  S  are  in  equilibrium. 


M 


Fig.  513- 

The  force  which  determines  the  direction  of  the  needle  thus  is  neither 
attractive  nor  repulsive,  but  simply  directive.  If  a  small  magnet  be  placed 
on  a  cork  floating  in  water,  it  will  at  first  oscillate,  and  then  gradually 
set  in  a  line  which  is  virtually  north  and  south.  But  if  the  surface  of  the 
water  be  quite  smooth,  the  needle  will  not  move  either  towards  the  north 
or  towards  the  south. 

If,  however,  a  magnet  be  approached  to  a  floating  needle,  attraction  or 
repulsion  ensues,  according  as  one  or  the  other  of  the  poles  is  presented. 
The  reason  of  the  different  actions  exerted  by  the  earth  and  by  a  magnet 
on  a  floating  needle  is  as  follows  : — When  the  north  pole,  for  instance,  of 
the  magnet  is  presented  to  the  south  pole  of  the  needle,  the  latter  is 
attracted  ;  it  is,  however,  repelled  by  the  south  pole  of  the  magnet.  Now 
the  force  of  magnetic  attraction  or  repulsion  decreases  with  the  distance, 
and  as  the  distance  between  the  south  pole  of  the  needle  and  the  north 
pole  of  the  magnet  is  less  than  the  distance  between  the  south  pole  of  the 
needle  and  the  south  pole  of  the  magnet,  the  attraction  predominates  over 
the  repulsion,  and  the  needle  moves  towards  the  magnet.  But  the  earth's 
magnetic  north  pole  is  so  distant  from  the  floating  needle  that  its  length 
may  be  considered  infinitely  small  in  comparison,  and  one  pole  of  the 
needle  is  just  as  strongly  repelled  as  the  other  is  attracted. 

653.  Mag-netic  elements.  Declination. — In  order  to  obtain  a  full 
knowledge  of  the  earth's  magnetism  at  any  place  three  essentials  are 
requisite,  these  are  :  i.  Declination;  ii.  Inclination;  iii.  Intensity.  These 
three  are  termed  the  magnetic  elements  of  the  place.  We  shall  explain 
them  in  the  order  in  which  they  stand. 

The  geographical  meridian  of  a  place  is  the  imaginary  plane  passing 
through  this  place  and  through  the  two  terrestrial  poles,  and  the  meridian 
is  the  outline  of  this  plane  upon  the  surface  of  the  globe.  Similarly  the 
magnetic  meridian  of  a  place  is  the  vertical  plane  passing  at  this  place 
through  the  two  poles  of  a- movable  magnetic  needle  in  equilibrium  about 
its  vertical  axis. 

In  general  the  magnetic  meridian  does  not  coincide  with  the  geogra- 
phical meridian,  and  the  angle  which  the  magnetic  makes  with  the  geo- 
graphical meridian,  or,  what  is  the  same  thing,  the  angle  which  the  direction 
of  the  needle  makes  with  the  meridian,  is  called  the  declination  or  varia- 
tio7i  of  the  magnetic  needle.     The  declination  is  said  to  be  east  or  wesfy 


574 


On  Magnetism. 


[653 


Year 

Declination 

Year 

1580 

.     I  r°  30'  E. 

1825 

1663 

0 

1830 

1700 

.       8°  10'  W. 

1835 

1780 

.        .     19°  55'  W. 

1850 

1785 

.     22°         W. 

1855 

1805 

.     22°     5'W. 

i860 

1814 

.     22°  34'  W. 

1865 
1874 

according  as  the  north  pole  of  the  needle  is  to  the  east  or  west  of  the 
geographical  meridian. 

654.  Variations  in  declination. — The  declination  of  the  magnetic 
needle,  which  varies  in  dififerent  places,  is  at  present  west  in  Europe  and 
in  Africa,  but  east  in  Asia  and  in  the  greater  part  of  North  and  South 
America.  It  shows  further  considerable  variations  even  in  the  same 
place  ;  these  variations  are  of  two  kinds  ;  some  are  regular,  and  are 
either  secular,  annual,  or  diurnal ;  others,  which  are  irregular,  are  called 
perturbations  or  magnetic  storms. 

Secular  variatiotis.  —  ln  the  same  place,  the  declination  varies  in  the 
course  of  time,  and  the  needle  appears  to  make  oscillations  to  the  east  and 
west  of  the  meridian,  the  duration  of  which  extends  over  centuries.  The 
declination  has  been  known  at  Paris  since  1580,  and  the  following  table 
represents  the  variations  which  it  has  undergone : — 

Declination 
.       22°  22'  W. 
.       22°  12'  W. 
.       22°     4'W. 

.   20°  30'  \^^ 

.  i9°57'W. 

.  19°  32'  w. 

.  i8°44'W. 

.  17°  25    W. 

This  table  shows  that  since  1580  the  declination  has  varied  at  Paris  as 
much  as  34°,  and  that  the  greatest  westerly  declination  was  attained  in 
1 8 14,  since  which  time  the  needle  has  gradually  tended  towards  the  east. 

At  London,  the  needle  showed  in  1580  an  east  declination  of  11°  36'; 
in  1663  it  was  at  zero  ;  from  that  time  it  gradually  tended  towards  the 
west,  and  reached  its  maximum  declination  of  24°  41'  in  1818  ;  since  then 
it  has  steadily  diminished;  it  was  22°  30'  in  1850,  19°  32'  in  1873,  and  is 
now  (1875)  19°  16'  W. 

At  Yarmouth  and  Dover  the  variation  is  about  40'  less  than  at  London; 
at  Hull  and  Southampton  about  20'  greater ;  at  Newcastle  and  Swansea 
about  1°  45',  and  at  Liverpool  2°  o',  at  Edinburgh  3°  o',  and  at  Glasgow 
and  Dublin  about  3°  50',  greater  than  at  London. 

The  following  are  the  observations  of  the  magnetic  elements  at  Kew 
for  the  last  ten  years : — 

Year 

1865  . 

1866  . 

1867  . 

1868  . 

1869  . 

1870  . 

1871  . 

1872  . 

1873  • 

1874  . 


Declination 

Inclination 

Horizontal  Intensity 

•        .     20°  59' 

68°    7' 

3-829 

.     20°  51' 

68°    6' 

3-837 

.     20°  40' 

68°    3' 

3-844 

.        .     20°  33' 

68°    2' 

3-848 

.     20°  25' 

68°     V 

3-852 

.    20°  19' 

67°  58' 

3-857 

.     20°  10' 

67°  57' 

3-863 

.     20°    0' 

67°  54' 

3-869 

.        .     19°  57' 

67°  52' 

3-877 

.        .     19°  52' 

67'  50' 

3-881 

00  w 


-656]  Accidental  Magnetic  Variations,  575 

In  certain  parts  of  the  earth  the  magnet  coincides  with  the  geographical 
meridian.  These  points  are  connected  by  an  irregularly  curved  imaginary 
line,  called  a  line  of  110  variation,  or  agojiic  line.  Such  a  line  cuts  the 
east  of  South  America,  and,  passing  east  of  the  West  Indies,  enters  North 
America  near  Philadelphia,  and  traverses  Hudson's  Bay ;  thence  it  passes 
through  the  North  Pole,  entering  the  Old  World  east  of  the  White  Sea, 
traverses  the  Caspian,  cuts  the  east  of  Arabia,  turns  then  towards  Australia, 
and  passes  through  the  South  Pole,  to  join  itself  again. 

Isogonic  lines  are  lines  connecting  those  places  on  the  earth's  surface 
in  which  the  declination  is  the  same.  The  first  of  the  kind  was  constructed 
in  1700  by  Halley  ;  as  the  elements  of  the  earth's  magnetism  are  continu- 
ally changing,  the  course  of  such  a  line  can  only  be  determined  for  a 
certain  time.  One  of  the  newest  set  of  isogonic  hnes  has  been  constructed 
by  Captain  Evans  for  the  year  1857,  and  is  given  in  the  British  Asso- 
ciation Report  for  i86r. 

Maps  on  which  such  isogonic  lines  are  depicted  are  called  declination 
maps ;  and  a  comparison  of  these  in  various  years  is  well  fitted  to  show 
the  variations  which  this  magnetic  element  undergoes.  Plate  III. 
represents  a  map  in  Mercator's  projection  giving  these  lines  for  the  year 
i860.  It  extends  from  80°  N.  to  60°  S.  latitude,  and  from  the  nature  of 
the  case  cannot  include  both  poles,  for  which  a  map  in  polar  projection 
is  needed.  The  figures  attached  to  the  red  lines  represent  the  observed 
angles  of  declination  ;  the  dotted  red  lines  are  the  result  of  calculation. 

655.  Annual  variations. — Cassini  first  discovered  in  1780  that  the 
declination  is  subject  to  small  annual  variations.  At  Paris  and  London 
it  is  greatest  about  the  vernal  equinox,  diminishes  from  that  time  to  the 
summer  solstice,  and  increases  again  during  the  nine  following  months. 
It  does  not  exceed  from  15^  to  18',  and  it  varies  somewhat  at  different 
epochs. 

The  diurnal  variations  \i^x^  first  discovered  by  Graham  in  1722  ;  they 
can  only  be  observed  by  means  of  long  needles  or  delicate  indicators  such 
as  the  reflection  of  a  ray  of  light  and  very  sensitive  instruments  (664).  In 
this  country  the  north  pole  moves  every  day  from  east  to  west  from  sunrise 
until  one  or  two  o'clock  ;  it  then  tends  towards  the  east,  and  at  about  ten 
o'clock  regains  its  original  position.  During  the  night  the  needle  is  almost 
stationary.  Thus  the  westerly  declination  is  greatest  during  the  warmest 
part  of  the  day. 

At  Paris  the  mean  amplitude  of  the  diurnal  variation  from  April  to 
September  is  from  13' to  15',  and  for  the  other  months  from  8'  to  10'. 
On  some  days  it  amounts  to  25',  and  on  others  does  not  exceed  5'.  The 
greatest  variation  is  not  always  at  the  same  time.  The  amplitude  of  the 
daily  variations  decreases  from  the  poles  towards  the  equator,  where  it  is 
very  feeble.     Thus  in  the  island  of  Rewak  it  never  exceeds  3'  to  4'. 

656.  Accidental  variations  and  perturbations. — The  declination  is 
accidentally  disturbed  in  its  daily  variations  by  many  causes,  such  as 
earthquakes,  the  aurora  borealis,  and  volcanic  eruptions.  The  effect  ot 
the  aurora  is  felt  at  great  distances.  Auroras  which  are  only  visible  in 
the  north  of  Europe  act  on  the  needle  even  in  these  latitudes,  where 


5/6  On  Magnetism.  [656- 

accidental  variations  of  i°  or  2°  have  been  observed.  In  polar  regions  the 
needle  frequently  oscillates  several  degrees ;  its  irregularity  on  the  day 
before  the  aurora  borealis  is  a  presage  of  the  occurrence  of  this  pheno- 
menon. 

Another  remarkable  phenomenon  is  the  simultaneous  occurrence  of 
magnetic  perturbations  in  very  distant  countries.  Thus  Sabine  mentions 
a  magnetic  disturbance  which  was  felt  simultaneously  at  Toronto,  the 
Cape,  Prague,  and  Van  Diemen's  land.  Such  simultaneous  perturbations 
have  received  the  name  of  magnetic  storms. 

657.  Declination  compass. — The  declination  compass  is  an  instrument 
by  which  the  magnetic  declination  of  any  place  may  be  measured  when 
its  astronomical  meridian  is  known.  It  consists  of  a  brass  box,  AB  (fig. 
514),  in  the  bottom  of  which  is  a  graduated  circle,  M.  In  the  centre  is  a 
pivot,  on  which  oscillates  a  very  light  lozenge-shaped  magnetic  wheel,  ab. 


Fig.  514- 


To  the  box  are  attached  two  uprights  supporting  a  horizontal  axis,  X, 
on  which  is  fixed  an  astronomical  telescope,  L,  movable  in  a  vertical 
plane.  The  box  rests  on  a  foot,  P,  about  which  it  can  turn  in  a  horizontal 
plane,  taking  with  it  the  telescope.  A  fixed  circle,  OR,  which  is  called 
the  azitmithal  circle^  serves  to  measure  the  number  of  degrees  through 
which  the  telescope  has  been  turned,  by  means  of  a  vernier,  V,  fixed  to 
the  box.     The  inclination  of  the  telescope,  in  reference  to  the  horizon, 


-659] 


Mariner's  Compass. 


S77 


> 


may  be  measured  by  another  vernier,  K,  which  moves  with  the  axis  of  the 
telescope,  and  is  read  off  on  a  fixed  graduated  arc,  x. 

The  first  thing  in  determining  the  decHnation  is  to  adjust  the  compass 
horizontally  by  means  of  the  screws,  SS,  and  the  level,  Ji.  The  astro- 
nomical meridian  is  then  found  either  by  an  observation  of  the  sun  at 
noon  exactly,  or  by  any  of  the  ready  methods  known  to  astronomers.  The 
box,  AB,  is  then  turned  until  the  telescope  is  in  the  plane  of  the  astro- 
nomical meridian.  The  angle  made  by  the  magnetic  needle  with  the 
diameter,  N,  which  corresponds  with  the  zero  of  the  scale,  and  is  exactly 
in  the  plane  of  the  telescope,  is  then  read  off  on  the  graduated  limb,  and 
this  is  east  or  west,  according  as  the  pole,  a,  of  the  needle  stops  at  the 
east  or  west  of  the  diameter,  N.  <^ 

658.  Correction  of  errors. — These  indications  of  the  compass  are 
only  correct  when  the  magnetic  axis  of  the  needle,  that  is,  the  right  line 
passing  through  the  two  poles,  coincides  with  its  axis  of  figure,  or  the  hne 
connecting  its  two  ends.  This  is  not  usually  the  case,  and  a  correction 
must  therefore  be  made,  which  is  done  by  the  method  of  7-eversion.  For 
this  purpose  the  needle  is  not  fixed  in  the  cap,  but  merely  rests  on  it,  so 
that  it  can  be  removed  and  its  positions  reversed  ;  thus  what  was  before 
the  lower  is  now  the  upper  face.  The  mean  between  the  observations 
made  in  the  two  cases  gives  the  true  declination. 

For,  let  NS  be  the  astronomical  meridian,  ab  the  axis  of  figure  of  the 
needle,  and  inn  its  magnetic  axis  (fig.  515).     The  true  dechnation  is  not 


the  arc  N^;  but  the  arc  N;;z,  which  is  greater.  If  now  the  needle  be 
turned,  the  line  mn  makes  the  same  angle  with  the  meridian  NS  ;  but 
the  north  end  of  the  needle  which  was  on  the  right  of  nui  is  now  on  the 
left  (fig.  516),  so  that  the  declination  which  was  previously  too  small  by  a 
certain  amount;  is  now  too  large  by  the  same  amount.  Hence  the  true 
declination  is  given  by  the  mean  of  these  two  observations. 

659.  Mariner's  compass. — The  magnetic  action  of  the  earth  has 
received  a  most  important  application  in  the  fnariner's  compass.  This  is 
a  declination  compass  used  in  guiding  the  course  of  a  ship.  Figure  517 
represents  a  view  of  the  whole,  and  figure  518  a  vertical  section.     It  con- 

C  C 


578 


On  Magnetism. 


[659- 


sists  of  a  cylindrical  case,  which  to  keep  the  compass  in  a  horizontal 
position  in  spite  of  the  rolling  of  the  vessel,  is  supported  on  gimbals. 
These  are  two  concentric  rings,  one  of  which,  attached  to  the  case  itself. 


moves  about  the  axis  cd,  which  plays  in  the  outer  ring  AB,  and  this  moves 
in  the  supports  PQ,  about  the  axis  mil  at  right  angles  to  the  first. 

In  the  bottom  of  the  box  is  a  pivot,  on  which  is  placed  by  means  of  an 
agate  cap,  a  magnetic  bar  ab^  which  is  the  needle  of  the  compass.  On 
this  is  fixed  a  disc  of  mica,  a  little  larger  than  the  length  of  the  needle, 


Fig.  51S. 


on  which  is  traced  a  star  or  rose  with  thirty-two  branches,  making  the 
eight  points  or  rhumbs  of  the  wind,  the  demi-rhumbs  and  the  quarters. 
The  branch  ending  in  a  small  star  and  called  N,  corresponds  to  the  bar 
abj  which  is  underneath  the  disc. 

The  compass  is  placed  near  the  stern  of  the  vessel  in  the  bifuiade. 
Knowing  the  direction  of  the  compass  in  which  the  ship  is  to  be  steered, 
the  pilot  has  the  rudder  turned  till  the  direction  coincides  with  the  sight 
vane  passing  through  a  line  d  marked  on  the  inside  of  the  box,  and 
parallel  with  the  keel  of  the  vessel. 

Neither  the  inventor  of  the  compass,  nor  the  exact  time  of  its  invention, 
is  known.  Guyot  de  Provins,  a  French  poet  of  the  twelfth  century,  first 
mentions  the  use  of  the  magnet  in  navigation,  though  it  is  probable  that 
the  Chinese  long  before  this  had  used  it.     The  ancient  navigators,  who 


-660]  Magnetic  Inclinatioji.  579 

were  unacquainted  with  the  compass,  had  only  the  sun  or  pole  star  as  a 
guide,  and  were  accordingly  compelled  to  keep  constantly  in  sight  of  land 
for  fear  of  steering  in  a  wrong  direction  when  the  sky  was  clouded. 

660.  Inclination.  XVKagrnetic  equator. — It  might  be  supposed  from 
the  northerly  direction  which  the  magnetic  needle  takes,  that  the  force 
acting  upon  it  is  situated  in  a  point  of  the  horizon ;  this  is  not  the  case,, 
for  if  the  needle  be  so  arranged  that  it  can  move  freely  in  a  vertical  plane 
about  a  horizontal  axis,  it  will  be  seen  that,  although  the  centre  of  gravity 
of  the  needle  coincides  with  the  centre  of  suspension,  the  north  pole  ir 
our  hemisphere  dips  downwards.  In  the  other  hemisphere  the  south 
pole  is  inclined  downwards. 

The  angle  which  the  magnetic  needle  makes  with  the  horizon,  when 
the  vertical  plane,  in  which  it  moves,  coincides  with  the  magnetic 
meridian,  is  called  the  inclijiation  or  dip  of  the  needle.     In  any  other 


Fig.  519. 

plane  than  the  magnetic  meridian,  the  inclination  increases^  and  is  90°  in 
a  plane  at  right  angles  to  the  magnetic  meridian.  For  the  magnetic 
inclination  is  the  resultant  of  two  forces,  one  acting  in  a  horizontal  and 
the  other  in  a  vertical  plane.  When  the  needle  is  moved  so  that  it  is  at 
right  angles  to  the  magnetic  meridian,  the  horizontal  component  can  only 
act  in  the  direction  of  the  axis  of  suspension,  and,  therefore,  cannot  affect 
the  needle,  which  is  then  solely  influenced  by  the  vertical  component, 
and  stands  vertically.  The  following  considerations  will  make  this 
clearer : — 

Let  NS  (fig.  519)  represent  a  magnetic  needle  capable  of  moving  in  a 
vertical  plane.  Let  NT  represent  in  direction  and  intensity  the  entire 
force  of  the  earth's  magnetism  acting  on  the  pole  N.  Then  NT  can  be 
resolved  into  the  forces  N/^  and  NV  ;  TN/^  being  the  angle  of  inclination 
or  dip. 

1\^T  is  termed  the  total  force,  and  its  components  are 

N/^,  or  the  horizontal  force,  and 

NV,  or  the  vertical  force. 

Now,  it  is  clear  that  the  greater  the  angle  of  dip,  TN/^,  the  less  becomes 
N//,  or  the  horizontal  force,  and  the  greater  NV,  or  the  vertical  force. 
Hence,  in  high  latitudes  the  directive  force  of  a  compass,  which  depends 
on  the  horizontal  force,  is  less  than  in  low  latitudes.  At  the  magnetic 
poles  the  horizontal  force  will  be  nil,  and  the  vertical  force  a  maximum ; 
here,  therefore,  the  needle  will  be  vertical.  At  the  magnetic  equator  the 
reverse  is  the  case,  and  the  needle  will  be  horizontal.  Hence,  the 
oscillations  of  a  compass  needle,  by  which,  as  will  presently  be  explained, 

c  c  2 


58o  On  Magnetism.  [660- 

the  strength  of  the  earth's  magnetism  is  measured,  become  fewer  and 
fewer  in  a  given  time  as  the  magnetic  poles  are  approached,  although 
there  is  really  an  increase  in  the  total  force  of  the  earth. 

Again,  the  reason  why  a  dipping-needle  stands  vertical  when  placed  E. 
and  W.  is  clearly  because  in  those  positions  the  horizontal  force  now 
acting  at  right  angles  to  the  plane  of  motion  of  the  needle  is  ineffectual  to 
move  it,  and  therefore  merely  produces  a  pressure  on  the  pivot  which 
supports  the  needle.  But  the  vertical  component  of  the  total  force 
remains  unaffected  by  the  new  position  of  the  needle.  Acting,  therefore, 
entirely  alone  when  the  dipping-needle  is  exactly  E.  and  W.,  this  vertical 
component  drags  the  needle  into  a  line  with  itself,  that  is  90°  from  the 
horizontal  plane. 

The  value  of  the  dip,  like  that  of  the  declination,  differs  in  different 
localities.  It  is  greatest  in  the  polar  regions,  and  decreases  with  the 
latitude  to  the  equator,  where  it  is  approximately  zero.  In  London  at 
the  present  time,  1875,  the  dip  is  67°  42',  reckoning  from  the  horizontal 
line.  In  the  southern  hemisphere  the  inclination  is  again  seen,  but  in  a 
contrary  direction,  that  is,  the  south  pole  of  the  needle  dips  below 
the  horizontal  line. 

The  inag7ietic  poles  are  those  places  in  which  the  dipping-needle  stands 
vertical,  that  is,  where  the  inclination  is  90°.  In  1830  the  first  of  these, 
the  terrestrial  north  pole,  was  found  by  Sir  James  Ross  in  96°  43'  west 
longitude  and  70°  north  latitude.  The  same  observer  found  in  the  South 
Sea,  in  76°  south  latitude  and  168°  east  longitude,  that  the  inclination  was 
88°  37^  From  this  and  other  observations,  it  has  been  calculated  that 
the  position  of  the  magnetic  south  pole  was  at  that  time  in  about  1 54° 
east  longitude  and  75^°  south  latitude. 

The  line  of  no  declination  passes  through  these  poles,  and  the  lines  of 
equal  declination  converge  towards  them. 

The  magnetic  equator  or  aclinic  line  is  the  line  which  joins  all  those 
places  on  the  earth  where  there  is  no  dip,  that  is,  all  those  in  which  the 
dipping-needle  is  quite  horizontal.  It  is  a  somewhat  sinuous  hne,  not 
differing  much  from  a  great  circle  inclined  to  the  equator  at  an  angle  of 
12°,  and  cutting  it  in  two  points  almost  exactly  opposite  each  other,  one 
in  the  Atlantic  and  one  in  the  Pacific.  These  points  appear  to  be 
gradually  moving  their  position  and  travelling  from  east  to  west. 

Lines  connecting  places  in  which  the  dipping-needle  makes  equal 
angles  are  called   isocli7iic  lines. 

Plate  IV.  is  an  inclination  map  for  the  year  i860,  the  construction  of 
which  is  quite  analogous  to  that  of  the  map  of  declination. 

The  incHnation  is  subject  to  secular  variations,  like  the  dechnation ,  as 
is  readily  seen  from  a  comparison  of  maps  of  inclination  for  different  epochs. 
At  Paris,  in  167 1,  the  inclination  was  75°;  since  then  it  has  been  continually 
decreasing,  in  1835  it  was  67°  14' ;  in  1849  67°  ;  in  1859  66°  14' ;  and  in 
1874  65°  23^ 

The  following  table  gives  the  alterations  in  the  inclination  at  London, 
from  which  it  will  be  seen  that  since  1723,  in  which  it  was  at  its  maximum, 
it  has  continually  diminished  by  about  2°  6'  in  a  year. 


-661] 


Inclination  Compass. 


581 


Year 

Inclination 

Year 

Inclination 

1576 

.        7i°5o'    . 

1800 

•        .         70°  35' 

1600 

.        72° 

182I 

70°  31' 

1676          . 

.        73°  30'    . 

1828 

.        .         69°  47' 

1723          . 

.        74°  42'    . 

1838 

.         69°  17' 

1773          . 

•        72°  19'    . 

•           1854 

68°  31' 

1780 

72°  8'      . 

.           1859 

68°  21' 

1790          . 

.         71°  33'    . 

.           1874 

67°  43' 

661.  Inclination  compass. — An  inclination  compass  is  an  instrument 
for  measuring  the  magnetic  inclination  or  dip.  It  consists  of  a  graduated 
horizontal  brass  circle,  in  (fig.  520),  supported  on  three  legs,  provided  with 


Fig.  520. 

levelling  screws.  Above  this  circle  there  is  a  plate,  A,  movable  about  a 
vertical  axis,  and  supporting,  by  means  of  two  columns,  a  second  graduated 
circle,  M,  which  measures  the  inclination.  The  needle  rests  on  a  frame, 
r,  and  the  diameter  passing  through  the  two  zeros  of  the  circle,  M,  can 
be  ascertained  to  be  perfectly  horizontal  by  means  of  the  spirit  level,  n. 

To  observe  the  inclination,  the  magnetic  meridian  must  first  be  deter- 
mined, which  is  effected  by  turning  the  plate  A  on  the  circle  ?;z,  until  the 
needle  is  vertical,  which  is  the  case  when  it  is  in  a  plane  at  right  angles 
to  the  magnetic  meridian  (660).  The  plate  A  is  then  turned  90°  on  the 
circle  ;-^,  by  which  the  vertical  circle,  M,  is  brought  into  the  magnetic 
meridian.  The  angle,  dca,  which  the  magnetic  needle  makes  with  the 
horizontal  diameter  is  the  angle  of  inclination. 

There  are  here  several  sources  of  error,  which  must  be  allowed  for. 


582  On  Magnetism.        •  [661- 

The  most  important  are  three  : — i.  The  magnetic  axis  of  the  needle  may 
not  coincide  with  its  axis  of  figure  :  hence  an  error,  which  is  corrected  by 
a  method  of  reversion  analogous  to  that  already  described  (658).  ii.  The 
centre  of  gravity  of  the  needle  may  not  coincide  with  the  axis  of  suspen- 
sion, and  then  the  angle,  dca^  is  too  great  or  too  small,  according  as  the 
centre  of  gravity  is  below  or  above  the  centre  of  suspension ;  for  in  the 
first  case  the  action  of  gravity  is  in  the  same  direction  as  that  of  mag- 
netism, and  in  the  second  is  in  the  opposite  direction.  To  correct  this 
error,  the  poles  of  the  needle  must  be  reversed  by  first  demagnetising  it, 
and  then  imparting  a  contrary  magnetism  to  what  it  had  at  first.  The 
inchnation  is  now  redetermined,  and  the  mean  taken  of  the  results  ob- 
tained in  the  two  groups  of  operations,  iii.  The  plane  of  the  ring  m.ay 
not  coincide  with  the  true  magnetic  meridian.  It  should  be  in  that  plane 
when  the  needle  has  its  minimum  deviation;  an  observation  of  this  kind 
should  therefore  be  taken  along  with  that  previously  described,  by  which 
the  needle  is  moved  90°  from  its  maximum  deviation. 

662.  Astatic  needle  and  astatic  system. — An  astatic  needle  is  one 
which  is  uninfluenced  by  the  earth's  magnetism.  A  needle  movable 
about  an  axis  in  the  plane  of  the  magnetic  meridian  and  parallel  to  the 

inchnation  would  be  one  of  this  kind;  for  the 
terrestrial  magnetic  couple  acting  then  in  the 
direction  of  the  axis  cannot  impart  to  the 
needle  any  determinate  direction. 

An  astatic  system  is  a  combination  of  two 
needles  of  the  same  force  joined  parallel  to 
each  other  with  the  poles  in  contrary  direc- 
tions, as  shown  in  fig.  521.  If  the  two 
needles  have  exactly  the  same  magnetic 
force,  the  opposite  action  of  the  earth's 
magnetism  on  the  poles  a'  and  b  and  on 
Fig.  521.  the  poles  a  and  b'  counterbalance  each  other ; 

the   system  is  then   completely  astatic,  and 
sets  at  right  angles  to  the  magnetic  meridian. 

A  single  magnetic  needle  may  also  be  rendered  astatic  by  placing  a 
magnet  near  it.  By  repeated  trials  a  certain  position  and  distance  can  be 
found  at  which  the  action  of  the  magnet  on  the  needle  just  neutralises  that 
of  the  earth's  magnetism,  and  the  needle  is  free  to  obey  any  third  force. 

663.  Intensity  of  the  eartb's  magrnetism. — If  a  magnetic  needle  be 
moved  from  its  position  of  equilibrium,  it  will  revert  to  it  after  a  series  of 
oscillations,  which  follow  laws  analogous  to  those  of  the  pendulum  {^']). 
If  the  magnet  be  removed  to  another  place,  and  caused  to  oscillate  during 
the  same  length  of  time  as  the  first,  a  difl"erent  number  of  oscillations  will 
be  observed.  And  the  intensity  of  the  earth's  magnetism  in  the  two 
places  will  be  respectively  proportional  to  the  squares  of  the  number  of 
oscillations. 

If  at  M  the  number  of  oscillations  in  a  minute  had  been  25  =;/,  and  at 
another  place,  M^,  24  =  ?/',  we  should  have — 

Intensity  of  the  earth's  magnetism  at  M  _  ^^^_625_    .  0 
Intensity  of  the  earth's  magnetism  at  M'  ~  n^^     576  ~ 


-663] 


Magnetic  Intensity, 


583 


That  is,  if  the  intensity  of  the  magnetism  at  the  second  place  is  taken  as 
unity,  that  of  the  first  is  i"o85.  If  the  magnetic  condition  of  the  needle 
had  not  changed  in  the  interval  between  the  two  observations,  this 
method  would  give  the  relation  between  the  intensities  at  the  two  places. 
In  these  determinations  of  the  intensity,  it  would  be  necessary  to  have 
the  oscillations  of  the  dipping-needle,  which  are  produced  by  the  whole 
force  of  the  earth's  magnetism.  These,  however,  are  difficult  to  obtain 
with  accuracy,  and,  therefore,  the  oscillations  of  the  declina- 
tion needle  are  usually  taken.  The  force  which  makes  the 
declination  needle  oscillate  is  only  a  portion  of  the  total 
magnetic  force,  and  is  smaller  in  proportion  as  the  inclina- 
tion is  greater.  If  the  line  ac  (fig.  522)  =  M  represents  the 
total  intensity,  the  angle  i  the  inclination,  then  the  horizontal 
component  ab  is  M  cos  i.  Hence  to  express  the  intensities 
in  the  two  places  by  the  oscillations  of  the  declination  needle, 
we  must  substitute  in  the  preceding  equation  the  values  M 
cos  /  and  M'  cos  i'  for  M  and  M',  and  we  have — 


Fig.  522. 


M   cos  i 


TV*/ v-'-^J  smce  — 

M'  cos  I      n^  M 


M      n^  cos  i' 


n''^  cos  i 


That  is  to  say,  having  observed  in  two  different  places  tTie  number  of 
oscillations,  n  and  7i\  that  the  same  needle  makes  in  the  same  time,  the 
ratio  of  the  magnetic  force  in  the  two  places  will  be  found  by  multiplying 
the  ratio  of  the  square  of  the  number  of  oscillations  by  the  inverse  ratio 
of  the  cosine  of  the  angle  of  dip. 

The  magnetic  intensity  increases  with  the  latitude.  Humboldt  found  a 
point  of  minimum  intensity  on  the  magnetic  equator  in  Northern  Peru. 
In  the  following  table  this  has  been  taken  as  the  standard  to  which 
the  magnetic  intensities  of  the  other  places  specified  is  referred: — 


Locality 

St.  Anthony 

Carthagena 

Naples     . 

Paris 

Berlin      . 

Petersburg 

Spitzbergen 


Date 

Latitude 

1802 

o-o° 

1 801 

10*25  N. 

1805 

40-50 

1800 

48-52 

1829 

52-51 

1828 

59-66 

1823 

79-40 

Magnetic 
Intensity 

1-087 

1-294 

1-274 
1-348 
1-366 
I -410 
1-567 


According  to  Gauss  the  total  magnetic  action  of  the  earth  is  the  same 
as  that  which  would  be  exerted  if  in  each  cubic  yard  there  w^re  eight  bar 
magnets  each  weighing  a  pound. 

The  lines  connecting  places  of  equal  intensify  are  called  isodynaniic 
tines.  They  are  not  parallel  to  the  magnetic  equator,  but  appear  to  have 
about  the  same  direction  as  the  isothermal  hues. 

According  to  Kuppfer,  the  intensity  appears  to  diminish  at  greater 
heights ;  a  needle  which  made  one  oscillation  in  24"  vibrated  more  slowly 
by  0-0 1 ^'  at  a  height  of  1,000  feet:  but,  according  to  Forbes,  the  intensity 
is  only  ^^-^^  less  at  a  height  of  3,000  feet.     There  is  however,  some  doubt 


584  '  On  Magnetism.  [663- 

as  to  the  accuracy  of  these  observations,  owing  to  the  uncertainty  of  the 
correction  for  temperature. 

The  intensity  varies  in  the  same  place  with  the  time  of  day;  it  attains 
its  maximum  between  4  and  5  in  the  afternoon,  and  is  at  its  minimum 
between  10  and  1 1  in  the  morning. 

It  is  probable,  though  it  has  not  yet  been  ascertained  with  certainty, 
that  the  intensity  undergoes  secular  variations.  From  measurements 
made  at  Kew,  it  appears  that,  on  the  whole,  the  total  force  experiences  a 
very  slight  annual  increase. 

664.  Mag-netic  observatories. — During  the  last  few  years  great 
attention  has  been  devoted  to  the  observation  of  the  magnetic  elements, 
and  observatories  for  this  purpose  have  been  fitted  up  in  different  parts 
of  the  globe.  These  observations  have  led  to  the  discovery  that  the 
magnetism  of  the  earth  is  in  a  state  of  constant  fluctuation,  like  the 
waves  of  the  sea.  And  in  studying  the  variations  of  the  dechnation,  etc., 
the  mean  of  a  great  number  of  observations  must  be  taken,  so  as  to 
eliminate  the  irregular  disturbances,  and  bring  out  the  general  laws. 

The  principle  on  which  magnetic  observations  are  automatically 
recorded  is  as  follows.  Suppose  that  in  a  dark  room  a  bar  magnet  is 
suspended  horizontally,  and  at  its  centre  is  a  small  mirror  ;  suppose 
further  that  a  lamp  sends  a  ray  of  light  to  this  mirror,  the  inclination  of 
which,  is  such,  that  the  ray  is  reflected  and  is  received  on  a  horizontal 
drum  placed  underneath  the  lamp.  The  axis  of  the  drum  is  at  right 
angles  to  the  axis  of  the  magnet ;  it  is  covered  with  sensitive  photographic 
paper,  and  is  rotated  uniformly  by  clockwork. 

If  now  the  magnet  is  quite  stationary,  and  the  drum  rotates,  the 
reflected  spot  of  light  will  trace  a  straight  line  on  the  paper  with  which 
the  revolving  drum  is  covered.  But  if,  as  is  always  the  case,  the  position 
of  the  magnet  varies  during  the  twenty-four  hours,  the  effect  will  be  to  trace 
a  sinuous  line  on  the  paper.  These  lines  can  afterwards  be  fixed  by  the 
ordinary  photographic  methods. 

Knowing  the  distance  of  the  mirror  from  the  drum,  and  the  length  of 
the  paper  band  which  comes  under  the  influence  of  the  spot  of  light  in  a 
given  time,  twenty-four  hours  for  instance,  the  angular  deflection  at  any 
given  moment  may  be  deduced  by  a  simple  calculation  (491). 

The  observations  made  in  the  English  magnetic  observatories  have  been 
reduced  by  Sabine,  and  have  revealed  some  curious  facts  in  reference  to 
the  magnetic  storms.  He  finds  that  there  is  a  certain  periodicity  in  their 
appearance  and  that  they  attain  their  greatest  frequency  about  every  ten 
years.  Independently  of  this,  Schwabe,  a  German  astronomer,  who  had 
studied  the  subject  many  years,  has  found  that  the  spots  on  the  sun,  seen 
on  looking  at  it  through  a  coloured  glass,  vary  in  their  number,  size,  and 
frequency,  but  attain  their  maximum  between  every  ten  or  eleven  years. 
Now  Sabine  has  established  the  interesting  fact  that  the  period  of  their 
greatest  frequency  coincides  with  the  period  of  greatest  magnetic  disturb- 
ance. Other  remarkable  connections  between  the  sun  and  terrestrial 
magnetism  have  been  observed  ;  one,  especially,  of  recent  occurrence  has 
attracted  considerable  attention.     It  was  the  flight  of  a  large  luminous 


-666] 


Laws  of  Magnetic  Attraction. 


585 


mass  across  a  vast  sun  spot,  while  a  simultaneous  perturbation  of  the 
magnetic  needle  was  observed  in  the  observatory  at  Kew ;  subsequent 
examination  of  magnetic  observations  in  various  parts  of  the  world 
showed  that  within  a  few  hours  one  of  the  most  violent  magnetic  storms 
ever  known  had  prevailed. 

Magnetic  storms  are  nearly  always  accompanied  by  the  exhibition  of 
the  aurora  borealis  in  high  latitudes ;  that  this  is  not  universal  may  be 
due  to  the  fact  that  many  auroras  escape  notice.  The  converse  of  this  is 
true,  that  no  great  display  of  the  aurora  takes  place  without  a  violent 
magnetic  storm. 


CHAPTER    III. 


LAWS  OF   MAGNETIC  ATTRACTIONS  AND   REPULSIONS. 

665.  Ziaw  of  decrease  with  distance.—  Coulomb  discovered  the  re- 
markable law  in  reference  to  magnetism,  that  magnetic  attractio7is  and 
repulsions  are  iiivet'sely  as  the  squares  of  the  distances.  He  proved  this  by 
means  of  two  methods  : — (i.)  that  of  the  torsion  balance,  and  (ii.)  that  of 
oscillation. 

666.  i.  The  torsion  balance. — This  apparatus  depends  on  the  prin- 
ciple that,  when  a  wire  is  twisted  through  a  certain  space,  the  angle  of 
torsion   is   proportional   to    the 
force  of  torsion  (86).     It  consists  ii/f  f  d 
(fig.  523)  of  a  glass  case  closed 
by  a  glass  top,  with  an  aperture 
near  the  edge,  to  allow  the  in- 
troduction of  a  magnet,  A.     In 
another  aperture   in  the  centre 
of   the   top    a  glass   tube   fits, 
provided  at  its  upper  extremity 
with  a  micrometer.     This  con- 
sists of  two  circular  pieces  :  d^ 
which  is  fixed,  is  divided  on  the 
edge  into  360°,  while  on  one  e, 
which   is  movable,   there   is   a 
mark,  c,  to  indicate  its  rotation. 
D    and    E    represent    the   two 
pieces  of  the  micrometer  on  a 
larger  scale.     On   E  there   are 
two   uprights    connected    by   a 
horizontal  axis,  on   which  is  a 
very  fine  silver  wire  supporting  a  magnetic  needle,  ab.     On  the  side  of 
the  case  there  is  a  graduated  scale,  which  indicates  the  angle  of  the 
needle  ab,  and  hence  the  torsion  of  the  wire. 

When  the  mark  c  of  the  disc  E  is  at  zero  of  the  scale,  D,  the  case  is 
so  arranged  that  the  wire  supporting  the  needle  and  the  zero  of  the  scale 

CC3 


ig-  523- 


586  On  Magnetism.  [666- 

in  the  case  are  in  the  magnetic  meridian.  The  needle  is  then  removed 
from  its  stirrup,  and  replaced  by  an  exactly  similar  one  of  copper,  or  any 
unmagnetic  substance ;  the  tube,  and  with  it  the  pieces  D  and  E,  are 
then  turned  so  that  the  needle  stops  at  zero  of  tjie  graduation.  The 
magnetic  needle,  ab,  being  now  replaced,  is  exactly  in  the  magnetic 
meridian,  and  the  wire  exerts  no  torsion. 

Before  introducing  the  magnet,  A,  it  is  necessary  to  investigate  the 
action  of  the  earth's  magnetism  on  the  needle  ab,  when  the  latter  is  re- 
moved out  of  the  magnetic  meridian.  This  will  vary  with  the  dimensions 
and  force  of  the  needle,  with  the  dimensions  and  nature  of  the  particular 
wire  used,  and  with  the  intensity  of  the  earth's  magnetism  in  the  place  of 
observation.  Accordingl)^,  the  piece  E  is  turned  until  ab  makes  a  certain 
angle  with  the  magnetic  meridian.  Coulomb  found  in  his  experiments 
that  E  had  to  be  turned  35°  in  order  to  move  the  needle  through  1°;  that 
is,  the  earth's  magnetism  was  equal  to  a  torsion  of  the  wire  corresponding 
to  35°.  As  the  force  of  torsion  is  proportional  to  the  angle  of  torsion,  when 
the  needle  is  deflected  from  the  meridian  by  2,  3  .  .  .  degrees,  the 
directive  ;.ction  of  the  earth's  magnetism  is  equal  2,  3  .  .  .  times  35°. 

The  action  of  the  earth's  magnetism  having  been  determined,  the 
magnet  A  is  placed  in  the  case  so  that  similar  poles  are  opposite  each 
other.  In  one  experiment  Coulomb  found  that  the  pole  a  was  repelled 
through  24°.  Now  the  force  which  tended  to  bring  the  needle  into  the 
magnetic  meridian  was  represented  by  24°  +  24  x  35  =  864,  of  which  the 
part  24°  was  due  to  the  torsion  of  the  wire,  and  24  x  35°  was  the  equiva- 
lent in  torsion  of  the  directive  force  of  the  earth's  magnetism.  As  the 
needle  was  in  equilibrium,  it  is  clear  that  the  repulsive  force  which  coun- 
terbalanced those  forces  must  be  equal  to  864°.  The  disc  was  then 
turned  until  ab  made  an  angle  of  12°.  To  effect  this,  eight  complete 
rotations  of  the  disc  were  necessary.  The  total  force  which  now  tended 
to  bring  the  needle  into  the  magnetic  meridian  was  composed  of: — ist, 
the  12°  of  torsion  by  which  the  needle  was  distant  from  its  starting  point; 
2nd,  of  8  X  360°  =  2,b8o,  the  torsion  of  the  wire ;  and,  3rd,  the  force  of  the 
earth's  magnetism,  represented  by  a  torsion  of  12x35°.  Hence,  the 
forces  of  torsion  which  balance  the  repulsive  forces  exerted  at  a  distance 
of  24°  and  of  1 2°  are— 

24° 864 

12° 3312 

Now,  3;3i2  is  very  nearly  four  times  864;  hence,  for  half  the  distance 
the  repulsive  force  is  four  times  as  great. 

667.  ii.  l«etliod  of  oscillations. — A  magnetic  needle  oscillating 
under  the  influence '  of  the  earth's  magnetism  may  be  considered  as  a 
pendulum,  and  the  laws  of  pendulum  motion  apply  to  it.  The  method  of 
oscillations  consists  in  causing  a  magnetic  needle  to  oscillate  first  under 
the  influence  of  the  earth's  magnetism  alone,  and  then  successively  under 
the  combined  influence  of  the  earth's  magnetism,  and  of  a  magnet  placed 
at  unequal  distances. 

The  following  determination  by  Coulomb  will  illustrate  the  use  of  the 


-668]  Magnetic  Curves.  587 

method.  A  magnetic  needle  was  used  which  made  15  oscillations  m  a 
minute  under  the  influence  of  the  earth's  magnetism  alone.  A  magnetic 
bar  about  2  feet  long  was  then  placed  vertically  in  the  plane  of  the  mag- 
netic meridian,  so  that  its  north  pole  was  downwards  and  its  south  pole 
presented  to  the  north  pole  of  the  oscillating  needle.  He  found  that  at 
a  distance  of  4  inches  the  needle  made  41  oscillations  in  a  minute,  and  at 
a  distance  of  8  inches  24  oscillations.  Now,  from  the  laws  of  the  pen- 
dulum (51),  the  intensity  of  the  forces  are  inversely  as  the  squares  of  the 
times  of  oscillations.  Hence,  if  we  call  M  the  force  of  the  earth's  mag- 
netism, tn  the  attractive  force  of  the  magnet  at  the  distance  of  4  inches, 
ni'  at  the  distance  of  8  inches,  we  have 

M  :  M  +  ?«  =  15^  :  41-,  and 

M  :  M  +  w'  =  15-  :  24-', 
eliminating  M 

in  :  m'  =  ^\^-  15'  :  24- -152=  1456  :  351 

=  4:1  nearly, 
or  ni  :  ;«'  =  4  :  i. 

In  other  words,  the  force  acting  at  4  inches  is  quadruple  that  which 
acts  at  double  the  distance. 

The  above  results  do  not  quite  agree  with  the  numbers  required  by  the 
law  of  inverse  squares.  But  this  could  only  be  expected  to  apply  in  the 
case  in  which  the  repulsive  or  attractive  force  is  exerted  between  two 
pomts,  and  not,  as  is  here  the.  case,  between  the  resultant  of  a  system  of 
points.  And  it  is  to  this  fact  that  the  discrepancy  between  the  theoretical 
and  observed  results  is  due. 

In  the  case  of  the  torsion  balance,  one  pole  of  the  magnet  to  be  tested 
was  at  so  great  a  distance  that  it  could  not  appreciably  modify  the  action 
of  the  other.  When  the  distance  at  which  two  magnets  act  is  large  as 
compared  with  their  dimensions,  the  total  action  on  one  another  is  nearly 
inversely  as  the  third  power  of  the  distances  ;  which,  it  might  be  shown, 
is  a  necessary  consequence  of  the  law  that  the  action  of  the  magnetic 
elements  is  inversely  as  the  square  of  the  distance. 

When  a  magnet  acts  upon  a  mass  of  soft  iron,  the  law  of  the  variation 
with  the  distance  is  modified.  The  attraction  in  this  case  is  inversely 
proportional  to  the  distance  between  the  magnet  and  the  iron. 

When  the  distance  between  the  magnet  and  iron  is  small,  Tyndall  has 
found  that  the  attraction  is  directly  proportional  to  the  square  of  the 
strength  of  the  magnet :  but  when  the  iron  and  the  magnet  are  in  con- 
tact, then  the  attraction  is  directly  proportional  to  the  strength  of  the 
magnet. 

668.  Ma§rnetic  curves. — If  a  stout  sheet  of  paper  stretched  on  a  frame 
be  held  over  a  horse-shoe  magnet,  and  then  some  very  fine  iron  filings 
be  strewn  on  the  paper,  on  tapping  the  frame  the  filings  will  be  found  to 
arrange  themselves  in  thread-like  curved  lines,  stretching  from  pole  to 
pole  (fig.  524).  These  lines  form  what  are  called  7nag7tetic  curves.  The 
direction  of  the  curve  at  any  point  represents  the  direction  of  the  mag- 
netism at  this  point. 


588  On  Magnetism:  [668- 

To  render  these  curves  permanent,  the  paper  on  which  they  are  formed 
should  be  waxed  ;  if  then  a  hot  iron  plate  be  held  over  them,  this  melts 
the  wax,  which  rises  by  capillary  attraction  (128)  between  the  particles  of 
filings,  and  on  subsequent  cooling  connects  them  together. 

These  curves  are  a  graphic  representation  of  the  law  of  magnetic 
attraction  and  repulsion  with  regard  to  distance ;  for  under  the  influence 


I^'ig    524 

of  the  two  poles  of  the  magnet,  each  particle  itself  becomes  a  minute 
magnet,  the  poles  of  which  arrange  themselves  in  a  position  dependent 
on  the  resultant  of  the  forces  exerted  upon  them  by  the  two  poles,  and 
this  resultant  varies  with  the  distance  of  the  two  poles  respectively.  A 
small  magnetic  needle  placed  in  any  position  near  the  magnet  will  take  a 
direction  which  is  the  tangent  to  the  curve  at  this  place. 

669.  Magrnetic  field. — The  space  in  the  immediate  neighbourhood  of 
any  magnet  undergoes  some  change,  in  consequence  of  the  presence  of 
this  magnet,  and  such  a  space  is  spoken  of  as  a  tnagnetic  field -,  the  effect 
produced  by  the  magnet  is  often  said  to  be  due  to  the  magnetic  field. 
Magnets  of  different  powers  produce  magnetic  fields  of  different  intensity. 

The  direction  which  represents  the  resultant  of  the  magnetic  forces  in 
a  magnetic  field  is  spoken  of  as  the  direction  of  the  lines  of  force  of  this 
field.  In  the  above  figure  the  magnetic  curves  represent  the  direction  of 
the  lines  of  force  in  the  field  due  to  the  two  poles. 

A  uniform  magnetic  field  is  one  in  which  the  lines  of  force  are 
parallel.  This  is  practically  the  case  with  a  field  at  some  distance  from 
a  long  thin  magnet  of  uniform  magnetisation. 

The  dipping  needle,  when  free  to  oscillate  in  a  vertical  plane  in  the 
magnetic  meridian,  represents  the  direction  of  the  lines  of  force  due  to 
the  terrestrial  magnetic  field.     This  field  in  any  one  place  is  uniform. 


-673]  Magnetisation.  589 


CHAPTER  IV. 

PROCESSES   OF   MAGNETISATION. 

670.  IVKagrnetisation. — The  various  sources  of  magnetism  are  the  m- 
fluence  of  natural  or  artificial  magnets,  terrestrial  magnetism,  aAd  elec- 
tricity. The  three  principal  methods  of  magnetisation  by  magnets  are 
known  by  the  technical  names  of  single  touchy  separate  touch,  and  double 
touch. 

671.  XWIetliod  of  sing-le  touch. — This  consists  in  moving  the  pole  of 
a  powerful  magnet  from  one  end  to  the  other  of  the  bar  to  be  magnetised, 
and  repeating  this  operation  several  times  always  in  the  same  direction. 
The  neutral  fluid  is  thus  gradually  decomposed  throughout  all  the  length 
of  the  bar,  and  that  end  of  the  bar  which  was  touched  last  by  the  magnet 
is  of  opposite  polarity  to  the  end  of  the  magnet  by  which  it  has  been 
touched.  This  method  only  produces  a  feeble  magnetic  power,  and  is, 
accordingly,  only  used  for  small  magnets.  It  has  further  the  disadvan- 
tage of  frequently  developing  consequent  poles. 

672.  nCethod  of  separate  touch. — This  method,  which  was  first  used 
by  Dr.  Knight  in  1745,  consists  in  placing  the  two  opposite  poles  of  two 
magnets  of  equal  force  in  the  middle  of  the  bar  to  be  magnetised,  and  in 
moving  each  of  them  simultaneously  towards  the  opposite  ends  of  the 
bar.  Each  magnet  is  then  placed  in  its  original  position,  and  this  opera- 
tion repeated.  After  several  frictions  on  both  faces  of  the  bar  it  is  mag- 
netised. 

•  In  Knight's  method  the  magnets  are  held  vertically.  Duhamel  jper- 
fected  the  method  by  inclining  the  magnets,  as  represented  in  fig.  521  ; 
and  still  more,  by  placing  the  bar  to  be  magnetised  on  the  opposite  poles 
of  two  fixed  magnets,  the  action  of  which  strengthens  that  of  the  mov- 
able magnets.  The  relative  position  of  the  poles  of  the  magnets  is 
indicated  in  the  figure. 

This  method  produces  the  most  regular  magnets. 

673.  XMEetbod  of  double  touch. — In  this  method,  which  was  invented 
by  Mitchell,  the  two  magnets  are  placed  with  their  poles  opposite  each 
other  in  the  mitidle  of  the  bar  to  be  magnetised.  But,  instead  of  moving 
them  in  opposite  directions  towards  the  two  ends,  as  in  the  method  of 
separate  touch,  they  are  kept  at  a  fixed  distance  by  means  of  a  piece  of 
wood  placed  between  them  (fig.  525),  and  are  simultaneously  moved  first 
towards  one  end,  then  from  this  to  the  other  end,  repeating  this  operation 
several  times,  and  finishing  in  the  middle,  taking  care  that  each  half  of 
the  bar  receives  the  same  number  of  frictions. 

Epinus,  in  1758,  improved  this  method  by  supporting  the  bar  to  be 
magnetised,  as  in  the  method  of  separate  touch,  on  the  opposite  poles  of 
two  powerful  magnets,  and  by  inclining  the  bars  at  an  angle  of  15° 
to  20° 

In  practice,  instead  of  two  bar  magnets  it  is  usual  to  employ  a  horse- 
shoe magnet,  which  has  its  poles  conveniently  close  together. 


590  On  Magnetism.  [673- 

By  this  method  of  double  touch,  which  is  the  one  generally-  adopted, 
powerful  magnets   are   obtained,  but   they  have  frequently  consequent 


Fig.  525. 

poles.  As  this  would  be  a  serious  injury  to  qompass  needles,  these  are 
best  magnetised  by  separate  touch. 

674.  IVIagrnetisation  toy  the  action  of  the  earth. — The  action  of  the 
earth  on  magnetic  substances  resembles  that  of  a  magnet,  and  hence  the 
terrestrial  magnetism  is  constantly  tending  to  separate  the  two  magnetisms 
which  are  in  the  neutral  state  in  soft  iron  and  in  steel.  But  as  the  coercive 
force  is  very  considerable  in  the  latter  substance,  the  action  of  the  earth 
is  inadequate  to  produce  magnetisation,  except  when  continued  for  a  long 
time.  This  is  not  the  case  with  perfectly  soft  iron.  When  a  bar  of  this 
metal  is  held  in  the  magnetic  meridian  parallel  to  the  inclination,  the  bar 
becomes  at  once  endowed  with  feeble  magnetic  polarity.  The  lower 
extremity  is  a  north  pole,  and  if  the  north  pole  of  a  small  magnetic  needle 
be  approached,  it  will  be  repelled.  This  magnetisation  is  of  course  unstable, 
for  if  the  bar  be  turned,  the  poles  are  inverted,  as  pure  soft  iron  is  desti- 
tute of  coercive  force. 

While  the  bar  is  in  this  position,  a  certain  amount  of  coercive  force 
may  be  imparted  to  it  by  giving  it  several  smart  blows  with  a  hammer, 
and  the  bar  retains  for  a  short  time  the  magnetism  which  it  has  thus  ob- 
tained. But  the  coercive  force  thus  developed  is  very  small,  and  after  a 
time  the  magnetism  disappears. 

If  a  bar  of  soft  iron  be  twisted  while  held  vertically,  or,  better,  in  the 
plane  of  the  dip,  it  acquires  a  feeble  permanent  magnetism. 

It  is  this  magnetising  action  of  the  earth  which  developes  the  magnet- 
ism frequently  olDserved  in  steel  and  iron  instruments,  such  as  fire-irons, 
rifles,  lamp  posts,  railings,  gates,  lightning  conductors,  etc»,  which  remain 
for  some  time  in  a  more  or  less  inclined  position.  They  become  magnet- 
ised with  their  north  pole  downward,  just  as  if  placed  over  the  pole  of  a 
powerful  magnet.  The  magnetism  of  native  black  oxide  of  iron  has 
doubtless  been  produced  by  the  same  causes  ;  the  very  different  magnetic 
power  of  different  specimens  being  partly  attributable  to  the  different 
positions  of  the  veins  of  ore  with  regard  to  the  line  of  dip.  The  ordinary 
irons  of  commerce  are  not  quite  pure,  and  possess  a  feeble  coercive  force  ; 
hence  a  feeble  magnetic  polarity  is  generally  found  to  be  possessed  by  the 
tools  in  a  smith's  shop.  Cast-iron,  too,  has  usually  a  great  coercive  force, 
and  can  be  permanently  magnetised.  The  turnings,  also,  of  wrought  iron 
and  of  steel  produced  by  the  powerful  lathes  of  our  ironworks  are  found 
to  be  magnetised. 


-675]  Magnetism  of  Iron  Ships.  591 

675.  Magrnetisxn  of  iron  ships. — The  inductive  action  of  terrestrial 
magnetism  upon  the  masses  of  iron  always  found  in  ships  exerts  a  dis- 
turbing action  upon  the  compass  needle.  The  local  attraction,  as  it  is 
called,  may  be  so  considerable  as  to  render  the  indications  of  the  needle 
almost  useless  if  it  be  not  guarded  against.  A  full  account  of  the 
manner  in  which  local  attraction  is  produced,  and  in  which  it  is  com- 
pensated, is  inconsistent  with  the  limits  of  this  book,  but  the  most 
important  points  are  the  following  : — 

i.  A  vertical  mass  of  soft  iron  in  the  vessel,  say  in  the  bows,  would 
become  magnetised  under  the  influence  of  the  earth  ;  in  the  northern 
hemisphere,  the  lower  end  would  be  a  north  pole,  and  the  upper  end  a 
south  pole  ;  and  as  the  latter  may  be  assumed  to  be  nearer  the  north 
pole  of  the  compass  needle,  it  would  act  upon  it.  So  long  as  the  vessel 
was  sailing  in  the  magnetic  meridian  this  would  have  no  effect  ;  but  in 
any  other  direction  the  needle  would  be  drawn  out  of  the  magnetic 
meridian,  and  a  little  consideration  will  show  that  when  the  ship  was  at 
right  angles  to  the  magnetic  meridian  the  effect  would  be  greatest. 
This  vertical  itiduction  would  disappear  twice  in  swinging  the  ship  round 
and  would  be  at  its  maximum  twice  ;  hence  the  deviation  due  to  this 
cause  is  known  as  semicircular  deviation. 

ii.  Horizontal  masses  again,  such  as  deck-beams,  are  also  acted  upon 
inductively  by  the  earth's  magnetism,  and  their  induced  magnetism 
exerts  a  disturbing  influence  upon  the  magnetic  needle.  The  effect  of 
this  horizontal  induction  will  disappear  when  the  ship  is  in  the  magnetic 
meridian,  and  also  when  it  is  at  right  angles  thereto.  In  positions  inter- 
mediate to  the  above  the  disturbing  influence  will  attain  its  maximum. 
Hence  in  swinging  a  ship  round  there  would  be  four  positions  of  the 
ship's  head  in  which  the  influence  would  be  at  a  maximum  and  four  in 
which  it  would  be  at  a  minimum.  This  eftect  of  horizontal  induction  is 
accordmgly  spoken  of  as  guadrantal  deviation. 

The  influence  of  both  these  causes,  vertical  and  horizontal  induction, 
may  be  remedied  in  the  process  of  '  swinging  the  sl.ip.'  This  consists  in 
comparing  the  indications  of  the  ship's  compass  with  those  of  a  standard 
compass  placed  on  shore.  The  ship  is  then  swung  round  in  various 
positions,  and  by  arranging  small  vertical  and  horizontal  masses  of  soft 
iron  in  proximity  to  the  steering  compass,  positions  are  found  for  them  in 
which  the  inductive  action  of  the  earth  upon  them  quite  neutralises  the 
influence  of  the  earth's  magnetism  upon  the  ship  ;  and  in  all  positions 
of  the  ship,  the  compass  points  in  the  same  direction  as  the  one  on 
shore. 

iii.  The  extended  use  of  iron  in  ship-building,  more  especially  when 
the  frames  are  entirely  of  iron,  has  increased  the  difficulty.  In  the 
process  of  building  a  ship,  the  hammering  and  other  mechanical  ope- 
rations to  which  it  is  subject,  while  under  the  influence  of  the  earth's 
magnetism,  will  cause  it  to  become  to  a  certain  extent  permanently 
magnetised.  The  distribution  of  the  magnetism,  the  direction  of  its 
magnetic  axis,  will  depend  on  the  position  in  which  it  has  been  built ;  it 
may  or  may  not  coincide  with  the  direction  of  the  keel.     The  vessel 


592  On  Magnetism.  [675- 

becomes  in  short  a  huge  magnet,  and  will  exert  an  influence  of  its  own 
upon  the  compass  quite  independently  of  vertical  or  horizontal  induction. 
This  influence  is  semicircular,  that  is,  it  disappears  when  the  magnetic 
axis  of  the  ship  is  in  the  magnetic  meridian  and  is  greatest  at  right 
angles  to  it.  It  may  be  compensated  by  two  permanent  magnets  placed 
near  the  compass  in  suitable  positions  found  by  trial  during  the  process 
of  swinging  the  ship.  Supposing  the  inherent  magnetism  of  the  ship  to 
have  the  power  of  drawing  the  compass  a  point  to  the  east,  the  com- 
pensating magnets  may  be  so  arranged  as  to  tend  to  draw  it  a  point  to 
the  west,  and  thus  keep  it  in  the  magnetic  meridian.  If,  however,  the 
inherent  magnetism  be  destroyed,  from  whatever  cause,  it  is  clear  that 
the  magnets  will  now  draw  it  aside  a  point  too  much  to  the  west.  This 
IS  the  source  of  a  new  difficulty.  It  has  been  found  that  a  ship  which 
at  the  time  of  sailing  was  properly  compensated  would  on  returning 
from  a  long  voyage  have  its  compasses  over-compensated.  The  buffeting 
which  the  ship  had  experienced  had  destroyed  its  inherent  magnetism, 
and  numerous  instances  are  known  where  the  loss  of  a  vessel  can  be 
directly  traced  to  this  cause.  Fortunately,  it  has  been  found  that  after 
some  time  a  ship's  magnetic  condition  is  virtually  permanent,  and  is 
unaltered  by  any  further  wear  and  tear.  The  magnetism  which  it  then 
retains  is  called  its  permanent  magnetism,  in  opposition  to  the  sub-per- 
manent which  it  loses. 

The  difficulty  of  adequately  compensating  compasses,  which  is  greatly 
increased  by  the  armour-plated  and  turret  ships  now  in  use,  has  induced 
one  school  to  throw  over  any  attempt  at  correction  ;  but  by  careful 
observation  of  the  magnetic  condition  of  a  ship,  and  tabulating  the 
errors  to  construct  a  table,  by  comparing  which  with  the  indications  of 
the  compass  at  any  one  time,  the  true  course  can  be  made  out. 

In  the  Royal  Navy,  the  plan  now  adopted  is  to  combine  both  methods: 
compensate  the  errors  to  a  considerable  extent,  and  then  construct  a 
table  of  the  residual  errors. 

676.  Saturation. — Experiment  has  shown  that  to  a  certain  extent 
the  magnetic  force  which  can  be  imparted  to  a  bar  or  needle  increases 
with  the  power  of  the  magnets  used.  But  there  is  a  limit  to  the  mag- 
netic force  which  can  be  imparted  to  a  bar  or  needle,  and  when  this  is 
attained,  the  bar  is  said  to  be  saticrated  or  magnetised  to  saturation.  A 
bar  may  indeed  be  magnetised  beyond  this  point,  but  this  is  not 
permanent  ;  it  gradually  diminishes  until  it  has  sunk  to  the  point  of 
saturation. 

This  is  readily  intelligible,  for  the  magnetisms  once  separated  tend  to 
reunite,  and  when  their  attractive  force  is  equal  to  that  which  opposes 
their  separation,  that  is,  the  coercive  force  of  the  metal,  equilibrium  is 
attained,  and  the  magnet  is  saturated.  Hence,  more  magnetism  ought 
to  be  developed  in  'bars  than  they  can  retain,  in  order  that  they  may 
decline  to  their  permanent  state  of  saturation.  To  increase  the  magnet- 
ism of  an  unsaturated  bar,  a  less  feeble  magnet  must  not  be  used  than 
that  by  which  it  was  originally  magnetised. 


678] 


Magnetic  Battery. 


593 


677.  Magnetic  battery. — A  magnetic  battery  or  inagazme  consists  of 
a  number  of  magnets  joined  together  by  their  similar  poles.  Sometimes 
they  have  the  form  of  a  horse-shoe,  and  sometimes  a  rectilinear  form. 
The  battery  represented  in  fig.  526  consists  of  five  superposed  steel  plates. 
That  in  fig.  527  consists  of  twelve  plates,  arranged  in  three  layers  of  four 
each.  The  horse  shoe  form  is  best 
adapted  for  supporting  a  weight,  for 
then  both  poles  are  used  at  once.  In 
both  the  bars  are  magnetised  separ- 
ately, and  then  fixed  by  screws. 

The  force  of  a  battery  is  not  equal 
to  the- sum  of  the  forces  of  each  bar, 
owing  to  the  repulsive  action  exerted 
by  each  bar  on  the  adjacent  ones. 
The  force  is  increased  by  making  the 
lateral  plates  i  or  2  centimetres  shorter 
than  the  one  in  the  middle  (fig.  526). 

678.  Armatures. — When  even  a 
steel  bar  is  at  its  limit  of  saturation, 
it  gradually  loses  its  magnetism.  To 
prevent  this  armatures  or  keepers  are 
used ;  these  are  pieces  of  soft  iron,  A 
and  B  (fig.  527),  which  are  placed  in 
contact  with  the  poles.  Acted  on 
inductively,  they  become  powerful 
temporary  magnets,  possessing  oppo- 
site polarity  to  that  of  the  inducing 
pole ;  they  thus  react  in  turn  on  the  permanent  magnetism  of  the  bars, 
preserving  and  even  increasing  it. 


Fig.  526. 


Fig.  527. 

When  the  magnets  are  in  the  form  of  bars,  they  are  arranged  in  pairs, 
as  shown  in  fig.  528,  with  opposite  poles  in  juxtaposition,  and  the  circuit 
is  completed  by  two  small  bars  of  soft  iron,  AB.     Movable  magnetic 


Fig.  528. 


needles  set  spontaneously  towards  the  magnetic  poles  of  the  earth,  the 
'*      influence  of  which  acts  as  a  keeper. 


594 


On  Magnetism. 


[678- 


Fig.  529- 


A  horse-shoe  magnet  has  a  keeper  attached  to  it,  which  is  usually- 
arranged  so  as  to  support  a  weight.  The  keeper  becomes  magnetised 
under  the  influence  of  the  two  poles,  and  adheres 
with  great  force;  the  weight  which  it  can  support 
being  much  more  than  double  that  which  a  single 
pole  would  hold. 

In  respect  to  this  weight,  a  singular  and  hitherto 
inexplicable  phenomenon  has  been  observed.  When 
contact  is  once  made,  and  the  keeper  is  charged 
with  its  maximum  weight,  any  further  addition 
would  detach  it ;  but  if  left  in  contact  for  a  day, 
an  additional  weight  may  be  added  without  de- 
taching it,  and  by  slightly  increasing  the  weight 
every  day,  it  may  ultimately  be  brought  to  support 
a  far  greater  load  than  it  would  originally.  But 
if  contact  be  once  broken,  the  weight  it  can  now 
support  does  not  much  exceed  its  original  charge. 

It    is   advantageous   that   the    surfaces   of  the 
magnet  and  armatures  which  are  in  contact  should 
not  be  plane,  but  sHghtly  cylindrical,  so  that  they  touch  along  a  line. 

In  providing  a  natural  magnet  with  a  keeper,  the  line  joining  the  two 
poles  is  first  approximately  determined  by  means  of  iron  filings.  Two 
plates  of  soft  iron  (tig.  529),  each  terminating  in  a  massive  shoe,  are  then 
applied  to  the  faces  corresponding  to  the  poles.  Under  the  influence  of 
the  natural  magnet,  these  plates  become  magnetised,  and  if  the  letters  A 
and  B  represent  the  position  of  the  poles  of  the  natural  magnet,  the  poles 
of  the  armature  are  a  and  b. 

679.  Portative  Force.  Power  of  magrnets. — The  portative  force  is 
the  greatest  weight  which  a  magnet  can  support.  Hacker  found  that  the 
portative  force  of  a  saturated  horse-shoe  magnet,  which,  by  repeatedly  de- 
taching the  keeper,  has  become  constant,  maybe  represented  by  the  formula 

p  =  ^^7^ 

in  which  P  is  the  portative  force  of  the  magnet,  p  its  own  weight,  and 
a  a  coefficient,  which  varies  with  the  nature  of  the  steel  and  the  mode  of 
magnetising.  Hence  a  magnet  which  weighs  1,000  ounces  only  supports  25 
times  as  much  as  one  weighing  8  ounces  or  j^.-  as  heavy.  It  appears 
immaterial  whether  the  section  of  the  bar  is  quadratic  or  circular,  and 
the  distance  of  the  legs  is  of  inconsiderable  moment ;  it  is  important, 
however,  that  the  magnet  be  suspended  vertically,  and  that  the  load  be 
exactly  in  the  middle.  In  Hackers  magnets  the  value  of  a  was  10-33, 
while  in  Logemann's  it  was  23. 

The  strength  of  two  bar  magnets  may  be  compared  by  the  following 
simple  method,  which  is  known  as  Kiilp's  co?npe?isation  method : — A  small 
magnetic  compass  needle  is  placed  in  the  magnetic  meridian.  One  pole 
of  one  of  the  magnets  to  be  tested  is  then  placed  at  right  angles  to  the 
magnetic  meridian  in  the  same  plane  as  the  needle,  and  so  that  its  axis 
prolonged   would   bisect  the  needle.     The   compass  needle  is  thereby 


-680]  Cirannstanccs  ivhich  influence  the  Power  of  Magnets.  595 

deflected  through  a  certain  angle.  The  similar  pole  of  the  other  magnet 
is  then  placed  similarly  on  the  other  side  of  the  needle,  and  a  position 
found  for  it  in  which  it  exactly  neutralises  the  action  of  the  first  magnet, 
that  is,  when  the  needle  is  again  in  the  magnetic  meridian.  If  the  mag- 
nets are  not  too  long,  their  strengths  are  approximately  as  the  cubes  of 
the  distance  of  the  acting  poles  from  the  magnetic  needle. 

680.  Circumstances  wbich  Influence  tlie  power  of  magnets. — All 
bars  do  not  attain  the  same  state  of  saturation,  for  their  coercive  force 
varies.  Twisting  or  hammering  imparts  to  iron  or  steel  a  considerable  co- 
ercive force.  But  the  most  powerful  of  these  influences  is  the  operation 
of  tempering  (91).  Coulomb  found  that  a  steel  bar  tempered  at  dull 
redness,  and  magnetised  to  saturation,  made  ten  oscillations  in  93  seconds. 
The  same  bar  tempered  at  a  cherry-red  heat,  and  similarly  magnetised  to 
saturation,  only  took  63  seconds  to  make  ten  oscillations. 

Hence  it  would  seem,  the  harder  the  steel  the  greater  is  its  coercive 
force  ;  it  receives  magnetism  with  much  greater  difficulty,  but  retains  it 
more  effectually.  Very  hard  steel  bars  have,  however,  the  disadvantage 
of  being  very  brittle,  and  in  the  case  of  long  thin  bars,  a  hard  tempering 
is  apt  to  produce  consequent  poles.  Compass  needles  are  usually 
tempered  at  the  blue  heat,  that  is,  about  300°  C,  by  which  a  high  coercive 
force  is  obtained  without  great  fragility. 

Temperature. — Increase  of  temperature  always  produces  a  diminution 
of  magnetic  force.  If  the  changes  of  temperature  are  small,  those  of  the 
atmosphere  for  instance,  the  magnet  is  not  permanently  altered.  Kuppfer 
allowed  a  magnet  to  oscillate  at  different  temperatures,  and  found  a 
definite  decrease  in  its  power  with  increased  temperature,  as  indicated 
by  its  slower  oscillations.  In  the  case  of  a  magnet  2^  inches  in  length, 
he  observed  that  with  an  increase  of  each  degree  of  temperature  the 
duration  of  800  oscillations  was  0-4'^  longer.  If  71  be  the  number  of  oscil- 
lations at  zero,  and  Ji  the  number  at  /,  then 

n^  =  ti  (i  —ct), 

where  <:  is  a  constant  depending  in  each  case  on  the  magnet  used.  This 
formula  has  an  important  application  in  the  correction  of  the  observations 
of  magnetic  intensity  which  are  made  at  different  places  and  at  different 
temperatures,  and  which,  in  order  to  be  comparable,  must  first  be  reduced 
to  a  uniform  temperature. 

When  a  magnet  has  been  more  strongly  heated,  it  does  not  regain  its 
original  force  on  cooling  to  its  original  temperature,  and  when  it  has  been 
heated  to  redness,  it  is  demagnetized.  This  was  first  shown  by  Coulomb, 
who  took  a  saturated  magnet,  and  progressively  heated  it  to  higher  tem- 
peratures, and  observed  the  number  of  oscillations  after  each  heating. 
The  higher  the  temperature  to  which  it  had  been  heated  the  slower  its 
oscillations. 

A  magnet  heated  to  bright  redness  loses  its  magnetism  so  completely 
that  it  is  quite  indifferent,  not  only  towards  iron,  but  also  towards  another 
magnet.  Incandescent  iron  also  does  not  possess  the  property  of  being 
attracted  by  the  magnet.     Hence  there  is  in  the  case  of  iron  a  7nagnetic 


59^  On  Mag7ietism.  [680- 

litnit,  beyond  which  it  is  unaffected  by  magnetism.  Such  a  magnetic 
limit  exists  in  the  case  of  other  magnetic  metals.  With  cobalt^  for 
instance,  it  is  far  beyond  a  white  heat,  for  at  the  highest  temperatures 
hitherto  examined  it  is  still  magnetic ;  the  magnetic  limit  of  chromium  is 
somewhat  below  red  heat  ;  that  of  nickel  at  about  350°  C,  and  of  manga- 
nese at  about  1 5°  to  20°  C. 

Torsion. — Torsion  exerts  a  great  influence  on  the  magnetisation  of 
a  bar,  and  the  interesting  phenomenon  has  been  observed  that  tor- 
sion influences  magnetism  in  the  same  manner  as  magnetism  does 
torsion.  Thus  the  permanent  magnetism  of  a  steel  bar  is  diminished  by 
torsion,  but  not  proportionally  to  the  increase  of  torsion.  In  like  manner 
the  torsion  of  twisted  iron  wires  is  diminished  by  their  being  magnetised, 
though  less  so  than  in  proportion  to  their  magnetisation.  Repeated 
torsions  in  the  same  direction  scarcely  diminish  magnetisation,  but  a 
torsion  in  the  opposite  direction  produces  a  new  diminution  of  the 
magnetism.  In  a  perfectly  analogous  manner,  repeated  magnetisations 
in  the  same  sense  scarcely  diminish  torsion,  but  a  renewed  magnetisation 
in  the  opposite  direction  does  so. 

681.  Bistribution  of  free  mag'netism. — To  investigate  the  distribution 
of  magnetic  force  in  different  parts  of  a  magnet.  Coulomb  placed  a  large 
magnet  in  a  vertical  position  in  the  magnetic  meridian ;  he  then  took  a 
small  magnetic  needle  suspended  by  a  thread  without  torsion,  and,  having 
ascertained  the  number  of  its  oscillations  under  the  influence  of  the  earth's 
magnetism  alone,  he  presented  it  to  different  parts  of  the  magnet. 
The  oscillations  were  fewer  as  the  needle  was  nearer  the  middle  of  the 
bar,  and  when  they  had  reached  that  position,  their  number  was  the  same 
as  under  the  influence  of  the  earth's  magnetism  alone.  He  found  that 
with  saturated  bars  of  more  than  7  inches  in  length  the  distribution  could 
always  be  expressed  by  a  curve  whose  abscissae  were  the  distances 
from  the  ends  of  the  magnet,  and  whose  ordinates  were  the  force  of 
magnetism  at  these  points.  With  magnets  of  the  above  dimensions  the 
poles  are  at  the  same  distance  from  the  end  ;  Coulomb  found  the  distance 
to  be  I  -6  inches  in  a  bar  8  inches  long.  The  same  physicist  found  that, 
with  shorter  bars,  the  distance  of  the  poles  from  the  end  is  \  of  the  length  ; 
thus  with  a  bar  of  three  inches  it  would  be  half  an  inch. 

These  results  presume  that  the  other  dimensions  of  the  bar  are  very 
small  as  compared  with  its  length,  that  it  has  a  regular  shape,  and  is 
uniformly  magnetised.  When  these  conditions  are  not  fulfilled,  the 
positions  of  the  poles  can  only  be  determined  by  direct  trials  with  a 
magnetic  needle.  With  lozenge-shaped  magnets  the  poles  are  nearer  the 
middle.  Coulomb  found  that  these  lozenge-shaped  bars  have  a  greater 
directive  force  than  rectangular  bars  of  the  same  weight,  thickness,  and 
hardness. 


-683]  Frictional  Electricity.  597 


BOOK   IX. 

FRICTIONAL   ELECTRICITY. 


CHAPTER    I. 
FUNDAMENTAL   PRINCIPLES. 


682.  Electricity.  Its  nature. — Electricity  is  a  powerful  physical 
agent  which  manifests  itself  mainly  by  attractions  and  repulsions,  but 
also  by  luminous  and  heating  effects,  by  violent  commotions,  by  chemical 
decompositions,  and  many  other  phenomena.  Unlike  gravity,  it  is  not 
inherent  in  bodies,  but  is  evoked  in  them  by  a  variety  of  causes,  among 
which  are  friction,  pressure,  chemical  action,  heat,  and  magnetism. 

Thales,  six  centuries  before  Christ,  knew  that  when  amber  was  rubbed 
with  silk,  it  acquired  the  property  of  attracting  light  bodies  :  and  from 
the  Greek  form  of  this  word  {i)XficT.)<n;  electron)  the  term  electricity  has 
been  derived.  This  is  nearly  all  the  knowledge  left  by  the  ancients;  and 
it  was  not  until  towards  the  end  of  the  sixteenth  century  that  Dr.  Gilbert, 
physician  to  Queen  Elizabeth,  showed  that  this  property  was  not  hmited 
to  amber,  but  that  other  bodies,  such  as  sulphur,  wax,  glass,  etc.,  also 
possessed  it  in  a  greater  or  less  degree. 

683.  Bevelopment  of  electricity  by  friction. — When  a  glass  rod,  or 
a  stick  of  sealing-wax,  or  shellac,  is  held  in  the  hand,  and  is  rubbed  with 
a  piece  of  flannel  or  with  the  skin  of  a  cat,  the  parts  rubbed  will  be  found 
to  have  the  property  of  attracting  light  bodies,  such  as  pieces  of  silk,  wool, 
feathers,  paper,  bran,  gold  leaf,  etc.,  which,  after  remaining  a  short  time 
in  contact,  are  again  repelled.  In  order  to  ascertain  whether  bodies  are 
electrified  or  not,  instruments  called  electroscopes  are  used.  The  simplest 
of  these,  the  electric  peitduhim  (fig.  530),  consists  of  a  pith  ball  attached 
by  means  of  a  silk  thread  to  a  glass  support.  When  an  electrified  body 
is  brought  near  the  pith  ball,  the  latter  is  instantly  attracted,  but  after 
momentary  contact  is  again  repelled  (fig.  531). 

A  solid  body  may  also  be  electrified  by  friction  with  a  liquid  or  with 
a  gas.  In  the  ToricelHan  vacuum  a  movement  of  the  mercury  against 
the  sides  of  the  glass  produces  a  disengagement  of  electric  light  visible 
in  the  dark ;  a  tube  exhausted  of  air,  but  containing  a  few  drops  of  mer- 
cury, becomes  also  luminous  when  agitated  in  the  dark. 

If  a  quantity  of  mercury  in  a  dry  glass  vessel  be  connected  with  a  gold- 
leaf  electroscope  by  a  wire,  and  a  dry  glass  rod  be  immersed  in  it,  no  in- 
dications are  observed  during  the  immersion,  but  on  withdrawing  the  rod. 


598 


Frictional  Electricity. 


[684 


the  leaves  increasingly  diverge,  attaining  their  maximum  when  the  rod 
leaves  the  mercury. 

Some  substances,  particularly  metals,  do  not  seem  capable  of  receiving 
the  electric  excitement.  When  a  rod  of  metal  is  held  in  the  hand,  and 
rubbed  with  silk  or  flannel,  no  electrical  effects  are  produced  in  it ;  and 


Fig.  530-  Fig.  531. 

bodies  were  formerly  divided  into  ideoelectricSy  or  those  which  become 
electrical  by  friction,  and  anelectrics,  or  those  which  do  not  possess  this 
property.  These  distinctions  no  longer  obtain  in  any  absolute  sense  ;  it 
will  presently  be  seen  that,  under  appropriate  conditions,  all  bodies  may 
be  electrified  by  friction  (685). 

With  reference  to  the  cause  of  the  production  of  electricity  by  friction 
nothing  is  known.  Wollaston  attributed  it  to  oxidation;  but  Wilson 
and  Gray  have  shown  that  electrical  phenomena  may  be  produced  in 
vacuo,  and  Gay-Lussac  proved  that  electricity  may  be  developed  in  an 
atmosphere  of  carbonic  acid. 

684.  Conductors  and  nonconductors.^ — When  a  dry  glass  rod,  rubbed 
at  one  end,  is  brought  near  an  electroscope,  that  part  only  will  be  electri- 
fied which  has  been  rubbed ;  the  other  end  will  produce  neither  attraction 
nor  repulsion.  The  same  is  the  case  with  a  rod  of  shellac  or  of  sealing- 
wax.  In  these  bodies  electricity  does  not  pass  from  one  part  to  another 
— they  do  not  conduct  electricity.  Experiment  shows,  that  when  a  metal 
has  received  electricity  in  any  of  its  parts,  the  electricity  instantly  spreads 
throughout  its  entire  surface.  Metals  are  hence  said  to  be  good  coti- 
diictors  of  electricity. 

Bodies  have,  accordingly,  been  divided  into  conductors  and  noficon- 
ductors  or  insulators.  This  distinction  is  not  absolute,  and  we  may  ad- 
vantageously consider  bodies  as  offering  a  resistance  to  the  passage  of 


684] 


CondiLctors  and  Non-conductors. 


599 


electricity  which  varies  with  the  nature  of  the  substance.  Those  bodies 
which  offer  httle  resistance  are  then  conductors,  and  those  which  offer 
great  resistance  are  nonconductors  or  insulators :  electrical  conductivity 
is  thus  the  inverse  of  electrical  resistance.  We  are  to  consider  that  be- 
tween conductors  and  nonconductors  there  is  a  quantitative  and  not  a 
qualitative  difference ;  there  is  no  conductor  so  good  but  that  it  offers 
some  resistance  to  the  passage  of  electricity,  nor  is  there  any  substance 
which  insulates  so  completely  but  that  it  allows  some  electricity  to  pass. 
The  transition  from  conductors  to  nonconductors  is  gradual,  and  no  line 
of  sharp  demarcation  can  be  drawn  between  them. 

In  this  sense  we  are  to  understand  the  following  table,  ih  which  bodies 
are  classed  as  conductors,  semiconductors,  and  nonconductors-,  those 
bodies  being  conveniently  designated  as  conductors  which  when  applied 
to  a  charged  electroscope  discharge  it  almost  instantaneously  ;  semicon- 
ductors being  those  which  discharge  it  in  a  short  but  measurable  time,  a 
few  seconds,  for  instance;  while  nonconductors  effect  no  discharge  in  the 
course  of  a  minute. 


Conductors. 

Metals. 

Well-burnt  charcoal. 

Graphite. 

Acids. 

Aqueous  solutions. 

Water. 

Snow. 

Vegetables. 

Animals. 

Soluble  salts. 

Linen. 

Cotton. 


Sein  iconductors.  Nonconductors, 

Alcohol  and  ether.     Dry  oxides. 

Powdered  glass.         Ice  at  — 25°  C. 

Flour  of  sulphur.        Lime. 

Dry  wood.  Lycopodium. 

Paper.  Caoutchouc. 

Ice  at  0°.  Air  and  dry  gases. 

Dry  paper. 

Silk. 

Diamond  and  precious  stones. 

Glass. 

Wax. 

Sulphur. 

Resins. 

Amber. 

Shellac. 

This  list  is  arranged  in  the  order  of  decreasing  conductivity,  or  what  is 
the  same  thing,  of  increasing  resistance.  The  arrangement  is  not  in- 
variable however.  Conductivity  depends  on  many  physical  conditions. 
Glass,  for  example,  which  does  not  conduct  at  any  ordinary  temperatures, 
conducts  very  well  at  a  red  heat.  Shellac  and  resin  do  not  conduct  so 
well  when  they  are  heated.  Water,  which  is  a  good  conductor,  conducts 
but  little  in  the  state  of  ice  at  0°,  and  very  badly  at  —25°.  Powdered 
glass  and  flour  of  sulphur  conduct  very  well,  while  in  large  masses  they 
are  nonconductors  ;  probably  because  in  a  state  of  powder  each  particle 
becomes  covered  with  a  film  of  moisture  that  acts  as  a  conductor. 

According  to  Said  Effendi,  if  the  conducting  power  of  water  be  taken 
at  1,000,  the  conducting  power  of  petroleum  is  72;  alcohol  49;  ether  40; 
turpentine  23  :  and  benzole  16. 


6oo  Frictional  Electricity.  [685- 

685.  Xnsulatingr  bodies.  Cominon  reservoir. — Bad  conductors  are 
called  msiilators,  for  they  are  used  as  supports  for  bodies  in  which  elec- 
tricity is  to  be  retained.  A  conductor  remains  electrilied  only  so  long  as 
it  is  surrounded  by  insulators.  If  this  were  not  the  case,  as  soon  as  the 
electrified  body  came  in  contact  with  the  earth,  which  is  a  good  con- 
ductor, the  electricity  would  pass  into  the  earth,  and  diffuse  itself  through 
its  whole  extent.  On  this  account,  the  earth  has  been  named  the  co7nvion 
reservoi7\  A  body  is  insulated,  by  being  placed  on  a  support  with  glass 
feet,  or  on  a  resinous  cake,  or  by  being  suspended  by  silk  threads.  No 
bodies,  however,  insulate  perfectly  ;  all  electrified  bodies  lose  their  elec- 
tricity more  or  less  rapidly  by  means  of  the  supports  on  which  they  rest. 
Glass  is  always  somewhat  hygroscopic,  and  the  aqueous  vapour  which 
condenses  on  it  affords  a  passage  for  the  electricity;  the  insulating 
power  of  glass  is  materially  improved  by  coating  it  with  shellac  or  copal 
varnish.  Dry  air  is  a  good  insulator,  but  when  the  air  contains  moisture, 
it  conducts  electricity,  and  this  is  the  principal  source  of  the  loss  of 
electricity.  Hence  it  is  necessary  in  electrical  experiments,  to  rub  the 
supports  with  cloths  dried  at  the  fire,  and.  to  surround  electrified  bodies 
by  glass  vessels,  containing  substances  which  attract  moisture,  such  as 
chloride  of  calcium,  or  pumice  soaked  with  sulphuric  acid. 

It  is  from  their  great  conductivity,  that  metals  do  not  become  electri- 
fied by  friction.  But  if  they  are  insulated,  and  then  rubbed,  they  give 
good  indications.  This  may  be  seen  by  the  following  experiment  (fig. 
532).     A  brass  tube  i?  provided  with  a  glass  handle,  by  which  it  is  held. 


Fig.  532. 

and  then  rubbed  with  silk  or  flannel.  On  approaching  the  metal  to  the 
pendulum,  the  pith  ball  will  be  attracted.  If  the  metal  is  held  in  the 
hand  electricity  is  indeed  produced  on  it  by  friction — but  it  immediately 
passes  through  the  body  into  the  ground. 

If,  too,  the  cap  of  a  gold-leaf  electroscope  be  briskly  flapped  with  a 
dry  silk  handkerchief,  the  gold  leaves  will  diverge. 

686.  Distinction  of  the  two  kinds  of  electricity. — If  electricity  be 
developed  on  a  glass  rod  by  friction  with  silk,  and  the  rod  be  brought 
near  an  electrical  pendulum  (fig.  527),  the  ball  will  be  attracted  to  the 
glass,  and  after  momentary  contact  will  be  again  repelled.  By  this 
contact  the  ball  becomes  electrified,  and  so  long  as  the  two  bodies  retain 
their  electricity,  repulsion  follows  when  they  are  brought  near  each  other. 
If  a  stick  of  sealing-wax,  electrified  by  friction  with  flannel  or  cat's  skin,  be 
approached  to  another  electrical  pendulum,  the  same  effects  will  be  pro- 
duced, the  ball  will  fly  towards  the  wax,  and  after  contact  will  be  repelled. 
Two  bodies,  which  have  been  charged  with  electricity,  repel  one  another. 
But  the  electricities,  respectively  developed  in  the  preceding  cases,  are 
not  the  same.  If,  after  the  pith  ball  had  been  touched  with  an  electrified 
glass  rod,  an  electrified  stick  of  sealing-wax,  and  then  an  electrified  glass 
rod,  be  alternately  approached  to  it,  the  pith  ball  will  be  attracted  by  the 


k 


-688]       *  Theories  of  Electricity.  601 

former  and  repelled  by  the  latter.  Similarly,  if  the  pendulum  be  charged 
by  contact  with  the  electrified  sealing-wax,  it  will  bs  repelled  when  this  is 
approached  to  it,  but  attracted  by  the  approach  of  the  excited  glass  rod. 

On  experiments  of  this  nature,  Dufay  first  made  the  observation  that 
there  are  two  different  electricities  :  the  one  developed  by  the  friction 
of  glass,  the  other  by  the  friction  of  resin  or  shellac.  To  the  first  the 
name  vitreous  electricity  is  given  ;  to  the  second  the  name  resinous 
electricity. 

687.  Theories  of  electricity. — Two  theories  have  been  proposed  to 
account  for  the  different  effects  of  electricity.  Franklin  supposed  that 
there  exists  a  peculiar,  subtle,  imponderable  fluid,  which  acts  by  repulsion 
on  its  own  particles,  and  pervades  all  matter.  This  fluid  is  present  in  every 
substance  in  a  quantity  peculiar  to  it,  and  when  it  contains  this  quantity, 
it  is  in  the  natural  state,  or  in  a  state  of  equilibrium.  By  friction,  certain 
bodies  acquire  an  additional  quantity  of  the  fluid,  and  are  said  to  be 
positively  electrified  :  others,  by  friction,  lose  a  portion,  and  are  said  to  be 
negatively  electrified.  The  former  state  corresponds  to  vitreous  elec- 
tricity, and  the  latter  to  resinous  electricity.  Positive  electricity  is  repre- 
sented by  the  sign  + ,  and  negative  electricity  by  the  sign  —  ;  a  desig- 
nation based  on  the  algebraical  principle,  that  when  a  plus  quantity  is 
added  to  an  equal  minus  quantity  zero"  is  produced.  So  when  a  body 
containing  a  quantity  of  positive  electricity  is  touched  with  a  body 
possessing  an  equivalent  quantity  of  negative  electricity,  a  neutral  or  zero 
state  is  produced. 

The  theory  of  Syinmer  assumes  that  every  substance  contains  an 
indefinite  quantity  of  a  subtle  imponderable  matter,  which  is  called  the 
electrical  fluid.  This  fluid  is  formed  by  the  union  of  two  fluids — the 
positive^  and  the  negative.  When  they  are  combined  they  neutralise  one 
another,  and  the  body  is  then  in  the  natural  or  neutral  state.  By  frictioh, 
and  by  several  other  means,  the  two  fluids  may  be  separated,  but  one  of 
them  can  never  be  excited  without  a  simultaneous  production  of  the  other. 
There  may,  however,  be  a  greater  or  less  excess  of  the  one  or  the  other  in 
any  body,  and  it  is  then  said  to  be  electrified  positively  or  negatively. 
As  in  Franklin's  theory,  vitreous  corresponds  to  positive,  and  resinous  to 
negative  electricity.  This  distinction  is  merely  conventional :  it  is  adopted 
for  the  sake  of  convenience,  and  there  is  no  other  reason  why  resinous 
electricity  should  not  be  called  positive  electricity. 

Fluids  of  the  same  name  repel  one  another,  and  fluids  of  opposite  kinds 
attract  each  other.  The  fluids  can  circulate  freely  on  the  surface  of  cer- 
tain bodies,  which  are  called  conductors,  but  remain  confined  to  certain 
parts  of  others,  which  are  called  non-conductors. 

It  must  be  added  that  this  theory  is  quite  hypothetical ;  but  its  general 
adoption  is  justified  by  the  convenient  explanation  which  it  gives  of  elec- 
trical phenomena. 

688.  Action  of  electrified  bodies  on  each  other. — Admitting  the 
two-fluid  hypothesis,  the  phenomena  of  attraction  and  repulsion  may  be 
enunciated  in  the  following  law,  which  is  the  basis  of  all  the  theories  of 
frictional  electricity : 

D  D 


6o2  Frictional  Electricity.  *       [688- 

Two  bodies  charged  with  the  same  electricity  repel  each  other  ;  two 
bodies  charged  with  opposite  electricities  attract  each  other. 

These  attractions  and  repulsions  take  place  in  virtue  of  the  action 
which  the  two  electricities  exert  on  themselves,  and  not  in  virtue  of  their 
action  on  the  particles  of  matter. 

'689.  Kawof  the  development  of  electricity  by  friction. — Whenever 
two  bodies  are  rubbed  together,  the  neutral  electricity  is  decomposed. 
Two  electricities  are  developed  at  the  same  time  and  in  equal  quantities 
— one  body  takes  the  positive,  and  the  other  the  negative  electricity. 
This  may  be  proved  by  the  following  simple  experiment  devised  by  Fara- 
day : — A  small  flannel  cap  provided  with  a  silk  thread  is  fitted  on  the  end 
of  a  stout  rod  of  shellac,  and  rubbed  round  a  few  times.  When  the  cap  is 
removed  by  means  of  a  silk  thread,  and  presented  to  a  pith-ball  pendulum 
charged  with  positive  electricity,  the  latter  will  be  repelled,  proving  that 
the  flannel  is  charged  with  positive  electricity;  while,  if  the  shellac  is 
presented  to  the  pith  ball,  it  will  be  attracted,  showing  that  the  shellac  is 
charged  with  negative  electricity.  Both  electricities  are  present  in  equal 
quantities  :  for  if  the  rod  be  presented  to  the  electroscope  before  re- 
moving the  cap,  no  action  is  observed. 

The  electricity  developed  on  a  body  by  friction  depends  on  the  rubber 
as  well  as  the  body  rubbed.  Thus  glass  becomes  negatively  electrified 
when  rubbed  with  cat's  skin,  but  positively  when  rubbed  with  silk.  In 
the  following  list  the  substances  are  arranged  in  such  an  order  that  each 
becomes  positively  electrified  when  rubbed  with  any  of  the  bodies  fol- 
lowing, but  negatively  when  rubbed  with  any  of  those  which  precede  it  : — 


I. 

Cat's  skin. 

9.  Wood. 

2. 

Flannel. 

10.  Metals. 

3. 

Ivory. 

II.  Caoutchouc. 

4- 

Rock  crystal. 

12.  Sealing-wax. 

5. 

Glass. 

13.  Resin. 

6. 

Cotton. 

14.  Sulphur. 

7. 

Silk. 

15.  Gutta  percha. 

8. 

The  hand. 

16.  Gun-cotton. 

The  nature  of  the  electricity  set  free  by  the  friction  depends  also  on  tbe 
degree  of  polish,  the  direction  of  the  friction,  and  the  temperature.  If 
two  glass  discs  of  different  degrees  of  polish  are  rubbed  against  each 
other,  that  which  is  most  polished  is  positively,  and  that  which  is  least 
polished  is  negatively  electrified.  If  two  silk  ribbons  of  the  same  kind 
are  rubbed  across  each  other,  that  which  is  transversely  rubbed  is  nega 
tively,  and  the  other  positively  electrified.  If  two  bodies  of  the  same  sub- 
stance, and  of  the  same  polish,  but  of  different  temperatures,  are  rubbed 
^  together,  that  which  is  most  heated  is  negatively  electrified.  Generally 
t  speaking,  the  particles  which  are  most  readily  displaced  are  negatively 
electrified. 

690.  Development  of  electricity  by  pressure  and  cleavagre. — 
Electrical  excitement  may  be  produced  by  other  causes  than  friction.  If 
a  disc  of  wood,  covered  with  oiled  silk,  and  a  metal  disc,  each  provided 


-691]  Pyroelectricity.  603 

with  an  insulating  handle,  be  pressed  together,  and  then  suddenly  sepa- 
rated, the  metal  disc  is  negatively  electrified.  A  crystal  of  Iceland  spar 
pressed  between  the  fingers  becomes  positively  electrified,  and  retains 
this  state  for  some  time.  The  same  property  is  observed  in  several  other 
minerals,  even  though  conductors,  provided  they  be  insulated.  If  cork 
and  caoutchouc  be  pressed  together,  the  first  becomes  positively,  and  the 
other  negatively  electrified.  A  disc  of  wood  pressed  on  an  orange  and 
separated,  carries  away  a  good  charge  of  electricity,  if  the  contact  be 
rapidly  interrupted.  But  if  the  disc  is  slowly  removed  the  quantity  is 
smaller,  for  the  two  fluids  recombine  at  the  moment  of  their  separation. 
For  this  reason  there  is  no  apparent  effect  when  the  two  bodies  pressed 
together  are  good  conductors. 

Cleavage  also  is  a  source  of  electricity.  If  a  plate  of  mica  be  rapidly 
split  in  the  dark,  a  slight  phosphorescent  light  is  perceived.  Becquerel 
fixed  glass  handles  to  each  side  of  a  plate  of  mica,  and  then 
rapidly  separated  them.  On  presenting  each  of  the  plates  thus  separated 
to  an  electroscope,  he  found  that  one  was  negatively  and  the  other  posi- 
tively electrified. 

All  badly  conducting  crystalline  substances,  exhibit  electrical  in- 
dications by  cleavage.  The  separated  plates  are  always  in  opposite 
electrical  conditions,  provided  they  are  not  good  conductors :  for  if 
they  were,  the  separation  would  not  be  sufficiently  rapid  to  prevent 
the  recombination  of  the  two  electricities.  To  the  phenomena  here 
described  is  due  the  luminous  appearance  seen  in  the  dark  when  sugar 
is  broken. 

691.  Pyroelectricity. — Certain  minerals,  when  warmed,  acquire,  elec- 
trical properties ;  a  phenomenon  to  which  the  name  Pyroelectricity  is 
given.  It  is  best  studied  in  tourmaline  in  which  it  was  first  discovered, 
from  the  fact  that  this  mineral  has  the  power  of  first  attracting  and  then 
repelling  hot  ashes  when  placed  among  them. 

To  observe  this  phenomenon,  a  crystal  of  tourmaline  is  suspended  hori- 
zontally by  a  silk  thread,  in  a  glass  cylinder  placed  on  a  heated  metal  plate. 
On  subsequentlyinvestigatingtheelectric  condition  of  the  endsby  approach- 
ing to  them  successively  an  electrified  glass  rod,  one  end  will  be  found  to  be 
positively  electrified,  and  the  other  end  negatively  electrified,  and  each 
end  shows  this  polarity  as  long  as  the  temperature  rises.  The  arrange- 
ment of  the  electricity  is  thus  like  that  of  the  magnetism  in  a  magnet. 
The  points  at  which  the  intensity  of  free  electricity  is  greatest  are  called 
ihe  poles,  and  the  line  connecting  them  is  the  electric  axis.  When  a 
tourmahne,  while  thus  electrified,  is  broken  in  the  middle,  each  of  the 
pieces  has  its  two  poles. 

These  polar  properties  depend  on  the  change  of  temperature.  When 
a  tourmaline,  which  has  become  electrical  by  being  warmed,  is  allowed 
to  cool  regularly,  it  first  loses  electricity,  and  then  its  polarity  becomes 
reversed  ;  that  is,  the  end  which  was  positive  now  becomes  negative,  and 
that  which  was  negative  becomes  positive,  and  the  position  of  the  poles 
now  remains  unchanged  so  long  as  the  temperature  sinks.  Tourmaline 
only  becomes  pyroelectric  within  certain  limits  of  temperature;  these 


6o4 


Frictional  Electricity. 


\m\- 


vary  somewhat  with  the  length,  but  are  usually  between  io°  and  150°  C. 
Below  and  above  these  temperatures  it  behaves  like  any  other  body,  and 
shows  no  polarity. 

The  name  analogous  pole  is  given  to  that  end  of  the  crystal  which 
shows  positive  electricity  when  the  temperature  is  rising,  and  negative 
electricity  when  it  is  sinking :  antilogous  pole  to  that  end  which  becomes 
negative  by  being  heated,  and  positive  by  being  cooled. 

The  phenomena  of  pyroelectricity  are  intimately  connected  with  the 
crystaUine  form  of  the. mineral;  and  are  only  seen  in  those  crystals  whose 
forms  are  hemihedral,  or  which  are  differently  modified  at  the  ends  of 
their  crystallographical  principal  axis. 

Besides  tourmaline,  the  following  minerals  are  found  to  be  pyroelectric  : 
boracite,  topaz,  prehnite,  silicate  of  zinc,  scolezite,  axenite.  And  the 
following  organic  bodies  are  pyroelectric :  cane-sugar,  Pasteur's  salt 
(racemate  of  sodium  and  ammonium),  tartrate  of  potassium,  &c. 


CHAPTER    II. 

QUANTITATIVE   LAWS   OF   ELECTRICAL   ACTION. 

692.  Ziaws  of  electrical  attractions  and  repulsions. — The  laws 
which  regulate  the  attractions  and  repulsions  of  electrified  bodies  may  be 
thus  stated  : — 

I.  The  repulsiotis  or  attractions 
between  two  electrified  bodies  are  in 
the  inverse  ratio  of  the  squares  of  their 
distance. 

II.  The  distance  remaining  the 
same,  the  force  of  attraction  or  repul- 
sion between  two  electrified  bodies  is 
directly  as  the  product  of  the  quantities 
of  electricity  with  which  they  are 
charged. 

These  laws  were  established  by 
Coulomb,  by  means  of  the  torsion 
balance,  used  in  determining  the  laws 
of  magnetic  attractions  and  repulsions 
(666),  modified  in  accordance  with  the 
requirements  of  the  case.  The  wire, 
on  the  torsion  of  which  the  method 
depends,  is  so  fine  that  a  foot  weighs 
only  Y^y  of  a  grain.  At  its  lower  ex- 
tremity there  is  a  fine  shellac  thread, 
n  p  (fig.  533),  at  one  end  of  which  is 
a  small  disc  of  copper  foil,  n.  Instead 
of  the  vertical  magnetic  needle,  there  is  a  glass  rod,  ?',  terminated  by  a  gilt 
pith  ball,  w,  which  passes  through  the  aperture  r.     The  scale,  o  Cj  is  fixed 


Fig.  533- 


-692]    ^       Quantitative  Laws  of  Electrical  Action.  605 

round  the  sides  of  the  vessel,  and  during  the  experiment  the  ball  in  is 
opposite  the  zero  point,  0.  The  micrometer  consists  of  a  small  graduated 
disc,  e,  movable  independently  of  the  tube,  d,  and  of  a  fixed  index,  a, 
which  shows  by  how  many  degrees  the  disc  is  turned.  In  the  centre  of 
the  disc  there  is  a  small  button,  /,  to  which  is  fixed  the  wire  which  sup- 
ports 7lp. 

i.  The  micrometer  is  moved  until  the  zero  point  is  opposite  the  index, 
and  the  tube  d  is  turned  until  the  knob  ;/  is  opposite  zero  of  the  graduated 
circle  :  the  knob  m  is  in  the  same  position,  and  thus  presses  against  ;/. 
The  knob  m  is  then  removed  and  electrified,  and  replaced  in  the  appa- 
ratus, through  the  aperture  r.  As  soon  as  the  electrified  knob  in  touches 
n,  the  latter  becomes  electrified,  and  is  repelled,  and  after  a  few  oscil- 
lations remains  constant  at  a  distance  at  which  the  force  of  repulsion  is 
equal^to  the  force  of  torsion.  In  a  special  experiment  Coulomb  found  the 
angle  of  torsion  between  the  two  to  be  36° ;  and  as  the  force  of  torsion  is 
proportional  to  the  angle  of  torsion,  this  angle  represents  the  repulsive 
force  between  in  and  n.  In  order  to  reduce  the  angle  to  18°  it  was 
necessary  to  turn  the  disc  through  126°.  The  wire  was  twisted  126°  in  the 
direction  of  the  arrow  at  its  upper  extremity,  and  18°  in  the  opposite 
direction  at  its  lower  extremity,  and  hence  there  was  a  total  torsion  of 
144°.  On  moving  the  micrometer  in  the  same  direction,  until  the  angle 
of  deviation  was  8^°,  567°  of  torsion  were  necessary.  Hence  the  whole 
torsion  was  575|°.  Without  sensible  error  these  angles  of  deviation  may 
be  taken  at  36°,  18°,  and  9°,  and  on  comparing  them  with  the  correspond- 
ing angles  of  torsion  36°,  144^,  and  576^,  we  see  that  while  the  first  arc  as 

the  latter  are  as 

I  :  4 :  16;  / 

that  is,  that  for  a  distance  ^  as  great,  the  angle  of  torsion  is  4  times  as 
great,  and  that  for  a  distance  \  as  great  the  repulsive  force  is  J  6  times 
as  great. 

In  experimenting  with  this  apparatus,  the  air  must  be  thoroughly  dry, 
in  order  to  diminish,  as  far  as  possible,  loss  of  electricity.  This  is 
effected  by  placing  in  it  a  small  dish  containing  chloride  of  calcium. 

The  experiments  by  which  the  law  of  attraction  is  proved  are  made  in 
much  the  same  manner,  but  the  two  balls  are  charged  with  opposite 
electricities.  A  certain  quantity  of  electricity  is  imparted  to  the  move- 
able ball,  by  means  of  an  insulated  pin,  and  the  micrometer  moved  until 
there  is  a  certain  angle  below.  A  charge  of  electricity  of  the  opposite 
kind  is  then  imparted  to  the  fixed  ball.  The  two  balls  tend  to  move 
together,  but  are  prevented  by  the  torsion  of  the  wire,  and  the  movable 
ball  remains  at  a  distance  at  which  there  is  equilibrium  between  the 
force  of  attraction,  which  draws  the  balls  together,  and  that  of  torsion, 
which  tends  to  separate  them.  The  micrometer  s(^rew  is  then  removed 
to  a  greater  distance,  by  which  more  torsion  and  a  greater  angle  between 
the  two  balls  are  produced.  And  it  is  from  the  relation  which  exists 
between  the  angle  of  deflection  on  the  one  hand,  and  the  angle  which 
expresses  the  force  of  torsion  on  the  other,  that  the  law  of  attraction  has 
been  deduced. 


6o6 


Frictional  Electricity. 


[692 


ii.  To  prove  this  second  law  let  a  charge  be  imparted  to  m  ;  ii  being 
in  contact  with  it  becomes  charged  and  is  repelled  to  a  certain  distance. 
The  angle  of  deflection  being  noted,  let  the  ball  vi  be  touched  by  an 
insulated  but  unelectrified  ball  of  exactly  the  same  size  and  kind  ;  in  this 
way  half  its  charge  is  removed,  and  the  angle  of  deflection  will  now  be 
found  to  be  only  half  its  original  amount.  In  like  manner  if  either  m  or 
the  movable  body  be  now  again  deprived  of  half  its  electricity  the 
deflection  will  be  a  quarter  of  what  it  originally  was,  and  so  on. 

The  two  laws  are  included  in  the  formula  Y  =      -,  where  F  is  the  force: 

d~ 

e  and  e'  the  quantities  of  electricity  on  any  two  surfaces,  and  d  the  distance 
between  them.  If  e  and  e'  are  of  opposite  electricities  the  action  is  one 
of  attraction,  while  if  they  are  the  same  it  is  a  repulsive  action. 

693.  Bistribution  of  electricity. — When  an  insulated  sphere  of  con- 
ducting material  is  charged  with  electricity,  the  electricity  passes  to 
the  surface  of  the  sphere,  and  forms  an  extremely  thin  layer.  If,  in 
Coulomb's  balance,  the  fixed  ball  be  replaced  by  another  electrified 
sphere,  a  certain  repulsion  will  be  observed.  If  then  this  sphere  be 
touched  with  an  insulated  sphere  identical  with  the  first,  but  in  the 
neutral  state,  the  first  ball  will  be  found  to  have  lost  half  its  electricity, 
and  only  half  the  repulsion  will  be  observed.  By  repeating  this  experi- 
ment with  spheres  of  various  substances,  solid  and  hollow,  but  all  having 
the  same  superficies,  the  result  will  be  the  same,  excepting  that  with 
imperfectly  conducting  materials,  the  time  required  for  the  distribution 
will  be  greater.  From  this  it  is  concluded  that  the  distribution  of  elec- 
tricity depends  on  the  extent  of  the  surface,  and  not  on  the  mass,  and, 
therefore,  that  electricity  does  not  penetrate 
into  the  interior,  but  is  confined  to  the  sur- 
face. This  conclusion  is  further  established 
by  the  following  experiments  : — 

i.  A  thin  hollow  copper  sphere  provided 
with  an  aperture  of  about  an  inch  in  diameter 
(fig.  534),  and  placed  on  an  insulating  support, 
is  charged  in  the  interior  with  electricity. 
When  the  carrur  or  proof  pla7ie  (a  small 
disc  of  copper  foil  at  the  end  of  a  slender 
glass  or  shellac  rod)  is  applied  to  the  in- 
terior, and  is  then  brought  near  an  electro- 
scope, no  electrical  indications  are  produced. 
But  if  the  proof  plane  is  applied  to  the 
electroscope  after  having  been  in  contact 
with  the  exterior,  a  considerable  divergence 
ensues. 

The  action  of  the  proof  plane  as  a 
measure  of  the  quantity  of  electricity  is  as 
follows :  W^hen  it  touches  any  surface  the 
proof  plane  becomes  confounded  with  the  element  touched;  it  takes  in 
some   sense  its  place  relatively  to  the  electricity,  or  rather,  it  becomes 


Fig.  534- 


-693] 


Distribution  of  Electricity. 


607 


itself  the  element  on  which  the  electricity  is  diffused.     Thus  when  the 
proof  plane  is  removed  from  contact  we  have  in  effect  cut  away  from  the 


Fig-  535- 


surface  an  element  of  the  same  thickness  and  the  same  extent  as  its  own, 
and  have  transferred  it  to  the  balance  without  its  losing  any  of  the  elec- 
tricitv  which  covered  it. 


6o8 


Frictional  Electricity 


[693 


ii.  A  hollow  globe,  fixed  on  an  insulating  support,  is  provided  with 
two  hemispherical  envelopes  which  fit  closely,  and  can  be  separated  by- 
glass  handles.  The  interior  is  now  electrified,  and  the  two  hemispheres 
brought  in  contact.  On  then  rapidly  removing  them  (fig.  535)  the 
coverings  will  be  found  to  be  electrified,  while  the  sphere  is  in  its  natural 
condition. 

iii.  The  distribution  of  electricity  on  the  surface  may  also  be  shown  by 
means  of  the  following  apparatus.  It  consists  of  a  metallic  cylinder  on 
insulated  supports,  on  which  is  fixed  a  long  strip  of  tin  foil  which  can  be 
rolled  up  by  means  of  a  small  insulating  handle  (fig.  536).  A  quadrant 
electrometer  is  fitted  in  metallic  communication  with  the  qylinder.  When 
the  sphere  is  rolled  up,  a  charge  is  imparted  to  the  cylinder,  by  which  a 
certain  divergence  is  produced.  On  unrolling  the  tin  foil,  this  divergence 
gradually  diminishes,  and  increases  as  it  is  again  rolled  up.  The  quantity 
of  electricity  remaining  the  same,  the  electrical  force,  on  each  unit  of 
surface,  is  therefore  less  as  the  surface  is  greater. 

iv.  The  following  ingenious  experiment  by  Faraday  further  illustrates 
this  law  : — A  metal  ring  is  fitted  on  an  insulated  support,  and  a  conical 
gauze  bag,  such  as  is  used  for  catching  butterflies,  is  fitted  to  it  (fig.  537). 
By  means-  of  a  silk-thread,  the  bag  can  be 
drawn  inside  out.  After  electrifying  the  bag, 
it  is  seen  by  means  of  a  proof  plane  that  the 
electricity  is  on  the  exterior,  but  if  the  posi- 
tions are  reversed  by  drawing  the  bag  in- 
side out,  so  that  the  interior  has  now  become 
the  exterior,  the  electricity  will  still  be  found 
on  the  exterior. 

V.  The  same  point  may  be  further  illus- 
trated by  an  experiment  due  to  Terquem.  A 
bird  cage,  preferably  of  metal  wire,  is  sus- 
pended by  insulators,  and  contains  either  a 
gold  leaf  electroscope  or  pieces  of  Dutch 
metal,  feathers,  pith  balls,  etc.  When  the 
cage  is  connected  with- an  electrical  machine, 
the  articles  in  the  interior  are  quite  un- 
Flg.  537-  affected,    although    strong    'sparks   may   be 

taken  from  the  outside.  Bands  of  paper  may  be  fixed  to  the  inside  ; 
while  those  fixed  to  the  outside  diverge  widely.  A  bird  in  the  inside  is 
quite  unaffected  by  the  charge  or  discharge  of  the  electricity  of  the  cage. 
The  property  of  electricity,  of  accumulating  on  the  outside  of  bodies,  is 
ascribed  to  the  repulsion  which  the  particles  exert  on  each  other. 
Admitting  the  hypothesis  of  two  fluids,  and  that  opposite  electricities 
attract  each  other  in  the  inverse  ratio  of  their  distances,  while  like  elec- 
tricities repel  one  another  according  to  the  same  law,  Poisson,  by  the  aid 
of  mathematical  analysis,  has  arrived  at  the  same  conclusion  in  reference 
to  the  distribution  of  electricity  on  bodies  as  that  which  follows  from  the 
previous  experiments.  Electricity  tends  constantly  to  pass  to  the  surface 
of  bodies,  where  it  exists  in  very  thin  layers  ;  it  continually  tends  to 


-694] 


Electric  Density. 


609 


escape,  but  is  prevented  by  the  resistance  of  the  feebly  conducting  atmos- 
phere. 

694.  Electric  density.— On  a  metalHc  sphere  the  distribution  of  the 
electricity  will  be  uniform  in  every  part,  simply  from  its  symmetry. 
This  has  been  demonstrated  by  means  of  the  prpof  plane  and  the 
torsion  balance.  A  metallic  sphere  placed  on  an  insulating  support 
was  electrified,  and  touched  at  different  parts  of  its  surface  with  the 
proof  plane,  which  each  time  was  applied  to  the  movable  needle  of 
the  torsion  balance.  As  in  all  cases  the  torsion  observed  was  sensibly 
the  same,  it  was  concluded  that  the  proof  plane  had  each  time  received 
the  same  quantity  of  electricity.  In  the  case  of  an  elongated  ellipsoid 
(fig-  538)  it  is  found  that  the  distribution  of  electricity  is  different  at 


Fig-  538. 

different  points  of  the  surface.  The  electricity  accumulates  at  the  most 
acute  points.  This  is  demonstrated  by  successively  touching  the  elHpsoid 
at  different  parts  with  the  proof  plane,  and  then  bringing  this  into  the  torsion 
balance.  By  this  means  Coulomb  found  that  the  greatest  deflection  was 
produced  when  the  proof  plane  had  been  in  contact  with  the  point  a,  and 
the  least  by  contact  with  the  middle  space  e.  Laplace  has  found  by  calcula- 
tion that  the  iension  2i\.  G3.c\i  ^omt  \s  pi'oportional  to  the  sq^uare  of  the  thick- 
ness of  the  electric  layer. 

The  electric  density  or  electric  thickness  is  the  term  used  to  express 
the  quantity  of  electricity  found  at  any  moment  on  a  given  surface.  If  s 
represents  the  surface  and  Q  the  quantity  of  electricity  on  that  surface, 
then,  assuming  that   the   electricity  is  equally  distributed,  its  electrical 

density  is  equal  to  -^. 
s 

Coulomb  found,  by  quantitative  experiments,  that  tn  an  ellipsoid  the 

density  of  the  electricity  at  the  equator  of  the  ellipsoid  is  to  that  at  the 

ends,  in  the  same  ratio  as  the  length  of  the  minor  to  the  major  axis.     On 

an  insulated  cylinder,  terminated  by  two  hemispheres,  the  density  of  the 

electrical  layer  at  the  ends  is  greater  than  in  the  middle.     In  one  case, 

D  D  3 


6io  Friciiojial  Electricity.  [694- 

the  ratio  of  the  two  densities  was  found  to  be  as  2-3  :  i.     On  a  circular 
disc  the  density  is  greatest  at  the  edges. 

The  terms  electric  detisity  and  electrical  tension  are  often  confounded. 
The  latter  ought  rather  to  be  restricted,  as  Maxwell  proposes,  to  express 
the  state  of  strain  or  pressure  exerted  upon  a  dielectric  in  the  neighbour- 
hood of  an  electrified  body ;  a  strain  which  if  continually  increased  tends 
to  disruptive  discharge.  Electric  tension  may  thus  be  compared  to  the 
strain  on  a  rope  which  supports  a  weight,  and  the  dielectric  medium 
which  can  support  a  certain  tension  and  no  more,  is  said  to  have  a  certain 
strength  in  the  same  sense  as  a  rope  which  bears  a  certain  weight  with- 
out breaking,  is  said  to  have  a  certain  strength, 

695.  Power  of  points. — On  a  sphere,  the  electric  density  is  every- 
where uniform ;  the  further  a  body  is  removed  from  the  shape  of  a  sphere, 
the  more  irregular  is  its  accumulation.  A  pointed  rod  may  be  regarded 
as  an  elongated  ellipsoid,  and  hence,  at  its  extremity,  the  electric  density 
will  be  greatest.  But  the  greater  the  density,  the  greater  will  be  the 
tendency  of  electricity  to  overcome  the  resistance  of  the  air,  and  escape. 
If  the  hand  be  brought  near  a  point  on  an  electrified  conductor  a  slight 
wind  is  felt ;  and  if  the  disengagement  of  electricity  takes  place  in  the 
dark  a  luminous  brush  is  seen.  In  electrical  apparatus,  and  experiments, 
frequent  use  is  made  of  this  property  of  points. 

696.  Coxninunication  and  distribution  of  electricity  on  bodies  in 
contact. — If  two  conducting  bodies,  one  electrified  and  the  other  in  the 
natural  state,  be  brought  into  contact,  the  electricity  will  be  equally  dis- 
tributed over  the  two :  the  one  will  lose  and  the  other  gain  a  quantity  of 
electricity  proportional  to  its  surface.  If  the  bodies  are  not  conductors, 
there  will  only  be  loss  and  gain  at  the  points  in  contact. 

By  means  of  the  proof  plane  and  the  torsion  balance.  Coulomb  made 
numerous  determinations  of  the  distribution  of  electricity  on  bodies  in 
contact.  When  two  insulated  metal  spheres  were  placed  in  contact  and 
electrified,  he  found  that  the  electricity  was  unequally  distributed,  and 
that  in  proportion  to  their  diameters.  The  diameters  being  equal,  the 
electrical  density  was  zero  at  the  point  of  contact,  and  only  became 
sensible  at  23°  from  this  point;  it  increased  rapidly  from  20°  to  30°,  then 
more  slowly  from  60°  to  90°,  and  was  almost  constant  between  90°  and  180°. 

When  the  diameters  were  unequal,  and  in  the  ratio  of  2  :  i,  the  density 
of  the  point  of  contact  was  still  zero,  but  at  first  increased  most  rapidly 
on  the  large  sphere  :  it  then  increased  more  rapidly  on  the  small  one, 
and  at  180°  from  the  point  of  contact  its  density  was  greatest  on  the 
small  one. 

697.  Xioss  of  electricity. — Experience  shows  that  electrified  bodies 
gradually  lose  their  electricity,  even  when  placed  on  insulating  supports. 
This  loss  is  due  to  two  causes  :  firstly,  to  the  irhperfection  of  the  insulating 
supports,  and,  secondly,  to  the  conductivity  of  the  air. 

i.  All  substances  conduct  electricity  in  some  degree ;  those  which  are 
termed  insulators  are  simply  very  bad  conductors.  An  electrified  con- 
ductor resting  on  supports  must,  therefore,  lose  a  certain  quantity  of  its 
electricity. 


- 6 9 8 J  Loss  of  Electricity.  6 1 1 

ii.  The  loss  by  the  atmosphere  varies  with  the  electric  density,  with 
the  rapidity  with  which  the  air  is  renewed,  and  with  the  hygrometric 
state. 

Dry  air  is  a  very  imperfect  conductor,  but  when  it  contains  aqueous 
vapour,  it  conducts  pretty  well,  and  the  more  moisture  it  contains  the 
better  it  conducts.  Coulomb  has  attempted  to  show '  that  in  a  still  atmo- 
sphere, and  with  a  constant  hygrometric  state,  the  loss  for  a  very  short 
space  of  time  is  directly  proportional  to  the  tension  :'  a  law  analogous  to 
Newton's  law  of  cooling  (389). 

Coulomb  experimented  with  moist  air.  In  perfectly  dry  gases,  Mat- 
teucci  did  not  find  the  loss  of  electricity  in  accordance  with  Coulomb's 
law.  He  found  that  within  certain  limits,  the  loss  was  independent  of 
the  quantity  of  electricity,  and  proportional  to  the  time ;  in  other  words, 
that  in  equal  times  there  was  an  equal  loss  of  electricity. 

He  further  found  that  for  equal  temperatures  and  pressures  the  loss  is 
the  same  in  air,  carbonic  acid,  and  hydrogen,  provided  they  are  perfectly 
dry :  at  a  high  tension  the  loss  of  negative  electricity  is  greater  than  that 
of  positive ;  in  dry  gases,  under  a  constant  pressure,  the  loss  increases 
with  the  temperature  ;  and  lastly,  that  in  dry  gases  the  loss  is  independent 
of  the  nature  of  the  electrified  body ;  that  is,  it  is  the  same  whether  it  is  a 
conductor  or  not. 

Coulomb  found  not  only  that  supports  never  insulate  completely,  but 
that  they  are  the  cause  of  an  abundant  loss  of  electricity  in  bodies  strongly 
electrified.  The  loss  diminishes  gradually ;  it  is  constant  when  the  ten- 
sion is  low,  and  may  be  neglected  by  giving  to  the  supports  an  adequate 
length.  Brown  shellac  is  the  best  insulator;  glass  is  a  hygroscopic 
substance,  and  must  be  dried  with  great  care.  It  is  best  covered  with  a 
thin  layer  of  shellac  varnish,  as  has  already  been  stated. 

698.  Iioss  of  electricity  in  vacuo. — Inasmuch  as  electricity  is  retained 
on  the  surface  of  bodies  by  the  pressure  of  the  insulating  atmosphere, 
w^hen  the  pressure  diminishes,  the  loss  of  electricity  increases,  and  in 
an  ordinary  vacuum  all  electricity  escapes.  This  is  a  necessary  con- 
sequence of  the  mathematical  theory  of  electricity  (693),  which  accounts  for 
the  equilibrium  of  electricity  on  the  surface  of  bodies.  But  in  opposition 
to  this,  Hawksbee,  Cray,  Snow  Harris,  and  Becquerel  have  observed,  that 
feeble  electrical  charges  may  be  retained  in  vacuo.  Becquerel  showed 
that  in  a  vacuum  of  a  millimetre  a  body  retained  a  feeble  charge  for 
fifteen  days,  and  considers  it  is  probable,  that  if  an  electrified  body  were 
in  a  perfect  vacuum,  it  would  retain  an  electrical  charge,  provided  it  were 
sufficiently  removed  from  any  body  which  could  exert  upon  it  an  inductive 
action  (699).  Gassiott  has  proved  that  in  a  vacuum  produced  by  chemical 
means,  which  is  the  most  perfect  attainable,  an  electrical  discharge  does 
not  pass  ;  and  at  present  it  is  considered  that  a  ponderable  medium  is 
necessary  for  the  propagation  of  electricity. 


6l2 


Frictioiial  Electricity. 


[699 


CHAPTER    III. 

ACTION    OF  ELECTRIFIED  BODIES   ON  BODIES   IN   THE   NATURAL   STATE. 
INDUCED    ELECTRICITY.      ELECTRICAL   MACHINES. 

699.  Slectrlclty  by  influence  or  Induction.— An  insulated  conductor, 
charged  with  either  kind  of  electricity,  acts  on  bodies  in  a  natural  state 
placed  near  it  in  a  manner  analogous  to  that  of  the  action  of  a  magnet 
on  soft  iron,  that  is,  it  decomposes  the  neutral  fluid,  attracting  the  oppo- 
site, and  repelling  the  like  kind  of  electricity.  The  action  thus  exerted 
is  said  to  take  place  by  inflice7ice  or  induction. 

The  phenomena  of  induction  may  be  demonstrated  by  means  of  a  brass 
cylinder  placed  on  an  insulating  support,  and  provided  at  its  extremities 
with  two  small  electric  pendulums,  which  consist  of  pith  balls  suspended 
by  linen  threads  (fig.  539).     If  this  apparatus  is  placed  near  an  insulated 


conductor  w,  charged  with  either  kind  of  electricity,  for  instance,  the 
conductor  of  an  electrical  machine,  which  is  charged  with  positive 
electricity,  the  natural  electricity  of  the  cylinder  is  decomposed,  free  elec- 
tricity will  be  developed  at  each  end,  and  both  pendulums  will  diverge. 
If,  while  they  still  diverge,  a  stick  of  sealing-wax,  excited  by  friction  with 
flannel,  be  approached  to  that  end  of  the  cylinder  nearest  the  conductor, 
the  corresponding  pith  ball  will  be  repelled,  indicating  that  it  is  charged 
with  the  same  kind  of  electricity  as  the  sealing-wax,  that  is,  with  negative 
electricity  ;  while  if  the  excited  sealing-wax  is  brought  near  the  other  ball 
it  will  be  attracted,  showing  that  it  is  charged  with  positive  electricity. 
If,  further,  a  glass  rod,  excited  by  friction  with  silk,  and  therefore  charged 
with  positive  electricity,  be  approached  to  the  end  nearest  the  conductor, 
the  pendulum  will  be  attracted  ;  while  if  brought  near  the  other  end,  the 
corresponding  pendulum  will  be  repelled.     If  the  influence  of  the  charged 


-699]  Electrical  Indiictio7i.  6 1 3 

conductor  be  suppressed,  either  by  removing  it,  or  placing  it  in  commu- 
nication with  the  ground,  the  separated  electricities  will  recombine,  and 
the  pendulums  exhibit  no  divergence. 

The  cause  of  this  phenomenon  is  obviously  a  decomposition  of 
the  neutral  electricity  of  the  cylinder,  by  the  free  positive  electricity  of 
the  conductor ;  the  opposite  or  negative  electricity  being  attracted  to 
that  end  of  the  cylinder  nearest  the  conductor,  while  the  similar  elec- 
tricity is  repelled  to  the  other  end.  Between  these  two  extremities, 
there  is  a  space  destitute  of  free  electricity.  This  is  seen  by  arranging 
on  the  cylinders  a  series  of  pairs  of  pith  balls  suspended  by  threads. 
The  divergence  is  greatest  at  each  extremity,  and  there  is  a  line  at 
which  there  is  no  divergence  at  all,  which  is  called  the  Jieutral  line. 
The  two  fluids,  although  equal  in  quantity,  are  not  distributed  over 
the  cylinder  in  a  symmetrical  manner  ;  the  attraction  which  accumu- 
lates the  negative  electricity  at  the  one  end  is,  in  consequence  of  the 
greater  nearness,  greater  than  the  repulsion  which  drives  the  positive 
electricity  to  the  other  end,  and  hence  the  neutral  line  is  nearer  one  end 
than  the  other.  Nor  is  the  electricity  induced  at  the  two  ends  of  the 
cylinder  under  the  same  conditions.  That  which  is  repelled  to  the 
distant  extremity  is  free  to  escape  if  a  communication  be  made  with  the 
ground,  whilst  on  the  other  hand,  the  unlike  electricity  which  is  attracted 
is  held  bound  or  captive  by  the  inducing  action  of  the  electrified  body. 
Even  if  contact  be  made  with  the  ground  on  the  face  of  the  cylinder 
adjacent  to  the  inducing  body,  the  electricity  induced  on  that  face  will 
not  escape.  The  repelled  electricity  however  on  the  distant  surface  is 
not  thus  bound;  it  is  free  to  escape  by  any  conducting  channel,  and 
hence  will  immediately  disappear,  wherever  contact  be  made  between  the 
ground  and  the  cylinder.  Both  the  pith  balls  will  collapse,  and  all  signs 
of  electricity  on  the  cylinder  depart  with  the  escape  of  the  repelled  or  free 
electricity.  But  now,  if  communication  with  the  ground  be  broken 
and  the  inducing  body  be  discharged  or  removed  to  a  considerable  dis- 
tance, the  attracted  or  bound  electricity  is  itself  set  free,  and  diffusing 
over  the  whole  cylinder  causes  the  pith  balls  again  to  diverge,  but  now 
with  the  opposite  electricity  to  that  of  the  original  inducing  body.  The 
reason  for  the  escape  of  the  repelled  electricity  is  as  follows  : — If  the 
cylinder  be  placed  in  connection  with  the  ground,  by  metallic  contact 
with  the  posterior  extremity,  and  the  charged  conductor  be  still  placed 
near  the  anterior  extremity,  the  conductor  will  exert  its  inductive  action 
as  before.  But  it  is  now  no  longer  the  conductor  alone  which  is  influ- 
enced. It  is  a  conductor  consisting  of  the  conductor  itself,  the  metalhc 
wire,  and  the  whole  earth.  The  neutral  line  will  recede  indefinitely,  and 
since  the  conductor  has  become  infinite,  the  quantity  of  neutral  fluid 
decomposed  will  be  increased.  Hence,  when  the  posterior  extremity  is 
placed  in  contact  with  the  ground,  the  pendulum  at  the  anterior  extremity 
diverges  more  widely.  If  the  connecting  rod  be  now  removed,  neither 
the  quantity  nor  the  distribution  will  be  altered  ;  and  if  the  conductor 
be  removed,  or  be  discharged,  a  charge  of  negative  electricity  will  be 
left  on  the  cylinder.     It  will,  in  fact,  remain  charged  with  electricity, 


6 1 4  Friction  a  I  Electricity,  [699- 

the  opposite  of  that  of  the  charged  conductor.  Even  if,  instead  of  con- 
necting the  posterior  extremity  of  the  cyhnder  with  the  ground,  any  other 
part  had  been  so  connected,  the  general  result  would  have  been  the  same. 
All  the  parts  of  the  cylinder  would  be  charged  with  negative  electricity, 
and,  on  interrupting  the  communication  with  the  earth,  would  remain  so 
charged. 

Thus  a  body  can  be  charged  with  electricity  by  induction  as  well  as  by 
conduction.  But,  in  the  latter  case,  the  charging  body  loses  part  of  its 
electricity,  which  remains  unchanged  in  the  former  case.  The  electricity 
imparted  by  conduction  is  of  the  same  kind  as  that  of  the  electrified 
body,  while  that  excited  by  induction  is  of  the  opposite  kind.  To  impart 
electricity  by  conduction,  the  body  must  be  quite  insulated,  while  in  the 
case  of  induction  it  must  be  in  connection  with  the  earth,  at  all  events 
momentaneously. 

A  body  electrified  by  induction  acts  in  turn  on  bodies  placed  near  it, 
separating  the  two  fluids  in  a  manner  shown  by  the  signs  on  the  sphere. 

What  has  here  been  said  has  referred  to  the  inductive  action  exerted 
on  good  conductors.  Bad  conductors  are  not  so  easily  acted  upon  by 
induction,  owing  to  the  great  resistance  they  present  to  the  circulation  of 
electricity,  but,  when  once  charged,  the  electric  state  is  more  permanent. 

This  is  analogous  to  what  is  met  with  in  magnetism  ;  a  magnet  in- 
stantaneously evokes  magnetism  in  a  piece  of  soft  iron,  but  this  is  only 
temporary,  and  depends  on  the  continued  action  of  the  magnet ;  a  magnet 
magnetises  steel  with  far  greater  difficulty,  but  this  magnetism  is  per- 
manent. 

700.  Xiimit  to  the  action  of  induction. — The  inductive  action  which 
an  electrified  body  exerts  on  an  adjacent  body  in  decomposing  its  neutral 
fluid  is  limited.  On  the  surface  of  the  insulated  cylinder,  which  we  have 
considered  in  the  preceding  paragraph,  let  there  be  at  n  any  small  quan- 
tity of  neutral  electricity  (fig.  540).     The  positive  electricity  of  the  source 


y^         a 

Fig.  540^ 

m  first  decomposes  by  induction  the  neutral  electricity  in  7i,  attracting  its 
negative  towards  A,  and  repelling  positive  towards  B  ;  but  in  the  degree 
in  which  the  extremity  becomes  charged  with  negative  electricity,  and 
the  extremity  B  with  positive  electricity,  there  are  developed  at  A  and  B 
two  forces  /  and  /',  which  act  in  the  opposite  direction  to  the  original 
force.  For  the  forces /and/''  concur  in  driving  towards  B  the  negative 
fluid  of  n,  and  towards  A  its  positive  fluid.  But  as  the  inducing  force  F 
which  is  exerted  at  m  is  constant,  while  the  forces /and/  are  increasing, 
a  time  arrives  at  which  the  force  F  is  balanced  by  the  forces  /  and  /'. 
All  decomposition  of  the  neutral  fluid  then  ceases  ;  the  inducing  action 
has  attained  its  limit. 


-702]  Electrical  Induction.  615 

If  the  cylinder  be  removed  from  the  source  of  electricity,  as  the 
inducing  action  decreases,  a  portion  of  the  free  fluids  at  A  and  at  B 
recombine  to  form  the  neutral  fluid.  If,  on  the  other  hand,  they  are 
brought  nearer,  as  the  force  F  now  exceeds  the  forces  f  and  f'y  a  new 
decomposition  of  the  neutral  fluid  takes  place,  and  fresh  quantities  of 
positive  and  negative  fluids  are  respectively  accumulated  at  A  and  B. 

701.  Faraday's  theory  of  induction. — The  theory  of  electricity  by 
induction,  as  just  elucidated,  is  the  one  hitherto  admitted  by  all  physicists. 
The  researches  of  Faraday  on  electric  polarity  tend,  however,  to  modify 
it,  and  may,  perhaps,  lead  to  overturn  it  entirely.  Hitherto,  the  influence 
of  the  medium,  which  separates  the  electrified  from  the  unelectrified  body, 
has  been  neglected.  But  Faraday's  researches  prove  that  it  is  in  this 
medium  that  the  inductive  actions  take  place  ;  and  that  the  inductive 
action  is  not  an  action  at  a  distance,  or  rather  at  no  distance  greater  than 
that  between  any  two  molecules.  Faraday  supposes  that,  in  this  medium, 
successions  of  layers  become  alternately  positively  and  negatively  elec- 
trified. 

The  following  experiment  was  devised  by  Faraday  to  illustrate  this 
polai'isation  of  the  medium,  as  he  has  called  it.  He  placed  small 
filaments  of  silk  in  a  vessel  of  turpentine,  and  having  plunged  two  con- 
ductors in  the  liquid  in  opposite  sides,  he  charged  one  and  placed  the 
other  in  connection  with  the  ground.  The  particles  of  silk  immediately 
arranged  themselves  end  to  end,  and  adhered  closely  together,  forming 
a  continuous  chain  between  the  two  sides.  An  experiment  by  Matteucci 
also  supports  Faraday's  theory.  He  placed  several  thin  plates  of  mica 
closely  together,  and  provided  the  outside  ones  with  metallic  coatings, 
like  a  fulminating  pane  (724).  Having  electrified  the  system,  the  coatings 
were  removed  by  insulating  handles,  and  on  examining  the  plates  of  mica 
successively,  each  was  found  charged  with  positive  electricity  on  one 
side,  and  negative  electricity  on  the  other. 

On  the  new  view,  the  action  exerted  by  electrified  bodies  on  bodies  in 
the  neutral  state,  is  effected  by  the  polarisation  of  the  alternate  layers  of 
air  or  any  other  medium.  On  the  old  view,  the  air  was  supposed  to  be 
quite  passive,  or  at  most,  in  virtue  of  its  non-conductivity,  to  oppose  a 
resistance  to  the  recombination  of  the  two  fluids. 

Objections  have,  nevertheless,  been  raised  to  Faraday's  theory,  one  of 
the  most  formidable  of  which  is  the  action  which  electrified  bodies  exert 
on  others  at  a  distance  even  in  vacuo  ;  unless,  indeed,  it  be  admitted  that 
even  in  the  most  perfect  vacuum  obtainable,  sufficient  material  molecules 
remain  to  produce  the  polarisation  (698).  In  some  researches  which  Mat- 
teucci has  recently  made  on  the  propagation  of  electricity  in  insulators, 
he  has  arrived  at  conclusions  differing  from  those  of  Faraday. 

702.  Specific  inductive  capacity. — Faraday  names  the  property  which 
bodies  possess  of  transmitting  the  electric  influence,  the  inductive  power. 
All  insulating  bodies  do  not  possess  it  in  the  same  degree.  To  determine 
and  compare  the  inductive  power  Faraday  used  the  apparatus  represented 
in  fig.  541,  and  of  which  fig.  542  represents  a  vertical  section.  It  consists 
of  a  brass  sphere  made  up  of  two  hahes,  P  and  Q,  which  fit  accurately 


6i6 


Frictional  Electricity. 


[702 


into  each  other,  like  the  Magdeburg  hemispheres.  In  the  interior  of  this 
spherical  envelope,  there  is  a  smaller  brass  sphere,  C,  connected  with  a 
metal  rod,  terminating  in  a  ball,  B.  The  rod  is  insulated  from  the 
envelope  PQ,  by  a  thick  layer  of  shellac,  A.  The  space  mn  receives  the 
substance  whose  inductive  power  is  to  be  determined.  The  foot  of  the 
apparatus  is  provided  with  a  screw  and  stopcock,  so  that  it  can  be 
screAved  on  the  air  pump,  and  the  air  in  inn  either  rarefied  or  exhausted. 
Two  such  apparatus  perfectly  identical  are  used,  and  at  first  they  only 
contain  air.  The  envelopes  PQ  are  connected  with  the  ground,  and  the 
knob  B  of  one  of  them  receives  a.  charge  of  electricity.     The  sphere  C 


Fig-  541 


Fig.  542. 


thus  becomes  charged  like  the  inner  coating  of  a  Leyden  jar  (725).  The 
layer  inn  represents  the  insulator  which  separates  the  two  coatings.  By 
touching  B  with  the  proof  plane,  which  is  then  applied  to  the  torsion 
balance,  the  quantity  of  free  electricity  is  measured.  In  one  experiment 
Faraday  observed  a  torsion  of  250°,  which  represented  the  free  electricity 
on  B.  The  knob  B  was  then  placed  in  metallic  connection  with  the  knob 
B'  of  the  other  apparatus,  and  the  torsion  was  now  found  to  be  125°, 
showing  that  the  electricity  had  become  equally  distributed  on  the  two 
spheres,  as  might  have  been  anticipated,  since  the  pieces  of  apparatus 
w^ere  quite  equal  and  each  contained  air  in  the  space  inn. 

This  experiment  having  been  made,  the  space  mn  in  the  second  appa- 
ratus was  filled  with  the  substance  whose  inductive  power  was  to  be 
determined  ;  for  example,  shellac.  The  other  apparatus,  in  which  inn  is 
filled  with  air,  having  been  charged,  the  density  of  the  free  electricity  on 


- 703]  Electrical  Induction.  617 

C  was  measured.  Let  it  be  taken  at  290°,  the  number  observed  by  _ 
Faraday,  in  a  special  case.  When  the  knob  B  of  the  first  apparatus  was 
connected  with  the  knob  B'  of  the  second,  the  density  was  not  found  to 
be  145°,  as  would  be  expected.  The  apparatus  containing  air  exhibited  a 
density  of  1 14°,  and  that  with  shellac  of  113°  Hence  the  former  had  lost 
176°,  and  had  retained  114°,  while  the  latter  ought  to  have  exhibited  a 
density  of  176°  instead  of  113°.  The  second  apparatus  had  taken  more 
than  half  the  charge,  and  hence  a  larger  quantity  of  electricity  had  been 
dissimulated  by  the  shellac.  Of  the  total  quantity  of  electricity,  the 
shellac  had  taken  176°,  and  the  air  114°;  hence  the  specific  inductive 
capacity  of  air  is  to  that  of  shellac  as  114  :  176,  or  as  i  :  1*55.  That  is, 
the  inductive  power  of  shellac  is  more  than  half  as  great  again  as  air. 

Comparing  together  other  substances  by  this  general  method,  but 
varying  the  details,  the  following  values  have  been  obtained  for  the 
specific  inductive  capacity  oi  dielectrics,  as  they  are  called  in  opposition 
to  anelectrics  or  conductors  : — 

Air i-oo  Glass 1*90 

Spermaceti    .         .         .         •     i"45  Sulphur         .         .         .         .  i'93 

Resin 176  Shellac i*95 

Pitch I  80  India  Rubber        .         .         .  2-80 

Bees-wax      .         .         .         .1*86  Gutta  Percha         .         .         .  4*00 

By  the  following  simple  experiment  the  influence  of  the  dielectric  may 
be  shown.  At  a  fixed  distance  above  a  gold-leaf  electroscope,  let  an 
electrified  sphere  be  placed,  by  which  a  certain  divergence  of  the  leaves 
is  produced.  If  now,  the  charges  remaining  the  same,  a  disc  of  sulphur 
or  of  shellac  be  interposed,  the  divergence  increases,  showing  that  in- 
ductive action  takes  place  through  the  sulphur  to  a  greater  extent  than 
through  a  layer  of  air  of  the  same  thickness. 

Faraday  finds  that  all  gases  have  the  same  inductive  capacity,  and  that 
this  is  independent  of  the  temperature  and  pressure. 

703.  Communication  of  electricity  at  a  distance. —  In  the  experi- 
ment represented  in  figure  539  the  opposite  electricities  of  the  conductor, 
and  that  of  the  separated  cylinder,  tend  to  unite,  but  are  prevented  by 
the  resistance  of  the  air.  If  the  density  is  increased,  or,  if  the  distance  of 
the  bodies  be  diminished,  the  opposed  electricities  at  length  overcome 
this  obstacle ;  they  rush  together  and  combine,  producing  a  spark,  ac- 
companied by  a  sharp  sound.  The  negative  electricity  separated  on  the 
cylinder,  being  thus  neutralised  by  the  positive  electricity  of  the  charged 
body,  a  charge  of  positive  electricity  remains  on  the  cyhnder.  The  same 
phenomenon  is  observed  when  a  finger  is  presented  to  a  strongly  electri- 
fied conductor.  The  latter  decomposes  by  induction  the  neutral  electri- 
city of  the  body,  the  opposite  electricities  combine  with  the  production 
of  a  spark,  while  the  electricity  of  the  same  kind  as  the  electrified  con- 
ductor, which  is  left  on  the  body,  passes  off  into  the  ground. 

The  striking  distance  varies  with  the  density,  the  shape  of  the  bodies, 
their  conducting  power,  and  with  the  resistance  and  pressure  of  the  inter- 
posed medium. 


6i8  Frictiona I  Electricity.  [704- 

704.  Motion  of  electrified  bodies. — The  various  phenomena  of  at- 
traction and  repulsion  which  are  among  the  most  frequent  manifestations 

of  electrical  action  may  all  be  explained  by  means 
i\f  of  the  laws  of  induction.     If  M  (fig.  543)  be  a  fixed 

Cs.  ^  insulated  conductor  charged  with  positive  electri- 

\       ^-^     city,    and    N    be  a    movable-  insulated  body,   for 
/    '^iJ/^  instance,  an  electrical  pendulum,  there  are  three 
/  cases  to  be  considered  : — 

i.   The  movable  body  is  tmelectrijied^  and  is  a 
Fig.  543-  conductor.      In  this  case  M  acting  inductively  on 

N,  attracts  the  negative  and  repels  the  positive  electricity,  so  that  the  maxi- 
ma of  density  are  respectively  at  the  points  a  and  b.  Now  a  is  nearer  c 
than  it  is  to  b,  and  since  attractions  and  repulsions  are  inversely  as  the 
square  of  the  distance,  the  attraction  between  a  and  c  is  greater  than  the 
repulsion  between  b  and  c,  and,  therefore,  N  will  be  attracted  to  M  by  a 
force  equal  to  the  excess  of  the  attractive  over  the  repulsive  force. 

ii.  The  movable  body  is  a  conductor^  a7id  is  electrified. — I f  the  electricity 
of  the  movable  body  is  different  from  that  of  the  fixed  body,  there  is 
always  attraction,  but  if  they  are  of  the  same  kind,  there  is  at  first  re- 
pulsion and  afterwards  attraction.  This  anomaly  may  be  thus  explained  : 
Besides  its  charge  of  electricity,  the  movable  body  contains  neutral  fluid, 
This  is  decomposed  by  the  induction  of  the  positive  fluid  on  M,  and, 
consequently,  the  hemisphere  b  obtains  an  additional  supply  of  positive 
electricity,  while  a  becomes  charged  with  negative  electricity.  There  is 
thus  attraction  and  repulsion,  as  in  the  foregoing  case.  The  force  ot 
repulsion  is  at  first  greater,  because  the  quantity  of  positive  electricity  on 
N  is  greater  than  that  of  negative ;  but  as  the  distance  a  c  diminishes, 
the  attractive  force  increases  more  rapidly  than  the  repulsive  force,  and 
finally  exceeds  it. 

iii.  The  movable  body  is  a  bad  conductor. — If  N  is  charged,  repulsion 
or  attraction  takes  place,  according  as  the  electricity  is  of  the  same  or 
opposite  kind  to  that  of  the  fixed  body.  If  it  is  in  the  natural  state, 
since  a  powerful  and  permanent  source  of  electricity  can  more  or  less  de- 
compose the  neutral  fluid  even  of  bad  conductors,  the  body  M  will 
decompose  the  neutral  fluid  of  N,  and  attraction  will  take  place  as  in  the 
first  case. 

705.  Gold-leaf  electroscope. — The  name  electi'oscope  is  given  to 
instruments  for  detecting  the  presence,  and  determining  the  kind,  of 
electricity  in  any  body.  The  original  pith  ball  pendulum  is  an  electro- 
scope ;  but,  though  sometimes  convenient,  it  is  not  sufficiently  delicate. 
Many  successive  improvements  have  been  made  on  it,  and  have  resulted 
in  the  form  now  generally  used,  which  is  due  to  Bennett. 

Benjtett's,  or  the  gold-leaf  electroscope. — This  consists  of  a  tubulated 
glass  shade  B  (fig.  544),  standing  on  a  metal  foot,  which  thus  communi- 
cates with  the  ground.  A  metal  rod  terminating  at  its  upper  extremity  in 
a  knob  C,  and  holding  at  its  lower  end  two  narrow  strips  of  gold-leaf  n  n, 
fits  in  the  tubulure  of  the  shade,  the  neck  of  which  is  coated  with  an  insu- 
lating varnish.       The  air  in   the  inteiior  is  dried  by  quicklime,  or  by 


705] 


Electrical  Induction. 


619 


Fig  544- 


chloride  of  calcium,  and  on  the  insides  of  the  shade  there  are  two  strips 
of  gold  leaf  a  communicating  with  the  ground.  ^ 

When  the  knob  is  touched  with 
a  body  charged  with  either  kind 
of  electricity,  the  leaves  diverge ; 
usually,  however,  the  apparatus  is 
charged  by  induction  thus  : — 

If  an  electrified  body,  a  stick 
of  sealing  wax,  for  example,  be 
brought  near  the  knob,  it  will  de- 
compose the  natural  electricity  of 
the  system,  attracting  to  the  knob 
the  electricity  of  the  opposite  kind 
and  retaining  it  there,  and  repel- 
ling the  electricity  of  the  same 
kirtd  to  the  gold  leaves,  which 
consequently  diverge.  In  this 
way  the  presence  of  an  electrical 
charge  is  ascertained  but  not  its 
quality. 

To  ascertain  the  kmd  of  electricity  the  following  method  is  pursued  : — • 
If,  while  the  instrument  is  under  the  influence  of  the  body  A,  which  we 
will  suppose  has  a  negative  charge,  the  knob  be  touched  by  the  finger, 
the  negative  electricity  decomposed  by  induction  passes  off  into  the 
ground,  and  the  previously  divergent  leaves  will  collapse;  there  only 
remains  positive  electricity,  retained "  in  the  knob  by  induction  from  A. 
If  now  the  finger  be  first  removed,  and  then  the  electrified  body,  the 
positive  electricity  previously  retained  by  A  will  spread  over  the  system, 
and  cause  the  leaves  to  diverge.  If  now,  while  the  system  is  charged 
with  positive  electricity,  a  positively  electrified  body,  as,  for  example,  an 
excited  glass  rod,  be  approached,  the  leaves  will  diverge  more  widely  ; 
for  the  electricity  of  the  same  kind  will  be  repelled  to  the  extremities.  If, 
on  the  contrary,  an  excited  shellac  rod  be  presented,  the  leaves  will  tend 
to  collapse,  the  electricity,  with  which  they  are  charged,  being  attracted 
by  the  opposite  electricity.  Hence  we  may  ascertain  the  kind  of  electri- 
city, either  by  imparting  to  the  electroscope  electricity  from  the  body 
under  examination,  and  then  bringing  near  it  a  rod  charged  with  positive 
or  negative  electricity  ;  or  the  electroscope  maybe  charged  with  a  known 
kind  of  electricity,  and  the  electrified  body  in  question  brought  near  the 
electroscope. 

It  has  been  proposed  to  use  the  goldleaf  electroscope  as  an  electro- 
meter or  measurer  of  electricity,  by  measuring  the  angle  of  divergence  of 
the  leaves  ;  this  is  done  by  placing  behind  them  a  graduated  scale  ;  it  is 
said  that  for  small  angles  the  quantity  of  electricity  is  proportional  to  the 
sine  of  half  the  angle  of  deflection.  There  are,  however,  objections  to 
such  a  use,  and  the  electroscope  is  rarely  employed  for  this  purpose. 


620 


Frictioiial  Electricity. 


[706 


ELECTRICAL  MACHINES. 

706.  Electrophorus.— It  will  now  be  convenient  to  describe  tlie 
various  electrical  machines,  or  apparatus  for  generating  and  collecting 
large  supplies  of  statical  electricity.  One  of  the  most  simple  and  inex- 
pensive of  these  in  the  eleciropho7-tis,  which  was  invented  by  Volta.  Its 
operation,  like  that  of  all  other  electric  machines,  depends  on  the  action 
of  induction,  of  which  it  forms  an  excellent  illustration.  It  consists  of  a 
cake  of  resin,  B  (fig.  546),  say  about  12  inches  diameter,  and  an  inch 


Fig-  545. 


Fig.  546. 


thick,  which  is  placed  on  a  metallic  surface,  or  very  frequently  fits  in  a 
wooden  mould  lined  with  tinfoil,  which  is  called  the  form.  Resides 
this  there  is  a  metal  disc,  A  (fig.  546),  of  a  diameter  somewhat  less  than 
that  of  the  cake,  and  provided  with  an  insulating  glass  handle  ;  this  is 
the  cover.  The  mode  of  working  is  as  follows  :  All  the  parts  of  the  appa- 
ratus having  been  well  warmed,  the  cake,  which  is  placed  in  the  form,  or 
rests  on  a  metal  surface,  is  briskly  flapped  with  silk,  or,  better, 
with  catskin,  by  which  it  becomes  charged  with  negative  electricity. 
The  cover  is  then  placed  on  the  cake.  Owing,  however,  to  the  minute 
rugosities  of  the  surface  of  the  resin,  the  cover  only  comes  in  contact  with 
a  few  points,  and,  from  the  non-conductivity  of  the  resin,  the  negative 
electricity  of  the  cake  does  not  pass  off  to  the  cover.  On  the  contrary,  it 
acts  by  induction  on  the  neutral  electricity  of  the  cover,  and  decomposes 
it,  attracting  the  positive  electricity  to  the  under  surface,  and  repelling 
the  negative  electricity  to  the  upper  If  the  upper  surface  be  now 
touched  with  the  finger,  the  negative  electricity,  because  repelled  and 
free,  passes  off,  and  the  cover  remains  charged  with  positive  electricit}-, 
held,  however,  by  the  negative  electricity  of  the  cake  ;  the  two  electricities 
do  not  unite,  in  consequence  of  the  non-conductivity  of  the  cake  (fig.  545). 


-707]  Elcctrophonis.  62 1 

If  now  the  cover  be  raised  by  its  insulating  handle,  the  charge  diffuses 
itself  over  the  surface,  and,  if  a  conductor  be  brought  near  it,  a  smart 
spark  passes. 

The  metallic  form  on  which  the  cake  rests  plays  an  important  part 
in  the  action  of  the  electrophorus,  as  it  increases  the  quantity  of  elec- 
tricity, and  makes  it  more  permanent.  For  the  negative  electricity  of  the 
upper  surface  of  the  resin,  acting  inductively  on  the  neutral  electricity  of 
the  lower,  decomposes  it,  retaining  on  the  under  surface  the  positive  elec- 
tricity, while  the  negative  electricity  passes  off  into  the  ground.  The 
positive  electricity  thus  developed  on  the  under  surface  reacts  on  the 
negative  electricity  of  the  upper  surface,  binding  it,  and  causing  it  to 
penetrate  into  the  badly  conducting  mass,  on  thr.  surface  of  which  fresh 
quantities  of  electricity  can  be  excited,  far  beyond  the  limits  possible 
without  the  action  of  the  form.  It  is  for  this  reason  that  the  electro- 
phorus, once  charged,  retains  its  state  for  a  considerable  time,  and  sparks 
can  be  taken  from  it  everwafcer  a  long  interval.  If  the  form  be  insulated,  the 
charge  obtained  is  far  less  than  if  it  is  on  a  conducting  support.  For  the 
negative  electricity  developed  by  induction  on  the  lower  surface  being 
now  unable  to  escape,  the  condensing  action  referred  to  cannot  take 
place,  and  only  a  feeble  charge  can  be  given  to  the  resin.  The  retention 
of  electricity  is  greatly  promoted  by  keeping  the  cake  on  the  form,  and 
placing  the  cover  upon  it,  by  which  the  access  of  air  is  hindered.  Instead 
of  a  cake  of  resin,  a  disc  of  gutta  percha,  or  vulcanised  cloth,  or  vulcan- 
ite, may  be  substituted ;  and,  of  course,  if  glass,  or  any  material  which 
becomes  positively  electrified  by  friction,  be  used,  the  cover  acquires  a 
negative  charge. 

The  electrophorus  is  a  good  instance  of  the  conversion  of  work 
into  electro-potential  energy  (60).  When  the  cover  is  lifted  from  the 
excited  cake,  work  must  be  expended  in  order  to  overcome  the  attraction 
of  the  electricity  in  the  cake,  for  the  opposite  electricity  developed  by 
induction  on  the  cover;  and  the  equivalent  of  this  work  appears  in  the 
form  of  the  electricity  thus  detached.  Thus,  when  a  Leyden  jar  is  charged 
either  by  the  machine  or  by  the  electrophorus,  the  energy  of  the  charge 
is  a  transformation  of  the  work  of  the  operator. — Tait. 

707.  Plate  electrical  machine. — The  first  electrical  machine  was 
invented  by  Otto  von  Guericke,  the  inventor  also  of  the  air  pump.  It 
consisted  of  a  sphere  of  sulphur  which  was  turned  on  an  axis  by  means 
of  the  hand,  while  the  other,  pressing  against  it,  served  as  a  rubber. 
Resin  was  afterwards  substituted  for  the  sulphur,  which,  in  turn, 
Hawksbee  replaced  by  a  glass  cylinder.  In  all  these  cases  the  hand 
served  as  rubber;  and  Winckler,  in  1740,  first  introduced  cushions  of 
horsehair,  covered  with  silk,  as  rubbers.  At  the  same  time  Bose  col- 
lected electricity,  disengaged  by  friction,  on  an  insulated  cyhnder  of  tin 
plate.  Lastly,  Ramsden,  in  1760,  replaced  the  glass  cyhnder  by  a 
circular  glass  plate,  which  was  rubbed  by  cushions.  The  form  which  the 
machine  has  now  is  but  a  modification  of  Ramsden's  original  machine. 

Between  two  wooden  supports  (fig.  547)  a  circular  glass  plate,  P,  is 
suspended  by  an  axis  passing  through  the  centre,  and  which  is  turned 


622 


Frictional  Electricity. 


[707- 


by  means  of  a  glass  handle,  M.  The  plate  revolves  between  two  sets  of 
cushions  or  rubbers^  F,  of  leather  or  of  silk,  one  set  above  the  axis  and 
one  below,  which,  by  means  of  screws,  can  be  pressed  as  tightly  against 
the  glass  as  may  be  desired.  The  plate  also  passes  between  two  brass 
rods  shaped  like  a  horse-shoe,  and  provided  with  a  series  of  points  in  the 
sides  opposite  the  glass  :  these  rods  are  fixed  to  larger  metallic  cylinders, 
C,  which  are  called  the  prime  conductors.     The  latter  are  insulated  by 


Fig.  547- 


being  supported  on  glass  feet,  and  are  connected  with  each  other  by  a 
smaller  rod  r. 

The  action  of  the  machine  is  founded  on  the  excitation  of  electricity 
by  friction,  and  on  the  action  of  induction.  By  friction  with  the  rubbers, 
the  glass  becomes  positively  and  the  rubbers  negatively  electrified.  If 
now  the  rubbers  were  insulated,  they  would  receive  a  certain  charge  of 
negative  electricity  which  it  would  be  impossible  to  exceed,  for  the 
tendency  of  the  opposed  electricities  to  reunite  would  be  equal  to  the 
power  of  the  friction  to  decompose  the  neutral  fluid.  Btit  the  rubbers 
communicate  with  the  ground  by  m^ans  of  a  chain,  and,  consequently,  as 


-708]  Electrical  Machine.  623 

fast  as  the  negative  electricity  is  generated,  its  tension  is  reduced  to 
zero  by  contact  with  the  ground.  The  positive  electricity  of  the  glass 
acts  then  by  induction  on  the  conductor,  attracting  the  negative  electri- 
city. This  negative  electricity  collects  in  the  points  opposite  to  the 
glass.  Here  its  tendency  to  discharge  becomes  so  high  that  it  passes 
across  the  intervening  space  of  air,  and  neutralises  the  positive  electricity 
on  the  glass.  The  conductors  thus  lose  their  negative  electricity,  and 
remain  charged  with  positive  electricity.  The  plate  accordingly  gives 
up  nothing  to  the  prime  conductors ;  in  fact,  it  only  abstracts  from  them 
their  negative  electricity. 

If  the  hand  be  brought  near  the  conductor  when  charged,  a  spark 
follows,  which  is  renewed  as  the  machine  is  turned.  In  this  case,  the 
positive  electricity  decomposes  the  neutral  electricity  of  the  body,  attract- 
ing its  negative  electricity,  and  combining  with  it  when  the  two  have  a 
sufficient  tension.  Thus,  with  each  spark,  the  conductor  reverts  to  the 
neutral  state,  but  becomes  again  electrified  as  the  plate  is  turned. 

708,  Precautions  in  reference  to  the  macbine. — The  glass,  of  which 
the  plate  is  made,  must  be  as  little  hygroscopic  as  possible.  Of-  late 
ebonite  has  been  frequently  substituted  for  glass  ;  it  has  the  advantage 
of  being  neither  hygroscopic  nor  fragile,  and  of  readily  becoming  electri- 
cal by  friction.  The  plate  is  usually  from  ^r,  to  \  of  an  inch  in  thickness, 
and  from  20  to  30  inches  in  diameter,  though  these  dimensions  are  not 
unfrequently  exceeded. 

The  rubbers  require  great  care,  both  in  their  construction  and  in  their 
preservation.  They  are  commonly  made  of  leather,  stuffed  with  horse- 
hair. Before  use  they  are  coated  either  with  powdered  auriim  musiviim 
(sulphuret  of  tin),  or  graphite,  or  amalgam.  The  action  of  these  sub- 
stances is  not  very  clearly  understood.  Some  consider  that  it  merely 
consists  in  promoting  friction.  Others,  again,  believe  that  a  chemical 
action  is  produced,  and  assign,  in  support  of  this  view,  the  peculiar  smell 
noticed  near  the  rubbers  when  the  machine  is  worked.  Amalgams,  per- 
haps, promote  most  powerfully  the  disengagement  of  electricity.  Kien- 
niayer's  amalgain  is  the  best  of  them.  It  is  prepared  as  follows :  one 
part  of  zinc  and  one  part  of  tin  are  melted  together,  and  removed  from 
the  fire  and  two  parts  of  mercury  stirred  in.  The  mass  is  transferred 
to  a  wooden  box  containing  some  chalk,  and  then  well  shaken.  The 
amalgam,  before  it  is  quite  cold,  is  powdered  in  an  iron  mortar,  and  pre- 
served in  a  stoppered  glass  vessel.  For  use,  a  little  cacao  butter  or  lard 
is  spread  over  the  cushion,  some  of  the  powdered  amalgam  sprinkled 
over  it,  and  the  surface  smoothed  by  a  ball  of  flattened  leather. 

In  order  to  avoid  a  loss  of  electricity,  two  quadrant-shaped  pieces  of 
oiled  silk  are  fixed  to  the  rubbers,  so  as  to  cover  the  plate  on  both  sides, 
one  at  the  upper  part  from  a  to  F,  and  the  other  in  the  corresponding 
part  of  the  lower  rubbers.  These  flaps  are  not  represented  in  the  figure. 
Yellow  oiled  silk  is  the  best,  and  there  must  be  perfect  contact  between 
the  plate  and  the  cloth. 

Ramsden's  machine,  as  represented  in  fig.  547,  only  gives  positive 
electricity.     But  it  may  be  arranged  so  as  to  give  negative  electricity  by 


624  Friciioiial  Electricity.  [708- 

placing  it  on  a  table  with  insulating  supports.  By  means  of  a  chain,  the 
conductor  is  connected  with  the  ground,  and  the  machine  worked  as 
before.  The  positive  electricity  passes  off  by  the  chain  into  the  ground, 
while  the  negative  electricity  remains  in  the  supports  and  in  the  insulated 
table.  On  bringing  the  finger  near  the  uprights,  a  sharper  spark  than  the 
ordinary  one  is  obtained. 

709.  AKaximum  of  chargre. — It  is  impossible  to  exceed  a  certain 
limit  of  electrical  charge  with  the  machine,  whatever  precautions  are 
taken,  or  however  rapidly  the  plate  is  turned.  This  limit  is  attained 
when  the  loss  of  electricity  equals  its  production.  The  loss  depends  on 
three  causes :  i.  The  loss  by  the  atmosphere,  and  the  moisture  it  con- 
tains :  this  is  proportional  to  the  density,  ii.  The  loss  by  the  supports, 
iii.  The  recombination  of  the  electricities  of  the  rubbers  and  the  glass. 

The  first  two  causes  have  been  already  mentioned.  With  reference  to 
the  latter,  it  must  be  noticed  that  the  electrical  tension  increases  with  the 
rapidity  of  the  rotation,  until  it  reaches  a  point  at  which  it  overcomes  the 
resistance  presented  by  the  non-conductivity  of  the  glass.  At  this  point., 
a  portion  of  the  two  electricities  separated  on  the  rubbers  and  on  the 
glass  recombines,  and  the  tension  remains  constant.  It  is,  therefore, 
ultimately  independent  of  the  rapidity  of  rotation. 

710.  quadrant  electrometer.— The  electrical  charge  is  measured  by 
the  quadrant  or  Henley s  electrometer,  which  is  attached  to  the  conductor. 

This  is  a  small  electric  pendulum,  consisting  of  a 
wooden  rod,  d,  to  which  is  attached  an  ivory  or 
cardboard  scale,  c  (fig.  548).  In  the  centre  of  this 
is  a  small  whalebone  index,  movable  on  an  axis, 
and  terminating  in  a  pith  ball,  a.  Being  attached 
to  the  conductor,  the  index  diverges  as  the  machine 
is  charged,  ceasing  to  rise  when  the  limit  is  at- 
tained. When  the  rotation  is  discontinued  the 
index  falls  rapidly  if  the  air  is  moist,  but  in  dry 
air  it  only  falls  slowly,  showing,  therefore,  that  the 
loss  of  electricity  in  the  latter  case  is  less  than  in 
the  former. 

711.  Cylinder  electrical  machine. — The  con- 
struction of  the  cyhnder  machines,  as  ordinarily 
Pig.  548.  used  in  England,  is  due  to  Nairne.     They  are  well 

adapted  for  obtaining  either  kind  of  electricity.  In  Nairne's  machine 
(fig.  549)  the  cylinder  is  rubbed  by  only  one  cushion,  C,  which  is  made 
of  leather  stuffed  with  horsehair,  and  is  screwed  to  an  insulated  conductor, 
A.  On  the  opposite  side  of  the  cyhnder  there  is  a  similar  insulated  con- 
ductor B,  provided  with  a  series  of  points  on  the  sides  next  the  glass. 
To  the  lower  part  of  the  cushion  C  is  attached  a  piece  of  oiled  silk, 
which  extends  over  the  cylinder  to  just  above  the  points.  This  is  not  re- 
presented in  the  figure.  When  the  cylinder  is  turned,  A  becomes  charged 
with  negative  and  B  with  positive  electricity  by  the  loss  of  its  negative 
from  the  points  P.  The  two  opposite  electricities  will  now  unite  by  a 
succession  of  sparks  across  D  and  E.    If  use  is  to  be  made  of  the  electricity, 


-712] 


Armstrong s  Electrical  Machine. 


625 


either  the  rubber  or  the  prime  conductor  must  be  connected  with  the 
ground.  In  the  former  case  positive  electricity  is  obtained,  in  the  latter 
negative. 

M 


Fig-  549- 


712.  Armstrongr's  hydro-electric  macliine.— In  this  machine  elec- 
tricity is  produced  by  the  disengagement  of  aqueous  vapour  through 
narrow  orifices.  The  discovery  of  the  machine  was  occasioned  by  an 
accident.  A  workman  having  accidentally  held  one  hand  in  a  jet  of 
steam,  which  was  issuing  from  an  orifice  in  a  steam  boiler  at  high  pres- 
sure, while  his  other  hand  grasped  the  safety  valve,  was  astonished  at 
experiencing  a  smart  shock.  Sir  W.  Armstrong  (then  Mr.  Armstrong, 
of  Newcastle),  whose  attention  was  drawn  to  this  phenomenon,  ascer- 
tained that  the  vapour  was  charged  with  positive  electricity,  and  by  re- 
peating the  experiment  with  an  insulated  locomotive,  he  found  that  the 
boiler  was  negatively  charged.  Armstrong  believed  that  the  electricity 
was  due  to  a  sudden  expansion  of  the  vapour;  Faraday,  who  afterwards 
examined  the  question,  ascertained  its  true  cause,  which  will  be  best 
understood  after  describing  a  machine  which  Armstrong  devised  for  re- 
producing the  phenomenon. 

It  consists  of  a  boiler  of  wrought-iron  plate  (fig.  550),  with  a  central 
fire,  and  insulated  on  four  legs.  It  is  about  5  feet  long  by  2  feet  in 
diameter,  and  is  provided  at  the  side  with  a  gauge,  O,  to  show  the  height 
of  the  water  in  the  boiler.  C  is  the  stopcock,  which  is  opened  when  the 
vapour  has  sufficient  pressure.  Above  this  is  the  box,  B,  in  which  are 
the  tubes  through  which  the  vapour  is  disengaged.  On  these  are  fitted 
jets  of  a  pecuhar  construction,  which  will  be  understood  from  the  section 
of  one  of  them,  M,  represented  on  a  larger  scale.  They  are  lined  with 
hard  wood  in  a  manner  represented  by  the  diagram.  The  box  B  contains 
cold  water.  Thus,  the  vapour,  before  escaping,  undergoes  partial  con- 
densation, and  becomes  charged  with  vesicles  of  water ;  a  necessary  con- 

E  E 


626 


Frictional  Electi'icity. 


[712- 


dition,  for  Faraday  found  that  no  electricity  is  produced  when  the  vapour 
is  perfectly  dry. 

The  development  of  electricity  in  the  machine  was  at  first  attributed 
to  the  condensation  of  the  vapour,  but  Faraday  found  that  it  is  solely  due 
to  the  friction  of  the  globules  of  water  against  the  jet.  For  if  the  little 
cylinders  which  line  the  jets  are  changed,  the  kind  of  electricity  is 
changed  ;  and  if  ivory  is  substituted,  little  or  no  electricity  is  produced. 
The  same  effect  is  produced  if  any  fatty  matter  is  introduced  into  the 


Fig.  550- 

boiler.  In  this  case  the  linings  are  of  no  use.  It  is  only  in  case  the 
water  is  pure  that  electricity  is  disengaged,  and  the  addition  of  acid  or 
saline  solutions,  even  in  minute  quantity,  prevents  any  disengagement  of 
electricity.  If  turpentine  is  added  to  the  boiler,  the  effect  is  reversed — the 
vapour  becomes  negatively,  and  the  boiler  positively,  electrified. 

With  a  current  of  moist  air  Faraday  obtained  effects  similar  to  those 
of  this  apparatus,  but  with  dry  air  no  effect  is  produced. 

713.  Boltz's  electrical  machine.— Before  the  end  of  last  century 
electrical  machines  were  known  in  this  country  in  which  the  electricity 
was  not  developed  by  friction,  but  by  the  continuous  inductive  action  of 
a  body  already  electrified,  as  the  electrophorus ;    within  the   last  few 


-713] 


Holtzs  Electrical  Machine. 


627 


years  such  machines  have  been  reinvented  and  come  into  use.    The  form 
represented  in  fig.  551  was  invented  by  M.  Holtz,  of  Berhn. 

It  consists  of  two  circular  plates  of  thin  glass  at  a  distance  of  3  mm. 
from  each  other;  the  larger  one,  AA,  which  is  2  feet  in  diameter,  is  fixed 
by  means  of  4  wooden  rollers  <?,  resting  on  glass  axes  and  glass  feet.  The 
diameter  of  the  second  plate,  BB,  is  2  inches  less ;  it  turns  on  a  horizontal 
glass  axis,  which  passes  through  a  hole  in  the  centre  of  the  large  fixed 
plate  without  touching  it.  In  the  plate  A,  at  opposite  ends  of  the  same 
diameter,  are  two  notches,  or  windows,  YY'.  Along  the  lower  edge  of  the 
window  F,  on  the  posterior  face  of  the  plate,  a  band  of  paper,  /,  is  glued, 
and  on  the  anterior  face  a  sort  oi  tongiie  of  thin  cardboard,  «,  joined  Xo  p 
by  a  thin  strip  of  paper,  and  projecting  into  the  window.  At  the  upper 
edge  of  the  window,  F',  there  are  corresponding  parts,/'  and  71'.  The 
papers/  and /^' constitute  the  ar7natiires.     The  two  plates,  the  armatures, 


Fig.  551- 

and  their  tongues  are  carefully  covered  with  shellac  varnish,  but  more 
especially  the  edges  of  the  tongues. 

In  front  of  the  plate  B,  at  the  height  ot  the  armatures,  are  two  brass 
combs,  O  O',  supported  by  two  conductors  of  the  same  metal,  cc\  In  the 
front  end  of  these  conductors  are  two  pretty  large  brass  knobs,  through 
which  pass  two  brass  rods  terminated  by  smaller  knobs,  r ;-',  and  provided 
with  wooden  handles,  K  K'.     These  rods,  besides  moving  with  gentle 


628  Frictional  Electricity.  [713- 

friction  in  the  knobs,  can  also  be  turned  so  as  to  be  more  or  less  ap- 
proached and  inclined  towards  each  other.  The  plate  is  turned  by  means 
of  a  winch,  M,  and  a  series  of  pulleys  which  transmit  its  motion  to  the 
axis;  the  velocity  which  it  thus  receives  is  12  to  15  turns  in  a  second, 
and  the  rotation  should  take  place  in  the  direction  indicated  by  the  arrow — 
that  is,  towards  the  points  of  the  cardboard  tongues  ;/  71'. 

To  work  the  machine  the  armatures  p  p'  must  be  first  primed',  that 
is,  one  of  the  armatures  is  positively  and  the  other  negatively  electrified. 
This  is  effected  by  means  of  a  sheet  of  ebonite,  which  is  excited  by 
striking  it  with  flannel,  or,  better,  with  catskin  ;  the  two  knobs  r  r' 
having  been  connected,  ihe  electrified  ebonite  is  brought  near  one  of 
them,^,  for  instance,  and  the  plate  B  is  turned.  The  ebonite  is  charged 
Avith  negative  electricity,  which,  acting  inductively  on  the  armature  /, 
decomposes  its  neutral  fluid,  and  the  negative  electricity  repelled  is 
discharged  by  the  tongue  ;/,  on  to  the  movable  plate,  the  armature  re- 
maining charged  with  positive  electricity.  After  half  a  turn  the  negative 
electricity  of  the  plate  coming  in  front  of  the  window  F'  acts  in  the  same 
way  on  the  armature  p' ,  charging  it  with  negative  electricity  by  taking 
from  it  a  corresponding  quantity  of  positive  electricity  by  the  tongue  n'. 
After  a  few  turns  the  two  armatures  being  thus  electrified,  one  positively 
and  the  other  negatively,  the  inducing  plate  of  ebonite  is  removed,  and 
the  knobs  r  r'  separated,  as  represented  in  the  figure.  On  continuing  to 
turn  the  plate  an  uninterrupted  torrent  of  sparks  strikes  across  from  one 
knob  to  the  other. 

These  details  being  known,  the  following  explanation  of  the  action  of 
the  machine  is  given  by  Riess.  When  a  conductor  is  under  the  influence  of 
an  electrified  body,  it  becomes  charged  with  opposite  electricities  on  its  two 
opposite  surfaces  (699).  This  is  also  the  case  ^^ith  non-conductors,  with 
the  difference,  that  the  separation  of  the  two  electricities,  which  is  instan- 
taneous in  the  first  case,  takes  place  slowly  in  the  second.  But  if,  between 
the  source  of  electricity  and  a  good  conductor,  a  bad  conductor  such  as  a 
plate  of  glass,  be  interposed,  the  inductive  action  is  modified.  Supposing 
the  source  of  electricity  to  be  positive,  if  its  action  be  prolonged,  the  good 
and  the  bad  conductors  are  negatively  electrified  on  the  side  turned  towards 
the  source,  and  positively  on  the  opposite  side. 

If  the  inductive  action  is  of  short  duration  the  influence  is  weak,  and 
the  electricity  with  which  the  glass  plate  is  charged  on  its  posterior  face 
is  negative  electricity  imparted  by  the  good  conductor,  especially  if  it  is 
provided  with  points.  The  plate  B  is  thus  electrified  negatively  on  the 
two  faces  ;  a  phenomenon  which  Riess  calls  double  infiiieiice. 

That  being  granted,  let  fig.  552  represent  a  horizontal  projection  of  the 
details  of  fig.  551,  the  letters  having  in  both  cases  the  same  meaning.  The 
two  armatures  p  and  p',  having  been  electrified,  as  we  have  seen,  one  posi- 
tively and  the  other  negatively,  when  two  opposite  faces  7n  and  m\  of  a 
portion  of  the  plate  B,  pass  in  front  of  the  window  F.  then  from  what 
has  been  said  above,  the  faces  in  and  ?//',  in  the  presence  of  the  posi- 
tive armature  p,  both  become  negatively  electrified ;  the  conductor  Qr, 
having  imparted  its  negative  electricity  to  the  face  in'  of  the  plate  B, 


713] 


Holtzs  Electrical  Machine. 


629 


remains  positively  electrified.  Then,  the  rotation  continuing,  the  elements 
in  and  m'  both  come  in  front  of  the  window  F  F'  negatively  charged.  There 
the  element  /«',  adding  its  influence  to  that  of  the  negative  armature  p' ] 
withdraws  from  the  conductor  C  V  its  positive  electricity,  thus  charging  it 
with  negative  electricity.  The  element  ;/z,  acting  inductively  on  the  arma- 
ture/', withdraws  positive  fluid  from  it  by  induction,  and  thus  tmds  to 
keep  it  in  the  negative  state.  The  two  elements  rn  and  m'  thus  revert  to  the 


P     + 


?'  _ 


Fig.  552. 


neutral  state,  and  passing  in  front  of  the  window  F,  the  same  series  of 
phenomena  is  reproduced. 

In  Holtz's  machine  electricity  is  used  in  three  forms,  which  double  in- 
fluence can  develope.  The/re-^  electricity  of  conductors  is  used  in  experi- 
ments. The  electricity  induced  upon  the  external  face  of  the  movable 
disc,  and  the  electricity  comimmicated  to  the  inner  face  are  removed  by 
the  disc,  and  serve  to  keep  up  the  charge  of  the  armatures.  The  line  of 
the  combs  divides  this  disc  in  two  halves,  which  are  every  minute  elec- 
trified in  opposite  directions.  Each  of  them  is  of  the  same  kind  as  the 
conductor  or  armature  towards  which  it  is  moving,  and  of  opposite  sign 
to  the  comb  towards  which  the  rotation  carries  it.  The  nature  of  the 
electricity  is  observed  from  the  shape  of  the  brush  which  escapes  from  it  ; 
the  brushes  are  long  and  verging  on  the  positive  comb ;  short  and  like 
luminous  points  on  the  negative  comb. 

With  plates  of  equal  dimensions  Holtz's  machine  is  far  more  poweriul 
than  the  ordinary  electrical  machine  (705).  The  power  is  still  further 
increased  by  suspending  to  the  conductors  C  Q'  two  condensers,  H  H' 
(719),  which  consist  of  two  glass  tubes  coated  with  tin  foil,  inside  and 
out,  to  within  a  fifth  of  their  height.  Each  of  them  is  closed  by  a  cork, 
through  which  passes  a  rod,  communicating  at  one  end  with  the  inner 
coating,  and  suspended  to  one  of  the  conductors  by  a  crook  at  the  other 
end.  The  two  external  coatings  are  connected  by  a  conductor,  G.  They 
are,  in  fact,  only  two  small  Leyden  jars  (724),  one  of  them,  H,  becoming 
charged  with  positive  electricity  on  the  inside,  and  negative  on  the  out- 
side ;  the  other,  H',  with  negative  electricity  on  the  inside,  and  positive  on 
the  outside.  Becoming  charged  by  the  intervention  of  the  machine,  and 
being  discharged  at  the  same  rate  by  the  knobs  r  r',  they  strengthen  the 
spark,  which  may  attain  a  length  of  6  or  7  inches. 


630 


Frictional  Electricity. 


[713 


The  current  of  the  machine  is  utilised  by  placing  in  part  of  the  frame 
two  brass  uprights,  QQ',  with  binding  screws  in  which  are  copper  wires  ; 
then,  by  means  of  the  handles  KK',  the  rods  which  support  the  knobs  r  r'^ 
are  inclined,  so  that  they  are  in  contact  with  the  uprights.  The  current 
being  then  directed  by  the  wires,  a  battery  of  six  jars  can  be  charged  in 
a  few  minutes,  water  can  be  decomposed,  a  galvanometer  deflected,  and 
Geissler's  tubes  worked  as  with  the  voltaic  pile. 

The  electrical  current  of  a  Holtz's  machine  has  been  shown  by  Poggen- 
dorff  to  be  independent  of  the  resistance  of  the  circuit,  and  by  Kohlrausch 
to  be  proportional  to  the  velocity  of  rotation.  A  plate  46  inches  in 
diameter  revolving  5  times  in  three  seconds  produced  a  constant  current 
capable  of  decomposing  water  at  the  rate  of  3^^  milhonths  of  a  milH- 
gramme  per  second,  or  equal  to  that  of  a  Grove's  cell  in  a  circuit  of 
45,000  B  A  units  (861). 

714.  Bertitcli's  machine. — This  is  a  simpler,  though  at  the  same  time 


Fig.  553. 

less  powerful,  apparatus  than   Holtz's  machine,  with  which  it  has  other- 
wise much  similarity. 

It  consists  of  an  ebonite  plate,  P  P',  about  18  inches  in  diameter,  and 


I 


-715]  BcrtscJis  Electrical  MacJdne.  631 

mounted  on  a  glass  axis  (fig.  553).  The  inducing  plate  E,  represented^ 
separately  at  the  top  of  the  figure  as  E',  is  also  of  ebonite,  and  is  placed 
in  a  groove  at  the  base  of  the  machine,  near  the  plate  P  P^,  but  not  in 
contact  with  it.  The  inducing  plate  E  having  been  electrified,  with 
negative  electricity  suppose,  acts  through  the  plate  P  on  a  comb  «,  with- 
drawing from  it  positive  electricity,  which  passes  to  the  plate  and  repels 
negative  to  the  conductor  be.  The  plate,  continuing  to  turn,  arrives  charged 
with  positive  electricity  in  front  of  the  second  comb  m.  Hence  it  with- 
draws from  the  comb  w,  and  from  the  conductor  a,  negative  electricity, 
which  restores  it  to  the  neutral  state,  while  the  conductor  a  remains  posi- 
tively charged.  As  thp  rotation  of  the  plate  is  continued  the  conductors 
a  and  b  continue  to  become  charged  with  opposite  electricities,  and  if  the 
knobs  are  at  a  distance  of  3  to  4  inches,  an  uninterrupted  succession  of 
sparks  passes  between  them. 

The  intensity  of  the  sparks  increases  when  the  conductor  b  is  connected 
with  the  ground  by  means  of  a  chain  R.  It  is  further  increased  by  inter- 
posing a  condenser,  K,  between  the  conductors  a  and  b.  This  consists  of 
two  glass  tubes  cemented  together  at  the  bottoms.  At  each  end  is  a 
curved  wire  connected  with  the  internal  lining,  which  is  of  tinfoil.  A 
single  sheet  of  tinfoil  coats  the  outside,  so  that  they  are  no  more  than  two 
small  Leyden  jars  connected  by  their  outside  coatings.  They  become 
charged  with  contrary  electricities  from  the  conductors  a  and  b^  and  being 
discharged  at  the  same  time  as  them,  increase  the  spark. 

The  power  is  increased  by  placing  close  to  the  sector  E  a  second 
similar  one,  electrified  in  the  same  manner.  As  the  inducing  power  in- 
creases, the  tension  also  increases.  With  a  machine  thus  arranged,  a 
glass  plate  ^  to  ^  of  an  inch  may  be  perforated,  and  a  strong  battery 
rapidly  charged.  The  inducing  power  of  the  sectors  quickly  decreases, 
and  they  must  be  excited  afresh. 

Both  Holtz's  and  Bertsch's  machines  are  very  much  affected  by  the 
moisture  of  the  air;  but  M.  Ruhmkorff  has  found  that,  spreading  on  the 
table  a  few  drops  of  petroleum,  the  vapours  which  condense  on  the 
machine  protect  it  against  the  moisture  of  the  atmosphere. 

These  machines  are  small  in  compass,  and  not  very  expensive,  and 
require  less  force  for  working  them  than  frictional  machines.  When  the 
armatures  are  electrified,  more  resistance  is  experienced  in  turning  the 
plate  than  if  they  are  not  electrified ;  in  the  former  case  part  of  the 
mechanical  force  exerted  by  the  arm  of  the  operator  is  transformed  into 
electricity. 

715.  Carre's  dielectrical  xnacbine. — This  is  a  combination  of  the  old 
form  of  machine  with  that  of  Holtz. 

It  consists  of  two  plates  turning  in  opposite  directions  (fig.  554),  one.  A, 
of  glass  and  the  other,  B,  of  ebonite.  They  overlap  each  other,  to  about  §  to 
f  of  their  radii.  The  lower  one  is  slowly  turned  by  means  of  a  handle,  M, 
while  the  upper  one  is  rapidly  rotated  by  an  endless  cord,  which  passes 
from  the  large  over  the  small  wheel. 

The  plate  A,  after  having  been  electrified  positively  between  two  rubbers 
FF',  acts  inductively  through  the  plate  B  on  a  comb  /,  withdrawing  from  it 


632 


Frictioiial  Electricity. 


[715- 


negative  electricity,  which  then  passes  to  the  plate  B,  the  conductor  d  e 
remaining  positively  electrified  ;  but  as  the  plate  B  turns  very  quickly,  the 
negative  electricity,  as  it  collects  on  its  surface,  acts  inductively  on  a  second 
comb,  gj  vv^hich  it  charges  with  negative  electricity,  reverting  itself  to  the 
neutral  state,  while  the  two  conductors  C  and  D,  which  are  connected 
with  the  comb  ^,  become  charged  with  negative  electricity. 

These  conductors,  connected  as  they  are  by  two  ties,  m  and  «,  rest  on  two 
columns,  the  one,  a,  of  glass,  and  the  other,  b,  of  ebonite.     A  chain  in  con- 


i'"ig-  554- 


nection  with  the  ground  is  suspended  from  a  hook,  O,  which  can  be  raised 
at  pleasure,  and  put  in  connection  with  the  comb  /.  The  rubbers  F  F', 
moreover,  are  in  connection  with  the  ground  by  means  of  two  bands  of 
tin  foil  along  the  supports. 

Lastly,  at  p  (fig.  555)  is  a  sector  of  varnished  paper  cut  in  the  form 
of  a  comb,  and  fastened  to  an  insulating  segment,  P,  of  the  same  shape, 
which   is   used   as   support.     From   the   teeth   of  the  sector  p  positive 


717] 


Carre's  Dielectrical  Machine, 


633 


» 


1 


electricity  flows  on  the  plate  B  as  it  moves,  and  by  induction  this  sector 
/  yields  to  the  comb  g  a  surcharge  of  negative  electricity.  The  rod  d 
and  the  knob  e  may  be  withdrawn  at  will  from  the  conductor  C  (fig.  554), 
so  that-  sparks  of  different  lengths  may  be  taken.  At  r  is  a  hook  to 
which  can  be  attached  the  Leyden  jars  which  are  to  be  charged. 

Owing  to  the  direct  action,  and 

when  the  inducing  plate  is  as  the        >;^ \ 

maximum  charge,  Carre's  machine         \  C  ^' 

is  not  very  much  affected  by  mois-         L 

lure,  and  it  yields  a  larger  supply 

of  electricity.     With  plates  whose 

dimensions  are  respectively  38  and 

49  centimetres,   it  gives  sparks  of 

15    to    18   centimetres,   and    more 

when  a  condenser  is  added,  as  in 

Holtz's  and  Bertsch's  machines. 

7  K  6.  "Work    required    for    the  F'»  555 

production  of  electricity. — In  all  electrical  machines  electricity  is  only 
produced  by  the  expenditure  of  a  definite  amount  of  force,  as  will  at  once 
be  seen  by  a  perusal  of  the  preceding  descriptions.  The  action  of  those 
machines  however,  which  work  continuously,  is  somewhat  complex. 
Not  only  is  electricity  produced,  but  heat  also  ;  and  it  has  been  hitherto 
impossible  to  estimate  separately  the  work  required  for  the  heat  from 
that  required  for  the  electricity.  This  is  easily  done  in  theory,  but  not  in 
practice  ;  how  difficult,  for  instance,  it  would  be  to  determine  the  tempera- 
ture of  the  cushion  or  of  the  plate  of  a  Ramsden's  machine. 

In  lifting  the  plate  off"  a  charged  electrophorus,  a  definite  expenditure 
of  force  is  needed,  though  it  be  too  slight  to  be  directly  estimated  (706). 
With  a  Holtz's  machine  it  may  be  readily  shown  that  there  is  a  definite 
expenditure  of  force  in  working  it.  If  such  a  machine  be  turned  without 
having  been  charged,  the  work  required  is  only  that  necessary  to  over- 
come the  passive  res'stances.  If,  however,  one  of  the  sectors  be  charged 
and  the  electric  action  comes  into  play,  it  will  be  observed  that  there 
must  be  a  distinct  increase  in  the  force  necessary  to  work  the  machine. 


EXPERIMENTS  WITH   THE   ELECTRICAL   MACHINE. 

7 1 7.  Spark. — One  of  the  most  curious  phenomena  observed  with  the 
electrical  machine  is  the  spark  drawn  from  the  conductor  when  a  finger 
is  presented  to  it.  The  positive  electricity  of  the  conductor,  acting  in- 
ductively on  the  neutral  electricity  of  the  body,  decomposes  it,  repelling 
the  positive  and  attracting  the  negative.  When  the  attraction  of  the  op- 
posed electricities  is  sufficiently  great  to  overcome  the  resistance  of  the 
air,  they  recombine  with  a  smart  crack  and  a  spark.  The  spark  is 
instantaneous,  and  is  accompanied  by  a  sharp  prickly  sensation,  more 
especially  with  a  powerful  machine.     Its  shape  varies.     When  it  strikes 


EE3 


634 


Frictional  Electricity. 


[717- 


at  a  short  distance,  it  is  rectilinear,  as  seen  in  fig.  556.  Beyond  two  or 
three  inches  in  length,  the  spark  becomes  irregular,  and  has  the  form  of 
a  sinuous  curve  with  branches  (fig.  557).  If  the  discharge  is  very 
powerful,  the  spark  takes  a  zig-zag  shape  (fig.  558).  These  two  latter 
appearances  are  seen  in  the  lightning  discharge. 

A  spark  may  be  taken  from  the  human  body  by  the  aid  of  the  insulat- 
ing stool,  which  is  simply  a  low  stool  with  stout  glass  legs.  The  person 
standing  on  this  stool  touches  the  prime  conductor,  and  as  the  human 


Fig.  556. 


Fig.  557. 


Fig.  558. 


body  is  a  conductor,  the  electrical  fluid  is  distributed  over  its  surface  as 
over  an  ordinary  insulated  metallic  conductor.  The  hair  diverges  in 
consequence  of  repulsion,  a  peculiar  sensation  is  felt  on  the  face,  and  if 
another  person,  standing  on  the  ground,  presents  his  hand  to  any  part  of 
the  body,  a  smart  crack  with  a  pricking  sensation  is  produced. 

A  person  standing  on  an  insulated  stool  may  be  positively  electrified 
by  being  struck  with  a  catskin.  If  the  person  holding  the  catskin  stands 
on  an  insulated  stool,  the  striker  becomes  positively,  and  the  person 
struck  negatively,  electrified. 

718.  Electrical  chimes. — The  electrical  chimes  is  a  piece  of  apparatus 
consisting  of  three  bells  suspended  to  a  horizontal  metal  rod  (fig.  559). 
Two  of  them,  A  and  B,  are  in  metallic  connection  with  the  conductor ; 
the  middle  bell  hangs  by  a  silk  thread,  and  is  thus  insulated  from  the 
conductor,  but   is  connected  with   the  ground  by  means   of  a  chain. 


719] 


Experiments  ivith  the  Electrical  Machine. 


63  s 


Between  the  bells  are  small  copper  balls  suspended  by  silk  threads. 
When  the  machine  is  worked,  the  bells  A  and  B,  being  positively 
electrified,  attract  the  copper  balls, 
and  after  contact  repel  them.  Being 
now  positively  electrified,  they  are 
in  turn  attracted  by  the  middle 
bell,  C,  which  is  charged  with  nega- 
tive electricity  by  induction  from 
A  to  B.  After  contact  they  are 
again  repelled,  and  this  process  is 
repeated  as  long  as  the  machine 
is  in  action. 

Fig.  560  represents  an  apparatus 
originally  devised  by  Volta  for  the 
purpose  of  illustrating  what  he  sup- 
posed to  be  the  motion  of  hail  between  two  clouds  oppositely  electrified. 
It  consists  of  a  tubulated  glass  shade,  with  a  metal  base,  on  which  are 


Fi^.  559- 


Fig.  560. 


Fig.  561 


some  pith  balls.  The  tubulure  has  a  metal  cap,  through  which  passes  a 
brass  rod,  provided  with  a  metallic  disc  or  sphere  at  the  lower  end,  and 
at  the  upper  with  a  knob,  which  touches  the  prime  conductor. 

When  the  machine  is  worked,  the  sphere  becoming  positively  electri- 
fied, attracts  the  light  pith  balls,  which  are  then  immediately  repelled,  and, 
having  lost  their  charge  of  positive  electricity,  are  again  attracted,  again 
repelled,  and  so  on,  as  long  as  the  machine  continues  to  be  worked.  An 
amusing  modification  of  this  experiment  is  frequently  made  by  placing 
between  the  two  plates  small  pith  figures,  somewhat  loaded  at  the  base. 
When  the  machine  is  worked,  the  figures  execute  a  regular  dance. 

719.  Electrical  whirl  or  vane. — The  electrical  whirl  or  vane  consists 
of  5  or  6  wires,  terminating  in  points,  all  bent  in  the  same  direction,  and 


6s6 


Frictional  Electricity. 


[719 


fixed  in  a  central  cap,  which  rotates  on  a  pivot  (fig.  561).  When  the 
apparatus  is  placed  on  the  conductor,  and  the  machine  worked,  the 
whirl  begins  to  revolve  in  a  direction  opposite  that  of  the  points.  This 
motion  is  not  analogous  to  that  of  the  hydraulic  tourniquet  (205).  It  is 
not  caused  by  a  flow  of  material  fluid,  but  is  owing  to  a  repulsion  between 
the  electricity  of  the  points  and  that  which  they  impart  to  the  adjacent 
air  by  conduction.  The  electricity  being  accumulated  on  the  points  in  a 
high  state  of  density,  passes  into  the  air,  and  imparting  thus  a  charge  of 
electricity,  repels  this  electricity,  while  it  is  itself  repelled.  That  this  is 
the  case  is  evident  from  the  fact  that,  on  approaching  the  hand  to  the 
whirl  while  in  motion,  a  slight  draught  is  felt,  due  to  the  movement  of  the 
electrified  air,  while  in  vacuo  the  apparatus  does  not  act  at  all.  This 
draught  or  wind  is  known  as  the  electrical  aura. 

When  the  electricity  thus  escapes  by  a  pomt,  the  electrified  air  is 
repelled  so  strongly  as  not  only  to  be  perceptible  to  the  hand,  but  also  to 
engender  a  current  strong  enough  to  blow  out  a  candle.     Fig.  562  shows 


Fig.  562. 


Fig.  563- 


this  experiment.  The  same  effect  is  produced  by  placing  a  taper  on  the 
conductor,  and  bringing  near  it  a  pointed  wire  held  in  the  hand  (fig.  563). 
The  current  arises  in  this  case  from  the  contrary  fluid,  which  escapes 
by  the  point  under  the  influence  of  the  machine. 

The  electrical  orrery  and  the  electrical  inclined  plane  are  analogous  to 
these  pieces  of  apparatus. 


CHAPTER   IV. 

CONDENSATION   OF    ELECTRICITY. 

720.  Condensers.  Theory  of  condensers. — A  r^^/z^tv/j-^r  is  an  appa- 
ratus for  condensing  a  large  quantity  of  electricity  on  a  comparatively 
small  surface.  The  form  may  vary  considerably,  but  in  all  cases  consists 
essentially  of  two  insulated  conductors,  separated  by  a  non-conductor,  and 
the  working  depends  on  the  action  of  induction. 

Epinus's  condenser  consists  of  two  circular  brass  plates,  A  and   B 


720] 


Condensation  of  Electricity. 


637 


(fig.  564),  with  a  sheet  of  glass,  C,  between  them.  The  plates,  each  provided 
with  a  pith  ball  pendulum,  are  mounted  on  insulated  glass  legs,  and  can 
be  moved  along  a  support,  and  fixed  in  any  position.     When  electricity  is 


F'g-  564- 

to  be  accumulated,  the  plates  are  placed  in  contact  with  the  glass, 
and  then  one  of  them,  B  for  instance,  is  connected  with  the  electrical 
machine,  and  the  other  placed  in  connection  with  the  ground,  as  shown 
in  fig.  565. 

In  explaining  the  action  of  the  condenser,  it  will  be  convenient  in  each 


Fip.  565. 


case  to  call  that  side  ot  the  metal  plate  nearest  the  glass  the  anterior, 
and  the  other  the  posterior  side.     And  first  let  A  be  at  such  distance 


638 


Frictional  Electricity 


[720 


Fig.  566. 


from  B  as  to  be  out  of  the  sphere  of  its  action.  The  plate  B,  which  is 
then  connected  with  the  conductor  of  the  electrical  machine,  takes  its 
maximum  charge,  which  is  distributed  equally  on  its  two  faces,  and  the 
pendulum  diverges  widely.  If  the  connection  with  the  machine  be 
interrupted,  nothing  would  be  changed ;  but  if  the  plate  A  be  slowly 
approached,  its  neutral  fluid  being  decomposed  by  the  influence  of  B,  the 
negative  is  accumulated  on  its  anterior  face,  71  (fig.  566),  and  the  positive 
passes  into  the  ground.     But  as  the  negative  electricity  of  the  plate  A 

reacts  in  its  turn  on  the  positive  of  the 
plate  B,  the  latter  fluid  ceases  to  be 
equally  distributed  on  both  faces,  and 
is  accumulated  on  its  anterior  face,  m. 
The  posterior  face,  p,  having  thus  lost 
a  portion  of  its  electricity,  its  density 
has  diminished,  and  is  no  longer  equal 
to  that  of  the  machine,  and  the  pen- 
dulum, b^  diverges  less  widely.  Hence 
B  can  receive  a  fresh  quantity  from 
the  machine,  which,  acting  as  just 
described,  decomposes  by  induction  a  second  quantity  of  neutral  fluid  on 
the  plate  A.  There  is  then  a  new  accumulation  of  negative  fluid  on  the 
face  n,  and  consequently  of  positive  fluid  on  7n.  But  each  time  that  the 
machine  gives  off  electricity  to  the  plate,  only  a  part  of  this  passes  to  the 
face  ;«,  the  other  remaining  on  the  face/;  the  tension  here,  therefore, 
continues  to  increase  until  it  equals  that  of  the  machine.  From  this 
moment  equilibrium  is  established,  and  a  limit  to  the  charge  attained 
which  cannot  be  exceeded.  The  quantity  of  electricity  accumulated  now  • 
on  the  two  faces  m  and  71  is  very  considerable,  and  yet  the  pendulum  di- 
verges just  as  much  as  it  did  when  A  was  absent,  and  no  more ;  in  fact, 
the  density  at/  is  just  what  it  was  then— namely,  that  of  the  machine. 

When  the  condenser  is  charged — that  is,  when  the  opposite  electricities 
are  accumulated  on  the  anterior  faces — connection  with  the  ground  is 
broken  by  raising  the  wires.  The  plate  A  is  charged  with  negative 
electricity,  but  simply  on  its  anterior  face  (fig.  566),  the  other  side  being 
neutral.  The  plate  B,  on  the  contrary,  is  electrified  on  both  sides,  but 
unequally  ;  the  accumulation  is  only  on  its  anterior  face,  while  on  the 
posterior,  /,  the  density  is  simply  equal  to  that  of  the  machine  at  the 
moment  the  connections  are  interrupted.  In  fact,  the  pendulum  b  di- 
verges and  a  remains  vertical.  But  if  the  two  plates  are  removed,  the  two 
pendulums  diverge  (fig.  564),  which  is  owing  to  the  circumstance  that,  as 
the  plates  no  longer  act  on  each  other,  the  positive  fluid  is  equally  distri- 
buted on  the  two  faces  of  the  plate  B,  and  the  negative  on  those  of  the 
plate  A. 

721.  Slow  discbargre  and  instantaneous  discliargre. — While  the 
plates  A  and  B  are  in  contact  with  the  glass  (fig.  565),  and  the  connec- 
tions interrupted,  the  condenser  may  be  discharged— that  is,  restored  to 
the  neutral  state,  in  two  ways;  either  by  a  slow  or  by  an  instantaneous 
discharge.     To  discharge  it  slowly,  the  plate  B — that  is,  the  one  containing 


-721]       Sloiv  Discharge  and  Instantaneous  Discharge .        639 

an  excess  of  electricity — is  touched  witli  the  finger  ;  a  spark  passes,  all 
the  electricity  on  p  passes  into  the  ground,  the  pendulum  b  falls,  but  a 
diverges.  For  B,  having  lost  part  of  its  electricity,  only  retains  on  the 
face  m  that  held  by  the  inductive  influence  of  the  negative  on  A.  But  the 
quantity  thus  retained  at  B  is  less  than  that  on  A;  this  has  free  electricity, 
which  makes  the  pendulum  a  diverge,  and  if  it  now  be  touched,  a  spark 
passes,  the  pendulum  a  sinks  while  b  rises,  and  so  on  by  continuing  to 
touch  alternately  the  two  plates.  The  discharge  only  takes  place  slowly ; 
in  very  dry  air  it  may  require  several  hours.  If  the  plate  A  were 
touched  first,  no  electricity  would  be  removed,  for  all  it  has  is  retained  by 
that  of  the  plate  B.  To  remove  the  total  quantity  of  electricity  by  the 
method  of  alternate  contacts,  an  infinite  number  of  such  contacts  would 
theoretically  be  required,  as  will  be  seen  from  the  following  calcula- 
tion : 

Let  the  total  quantity  of  positive  electricity  on  B  be  taken  =  i  ;  by 
induction  it  retains  on  A  a  quantity  less  than  its  own  of  negative  elec- 
tricity ;  let  this  quantity  be  called  m  ;  in  being  a  fraction  in  all  cases  less 
than  unity,  but  which  varies  with  the  distance  of  the  plates  and  the  nature 
of  the  dielectric.  Now  the  m  of  negative  electricity  on  A,  reacting  in  turn 
on  the  positive  on  B,  retains  there  my.m  =  in-  of  positive  electricity,  and 
therefore  the  free  electricity  on  B,  that  which  makes  the  pendulum  b 
diverge  is  i  —  w^,  and  if  B  be  touched  this  quantity  is  removed.  The  in 
of  negative  on  A  now  retains,  on  B,  in"^  of  positive  ;  this  binds  in  turn  m 
times  its  own  quantity — that  is,  in^  of  negative  on  A — and  the  free  negative 
electricity  which  now  makes  the  pendulum  a  diverge  is  represented  by  in 
—  m^  =  w(i  —  m^).  If  A  be  now  touched,  this  quantity  is  removed,  the  pen- 
dulum a  sinks  and  b  rises ;  for  B  has  now  an  excess  of  free  electricity, 
which  it  is  readily  seen  is  presented  by  ni^ii—rn^).  By  pursuing  this 
reasoning,  it  will  be  seen  that  the  following  expresses  the  quantities 
removed  and  left  after  each  successive  contact  :  — 

Positive.  Negative. 

I  m 

\—in^\             m^  m^  \  in{\—m^) 

{\—m^)m'^\      w*  nv' \  in^{\~in^) 

(i— ;;z-)w*;       m^  in'';  m^\\—in^) 

(i  —  in^)in^  ^  ;    m^  111^  +  ^  ;  in"~\i  —  m^) 

An  instantaneous  discharge  maybe  effected  by  means  oi tht discharg- 
ing rod  (fig.  567).  This  consists  of  two  bent  brass  wires,  terminating  in 
knobs,  and  joined  by  a  hinge.  When  provided  with  glass  handles  as 
in  fig.  567,  it  forms  a  glass  discharging  rod.  In  using  this  apparatus  one 
of  the  knobs  is  pressed  against  one  plate  of  the  condenser,  and  the 
other  knob  brought  near  the  other.  At  a  certain  distance  a  spark  strikes 
from  the  plate  to  the  knob,  caused  by  the  sudden  recomposition  of  the 
two  opposite  electricities. 

When  the  condenser  is  charged  by  the  discharger  no  sensation  is 
experienced,  even  though  the  latter  be  held  in  the  hand ;  of  the  two  con- 
ductors, the  electric  fluid  always  chooses  the  better,  and  hence  the  dis- 


640  Frlctional  Electricity.  [721  - 

charge  is  effected  through  the  metal,  and  not  through  the  body.  But  if, 
while  one  hand  is  in  contact  with  one  plate,  the  other  touches  the  second, 
the  discharge  takes  place  through  the  breast  and  arms,  and  a  considerable 
shock  is  felt ;  and  the  larger  the  surface  of  the  con- 
denser, and  the  greater  the  electric  density,  the 
more  violent  is  the  shock. 

722.  Calculation  of  the  condensingr  force. — 
The  condensing  force  is  the  relation  between  the 
whole  charge,  which  the  collecting  plate  can  take 
while  under  the  influence  of  the  second  plate, 
to  that  which  it  would  take  if  alone  ;  in  other 
words,  it  is  the  relation  of  the  total  quantity  of 
eLectricity  on  the  collecting  plate  to  that  which 
P-      g  remains  free ;  for  it  is  assumed  that  the  quantity  of 

free  electricity  on  the  collecting  plate  is  the  same 
as  that  which  it  would  take  if  it  were  alone. 

To  calculate  the  condensing  force,  let  us,  as  before,  express  the  total 
quantity  of  positive  electricity  which  the  collecting  plate  B  can  take, 
while  under  the  influence  of  the  condensing  plate,  by  I,  then  in  is  the 
whole  quantity  of  negative  electricity  on  the  second  plate.  But,  as  we 
have  just  seen,  the  quantity  of  free  electricity  on  B  is  \  —  m^.     Hence 

is  the  fraction  which  expresses  the  condensing  force. 

The  value  of  in  is  determined  experimentally  by  means  of  the  proof 
plane  and  the  torsion  balance.  Thus,  if  in  were  0-99,  the  quantity  of 
electricity  which  could  be  accumulated  on  the  collecting  plate  B,  under 
the  influence  of  A,  would  be  50  times  as  much  as  the  quantity  it  could 
receive  if  alone;  while,  if  m  were  075,  the  quantity  would  be  2-28  times 
as  great. 

723.  Limit  of  the  chargre  of  condensers. — The  quantity  of  electricity 
which  can  be  accumulated  on  each  plate  is,  cceteris  paribus,  proportional 
to  the  density  of  the  electricity  on  the  conductor,  and  to  the  surface  of 
the  plates  :  it  decreases  as  the  insulating  plate  is  thicker,  and  it  differs 
with  the  specific  inductive  capacity  of  the  substance.  Two  causes  limit 
the  quantity  of  electricity  which  can  be  accumulated.  First,  that  the 
electric  density  of  the  collecting  plates  gradually  increases,  and  ultimately 
equals  that  of  the  machine,  which  cannot,  therefore,  impart  any  free 
electricity.  The  second  cause  is  the  imperfect  resistance  which  the 
insulating  plate  offers  to  the  recombination  of  the  two  opposite  electricities  ; 
.for  when  the  force  which  impels  the  two  fluids  to  recombine  exceeds  the 
resistance  offered  by  the  insulating  plate,  it  is  perforated,  and  the  contrary 
fluids  unite. 

724,  Fulminating-  pane.  Franklin's  plate. — This  is  a  simple  form 
of  the  condenser,  and  is  more  suitable  for  giving  strong  shocks  and  sparks. 
It  consists  of  a  glass  plate  fixed  in  a  wooden  frame  (fig.  568);  on  each 
side  of  the  glass  pieces  of  tin  foil  are  fastened  opposite  each  other,  leaving 
a  space  free  between  the  edge  and  the  frame.  It  is  well  to  cover  this  part 
of  the  glass  with  an  insulating  layer  of  shellac  varnish.    One  of  the  sheets 


-725] 


Fulminating  Pane. 


641 


of  tin  foil  is  connected  with  a  ring  on  the  frame  by  a  strip  of  tin  foil,  so 
that  it  can  be  put  in  communication  with  the  ground  by  means  of  a  chain. 
To  charge  the  pane  the  insulated  side  is  connected  with  the  machine. 
As  the  other  side  communicates  with  the  ground,  the  two  coatings  play 
exactly  the  part  of  the  condenser.  On  both  plates  there  are  accumulated 
large  quantities  of  contrary  electricities. 

The  pane  may  be  discharged  by  simply  pressing  the  knob  of  the  dis- 


Flg.  568. 

charger  against  the  lower  surface,  while  the  other  knob  is  brought  near 
the  upper  coating.  A  spark  ensues,  due  to  the  recomposition  of  the  two 
electricities  ;  but  the  operator  experiences  no  sensation,  for  the  discharge 
takes  place  through  the  wire.  But  if  the  connection  between  the  two 
coatings  be  made  by  touching  them  with  the  hands,  a  violent  shock  is 
felt  in  the  hands  and  breast,  for  the  combination  then  takes  place  through 
the  body. 

725.  Xieydenjar. — The  Leydenjar,  so  named  from  the  town  of  Leyden, 
where  it  was  invented,  is  nothing  more  than  a  modified  condenser  or  ful- 
minating pane  rolled  up.  Fig.  569  represents  a  Leyden  jar  of  the  usual 
French  shape  in  the  process  of  being  charged.  It  consists  of  a  glass  bottle 
of  any  convenient  size,  the  interior  of  which  is  either  coated  with  tin  foil 
or  filled  with  thin  leaves  of  copper,  or  with  gold  leaf.  Up  to  a  certain 
distance  from  the  neck  the  outside  is  coated  with  tin  foil.  The  neck  is 
provided  with  a  cork,  through  which  passes  a  brass  rod,  which  terminates 
at  one  end  in  a  knob,  and  communicates  with  the  metal  in  the  interior. 
The  metallic  coatings  are  called  respectively  the  iiitenial  and  external 
coatings.  Like  the  condenser,  the  jar  is  charged  by  connecting  one  of  the 
coatings  with  the  ground,  and  the  other  with  the  source  of  electricity. 
When  it  is  held  in  the  hand  by  the  external  coating,  and  the  knob  pre- 
sented to  the  positive  conductor  of  the  machine,  positive  electricity  is 


642 


Frictional  Electricity. 


[725- 


accumulated  on  the  inner,  and  negative  electricity  on  the  outer  coating. 
The  reverse  is  the  case  if  the  jar  is  held  by  the  knob,  and  the  external 


Fig.  569. 

coating  presented  to  the  machine.  The  positive  charge  acting  induc- 
tively across  the  dielectric,  glass,  decomposes  the  electricity  of  the  outer 
coating,  attracting  the  negative,  and  repelling  the  positive,  which  escapes 
by  the  hand  to  the  ground.  Thus  it  will  be  seen  that  the  theory  of  the 
jar  is  identical  with  that  of  the  condenser,  and  all  that  has  been  said  of 
this  applies  to  the  jar,  substituting  the  two  coatings  for  the  two  plates,  A 
and  B,  of  fig.  565. 


Fig.  570- 


Fig.  571. 


Like  any  other  condenser,  the  Leyden  jar  may  be  discharged  either 
slowly  or  instantaneously.  For  the  latter  purpose  it  is  held  in  the  hand  by 
the  outside  coating  (fig.  570),  and  the  two  coatings  are  then  connected  by 
means  of  the  simple  discharger.  Care  must  be  taken  to  touch  first  the 
external  coating  with  the  discharger,  otherwise  a  smart  shock  will  be  felt. 
To  discharge  it  slowly  the  jar  is  placed  on  an  insulated  plate,  and  first  the 
internal  and  then  the  external  coating  touched,  either  with  the  hand  or 
with  a  metallic  conductor.     A  slight  spark  is  seen  at  each  discharge. 

Fig.  571  represents  a  very  pretty  experiment  for  illustrating  the  slow  dis- 


-727] 


Ley  den  Jar. 


643 


charge.  The  rod  terminates  in  a  small  bell,  d,  and  the  outside  coating  is 
connected  with  an  upright  metallic  support,  on  which  is  a  similar  bell,  e. 
]5etween  the  two  bells  a  light  copper  ball  is  suspended  by  a  silk  thread. 
The  jar  is  then  charged  in  the  usual  manner  and  placed  on  the  support  in. 
The  internal  coating  contains  a  quantity  of  free  electricity ;  the  pendulum 
is  attracted  and  immediately  repelled,  striking  against  the  second  bell,  to 
which  it  imparts  its  free  electricity.  Being  now  neutralised,  it  is  again  at- 
tracted by  the  first  bell,  and  so  on  for  some  time,  especially  if  the  air  be 
dry,  and  the  jar  pretty  large. 

726.  Iieyden  jar  with  movable  coatingrs. — This  apparatus  (fig.  572) 
is  used  to  demonstrate  that  in  the  Leyden  jar,  the  opposite  electricities  are 


Fig.  572. 


not  distributed  on  the  coatings  merely,  but  reside  principally  on  the  oppo- 
site sides  of  the  glass.  It  consists  of  a  somewhat  conical  glass  vessel,  B, 
with  movable  coatings  of  zinc  or  tin,  C  and  D.  These  separate  pieces 
placed  one  in  the  other,  as  shown  in  figure  A,  form  a  complete  Leyden  jar. 
After  having  charged  the  jar,  it  is  placed  on  a  cake  of  resin ;  the  internal 
coating  is  first  removed  by  the  hand,  or  better  a  glass  rod,  and  then  the 
glass  vessel.  The  coatings  are  found  to  contain  very  little  electricity,  and 
if  they  are  placed  on  the  table  they  are  restored  to  the  neutral  state. 
Nevertheless,  when  the  jar  is  put  together  again,  as  represented  in  the 
figure  at  A,  a  shock  may  be  taken  from  it  almost  as  strong  as  if  the 
coatings  had  not  been  removed.  It  is  therefore  concluded  that  the 
coatings  merely  play  the  part  of  conductors,  distributing  the  electricity 
over  the  surface  of  the  glass,  which  thus  becomes  polarised,  and  retains 
this  state  even  when  placed  on  the  table,  owing  to  its  imperfect  con- 
ductivity. 

The  experiment  may  be  conveniently  made  by  forming  a  Leyden  jar, 
of  which  the  inside  and  outside  coatings  are  of  mercury,  charging  it  ; 
then,  having  mixed  the  two  coatings,  the  apparatus  is  put  together  again, 
upon  which  a  discharge  may  be  once  more  taken. 

727.  Iiiclitenbergr's  fig^ures. — This  experiment  well  illustrates  the  oppo- 
site electrical  conditions  of  the  two  coatings  of  a  Leyden  jar.  Holding  a 
jar  charged  with  positive  electricity  by  the  hand,  a  series  of  lines  are  drawn 
with  the  knob  on  a  cake  of  resin  or  vulcanite ;  then  having  placed  the  jar 
on  an  insulator,  it  is  held  by  the  knob,  and  another  series  traced  by  means 


644  Frictional  Electricity,  [727- 

of  the  outer  coating.  If  now  an  intimate  mixture  of  red  lead  and  flour  of 
sulphur  be  projected  on  the  cake,  the  sulphur  will  attach  itself  to  the  posi- 
tive lines,  and  the  red  lead  to  the  negative  lines ;  the  reason  being  that  in 
mixing  the  powders  the  sulphur  has  become  negatively  electrified,  and  the 
red  lead  positively.  The  sulphur  will  arrange  itself  in  tufts  with  numerous 
diverging  branches,  while  the  red  lead  will  take  the  form  of  small  circular 
spots,  indicating  a  difference  in  the  two  electricities  on  the  surface  of  the 
resin. 

728.  Penetration  of  tbe  cbargre.  Residual  cliargre. — Not  only  do  the 
electricities  adhere  to  the  two  surfaces  of  the  insulating  medium  which 
separates  them,  but  they  penetrate  to  a  certain  extent  into  the  interior,  as 
is  shown  by  the  following  experiment.  A  condenser  is  formed  of  a  plate 
of  shellac,  and  movable  metal  plates.  It  is  then  charged,  retained  in 
that  state  for  some  time,  and  afterwards  discharged.  On  removing  the 
metal  coatings  and  examining  both  surfaces  of  the  insulator,  they  show 
no  signs  of  electricity.  After  some  time,  however,  each  face  exhibits  the 
presence  of  some  electricity  of  the  same  kind  as  that  of  the  plate  with 
which  it  was  in  contact  while  the  apparatus  was  charged.  This  can  be 
explained  by  assuming  that  the  electricity  had  slowly  penetrated  from  the 
exterior  to  the  interior  during  the  first  phase  of  the  experiment,  and  had 
returned  to  the  surface  during  the  second. 

A  phenomenon  frequently  observed  in  Leyden  jars  is  of  the  same  nature. 
When  a  jar  has  been  discharged  and  allowed  to  stand  a  short  time,  it  ex- 
hibits a  second  charge,  which  is  called  the  electric  residu:.  The  jar  may 
be  again  discharged,  and  a  second  residue  will  be  left,  feebler  than  the 
first,  and  so  on,  for  three  or  four  times.  Indeed  with  a  delicate  electroscope 
a  long  succession  of  such  residues  may  be  demonstrated.  Time  is  required 
for  the  penetration  of  the  electricities  into  the  mass  ;  and  hence  the  residue 
is  greater  the  longer  the  jar  has  remained  charged.  The  magnitude  of  the 
residue  further  depends  on  the  intensity  of  the  charge,  and  also  on  the 
degree  in  which  the  metal  plates  are  in  contact  with  the  insulator.  It 
varies  with  the  nature  of  the  substance,  but  there  is  no  residue  with 
either  liquids  or  gaseous  insulators.  Faraday  found  that  with  paraffin 
the  residue  was  greatest,  then  with  shellac,  while  with  glass  and  sulphur 
it  was  least  of  all.  Kohlrausch  has  found  that  the  residue  is  nearly  pro- 
portional to  the  thickness  of  the  insulator. 

729.  Electric  batteries. — The  charge  which  a  Leyden  jar  can  take 
depends  on  the  extent  of  the  coated  surface,  and  for  small  thicknesses  is 
inversely  proportional  to  the  thickness  of  the  insulator.  Hence,  the  larger 
and  thinner  the  jar  the  more  powerful  the  charge.  But  very  large  jars  are 
expensive,  and  liable  to  break;  and  when  too  thin,  the  accumulated 
electricities  are  apt  to  discharge  themselves  through  the  glass,  especially 
if  it  is  not  quite  homogeneous.  Leyden  jars  have  usually  from  ^  to  3 
square  feet  of  coated  surface.  For  more  powerful  charges  electric  batteries 
are  used. 

An  electric  battery  consists  of  a  series  of  Leyden  jars,  whose  internal  and 
external  coatings  are  respectively  connected  with  each  other  (fig.  573). 
They  are  usually  placed  in  a  wooden  box  lined  on  the  bottom  with  tin  foil. 


731] 


Electric  Batteries. 


645 


This  lining  is  connected  with  two  metal  handles  in  the  sides  of  the  box. 
The  internal  coatings  are  connected  with  each  other  by  metallic  rods,  and 
the  battery  is  charged  by  placing  the  internal  coatings  in  connection  with 
the  prime  conductor,  while  the  outer  coatings  are  connected  with  the 
ground  by  means  of  a  chain  fixed  to  the  handles.  A  quadrant  electrometer 
fixed  to  the  jar  serves  to  indicate  the  charge  of  the  battery.     Although 


Fig.  573- 


there  is  a  large  quantity  of  electricity  accumulated  in  the  apparatus  the 
divergence  is  not  great,  for  it  is  simply  due  to  the  free  electricity  on  the 
internal  coating.  The  number  of  jars  is  usually  four,  six,  or  nine.  The 
larger  and  more  numerous  they  are,  the  longer  is  the  time  required  to 
charge  the  battery,  but  the  effects  are  so  much  the  more  powerful. 

When  a  battery  is  to  be  discharged,  the  coatings  are  connected  by 
means  of  the  discharging  rod,  the  outside  coating  being  touched  first. 
Great  care  is  required,  for  with  large  batteries  serious  accidents  may 
occur,  resulting  even  in  death. 

730.  The  universal  discharg-er. — This  is  an  almost  indispensable 
apparatus  in  experiments  with  the  electric  battery.  On  a  wooden  stand 
(fig.  574)  are  two  glass  legs,  each  provided  with  universal  joints,  in  which 
movable  brass  rods  are  fitted.  Between  tliese  legs  is  a  small  ivory  table, 
on  which  is  placed  the  object  under  experiment.  The  two  metal  knobs 
being  directed  towards  the  objects,  one  of  them  is  connected  with  the 
external  coating  of  the  battery,  and  the  moment  communication  is  made 
between  the  other  and  the  internal  coating  by  means  of  the  glass  dis- 
charging rod,  a  violent  shock  passes  through  the  object  on  the  table. 

731.  Chargringr  by  cascade. — A  series  of  Leyden  jars  are  placed  each 
separately  on  insulating  supports.  The  knob  of  the  first  is  in  connection 
with  the  prime  conductor  of  the  machine,  and  its  outer  coating  joined  to 
the  knob  of  the  second,  the  outer  coating  of  the  second  to  the  knob  of  the 


646 


Frictional  Electricity. 


[731- 


third,  and  so  on  ;  the  outer  coating  of  the  last  communicating  with  the 
ground.  The  inner  coating  of  the  first  receives  a  charge  of  positive  elec- 
tricity from  the  machine,  and  the  corresponding  positive  electricity  set 
free  by  induction  on  its  outer  coating,  instead  of  passing  to  the  ground, 
gives  a  positive  charge  to  the  inner  coating  of  the  second,  which,  acting 
in  like  manner,  developes  a  charge  in  the  third  jar,  and  so  on,  to  the  last, 
where  the  positive  electricity  developed  by  induction  on  the  outer  coating 
passes  to  the  ground.  The  jars  may  be  discharged  either  singly,  by  con- 
necting the  inner  and  outer  coatings  of  each  jar,  or  simultaneously  by 
connecting  the  inner  coating  of  the  first  with  the  outer  of  the  last.     In 


Fig.  574- 


this  way  the  quantity  of  electricity  necessary  to  charge  one  jar  is  avail- 
able for  charging  a  series  of  jars. 

For  from  the  preceding  explanation  it  is  clear,  that  with  a  series  of 
similar  Leyden  jars  charged  by  cascade,  if  we  call  the  charge  of  positive 
electricity  which  the  inside  of  the  first  jar  receives  i,  it  will  develope  by 
induction  on  the  outside  a  quantity  in{in<  i)  of  negative  electricity  and 
the  same  quantity  771  of  positive  electricity  which  will  pass  into  the 
inside  of  the  second  jar  ;  this  in  turn  will  develope  m  x  771  =-771^  of  negative 
electricity  on  the  outside  of  that  jar,  and  the  same  quantity  711^  of  positive 
electricity  will  pass  into  the  inside  of  the  third  jar,  and  so  forth.     Thus  it 


732J 


Lanes  Electrometer. 


647 


ni  +  7n''  +  ;;/-*  +  nr  + 


will  be  seen  that  the  quantities  of  positive  electricity  developed  in  a  series 

of  n  similar  jars  by  the  unit  charge  of  positive  electricity  will  be 

J fji'^ 

I +m  + 7n'^  +  ?n^  +      .     .     .     .     ;;?"  — ^= ^, 

I  —m 

and  of  negative  electricity  on  the  corresponding  outsides  of 

.     .     .     m"  =  -A /, 

1  —m 

Thus,  if  there  be  six  jars  and  m  =  o'<^,  the  quantity  of  positive  electricity 
developed  by  the  unit  charge  is  4-69. 

If  the  external  coatings  of  a  charged  and  uncharged  jar  are  placed  in 
connection,  and  if  the  inner  coatings  are  now  connected,  after  separating 
them  they  are  both  found  to  be  charged  in  the  same  manner.  In  this 
process  a  current  has  been  produced  between  the  outside  coatings  and 
one  between  the  inner  ones,  to  which  Dove  has  given  the  name  charge 
current,  and  which  has  all  the  properties  of  the  ordinary  discharge  current. 

732.  XkXeasurement  of  tbe  cbarg^e  of  a  battery.  Ziane's  electro- 
meter.— When  the  outer  and  inner  coatings  of  a  charged  Leyden  jar 
are  gradually  brought  nearer  each  other,  at  a  certain  distance  a  spontaneous 
discharge  ensues.  This  distance  is  called  the  striking  distance.  It  is 
inversely  proportional  to  the  pressure  of  the  air  and  directly  proportional 
to  the  electric  density  of  that  point  of  the  inner  coating  at  which  the  dis- 
charge takes  place.  As  the  density  of  any  point  of  the  inner  coating, 
other  things  remaining  the  same,  is  proportional  to  the  entire  charge,  the 
striking  distance  is  proportional  to  the  quantity  of  electricity  in  a  jar. 
The  measurement  of  the  charge  of  a  battery,  however,  by  means  of  the 
striking  distance,  can  only  take  place  when  the  charge  disappears. 


Fig.  575- 

By  means  of  Lane's  electrometer,  which  depends  on  an  application 
of  this  principle,  the  charge  of  a  jar  or  battery  may  be  measured.  This 
apparatus,  c  (fig.  575),  consists  of  an  ordinary  Leyden  jar,  near  which 
there  is  a  vertical  metallic  support.  At  the  upper  end  is  a  brass  rod, 
with  a  knob  at  one  end,  which  can  be  placed  in  metallic  connection  with 
the  outside  of  the  jar  :  the  rod  being  movable,  the  knob  can  be  kept  at 
a  measured  distance  from  the  knob  of  the  inner  coating.  Fig.  575  repre- 
sents the  operation  of  measuring  the  charge  of  a  jar  by  means  of  this  ap- 
paratus.    The  jar  b,  whose  charge  is  to  be  measured,  is  placed  on  an  in- 


648 


Prictional  Electricity. 


[732- 


Fig.  576. 


sulated  stool  with  its  outer  coating  in  metallic  connection  with  the  inner 
coating  of  Lane's  jar  c,  the  outer  coating  of  which  is  in  connection  with 
the  ground,  or  still  better  with  a  system  of  gas  or  water  pipes  ;  a  is  the 
conductor  of  the  machine.  When  the  machine  is  worked,  positive  elec- 
tricity passes  into  the  jar  b  ;  a  proportionate  quantity  of  positive  electri- 
city is  repelled  from  its  outer  coating,  passes  into  the  inner  coating  of  the 
electrometer,  and  there  produces  a  charge.  When  this  has  reached  a 
certain  limit,  it  discharges  itself  between  the  two  knobs,  and  as  often  as 
such  a  discharge  takes  place,  the  same  quantity  of  positive  electricity  will 
have  passed  from  the  machine  into  the  battery  ;  hence  its  charge  is  pro- 
portional to  the  number  of  discharges  of  the  electrometer. 

Harris's  unit  jar  (fig.  576)  is  an  application  of  the  same  principle,  and 
is  very  convenient  for  measuring  quantities  of  electricity.  It  consists  of  a 
small  Leyden  phial  4  inches  in   length,  and  f  of  an  inch  in  diameter 

coated  to  about  an  inch  from  the 
end,  so  as  to  expose  about  6  inches 
of  coated  surface.  It  is  fixed  hori- 
zontally on  a  long  insulator,  and 
the  charging  rod  connected  at  P 
with  the  conductor  of  the  machine 
while  the  outer  coating  is  connected 
with  the  jar  or  battery  by  the  rod 
tp.  When  the  accumulation  of 
electricity  in  the  interior  has  reached 
a  certain  height  depending  on  the  distance  of  the  two  balls  ;;/  and  n,  a 
discharge  ensues,  and  marks  a  certain  quantity  of  electricity  received  as  a 
charge  by  the  battery,  in  terms  of  the  small  jar. 

733.  ]Laws  of  electric  cbargre. — Harris,  by  means  of  experiments  with 
the  unit  jar  suitably  modified,  and  Riess,  by  analogous  arrangements,  have 
found,  by  independent  researches,  that  for  small  distances  the  striking 
distaYice  is  directly  proportional  to  ihe  quantity  of  electricity,  and  inversely 
proportional  to  the  extent  of  coated  surface ;  in  other  words  it  is  propor- 
tional to  the  electric  density.  Thus,  taking  the  surface  of  one  jar  as 
unity,  if  a  battery  of  six  Leyden  jars  charged  by  ico  turns  of  the  machine 
has  a  striking  distance  of  9  millimetres,  a  battery  of  four  similar  jars 
charged  by  120  turns  will  have  the  striking  distance  of  16*2  millimetres. 
For 

100  I£0 

x=  i6-2. 
The  charge  also  depends  on  the  nature  of  the  glass,  or  other  dielectric,  of 
which  the  jar  is  made  ;  and  further,  is  stated  by  Wheatstone  to  be 
inversely  proportional  to  the  square  of  the  thickness  of  the  dielectric. 
Riess  has  also  found  that  when  a  battery  or  jar  is  discharged  in  the 
striking  distance,  a  charge  still  remains,  for  when  the  coatings  are  brought 
nearer  a  similar  discharge  may  be  taken,  and  so  on.  The  amount  of  this 
residual  charge  when  the  discharge  takes  place  at  the  greatest  striking 
distance  is  always  in  the  safjie  prop07'tion  to  the  entire  charge.     In  Riess's 


-734] 


Voltds  Condensing  Electroscope.  - 


649 


experiments,   0-846   or   j|  of  the   total   charge   disappear,   and  only  j\ 
remain. 

734.  Volta's  condensing-  electroscope. — The  condensing  electroscope 
invented  by  Volta  is  a  modification  of  the  ordinary  gold  leaf  electroscope 
(705).  The  rod  to  which  the  gold  leaves  are  affixed  terminates  in  a 
disc  instead  of  in  a  knob,  and  there  is  another  disc  of  the  same  size  pro- 
vided with  an  insulating  glass  handle.  The  discs  are  covfered  with  a  layer 
of  insulating  shellac  varnish  (fig.  577). 


Fig.  577- 


Fig.  578. 


To  render  very  small  quantities  of  electricity  perceptible  by  this  appa- 
ratus, one  of  the  plates,  which  thus  becomes  the  collecting  plate,  is  touched 
with  the  body  under  examination.  The  other  '^\2A.^^\\\q  condensing  plate, 
is  connected  with  the  ground  by  touching  it  with  the  finger.  The  elec- 
tricity of  the  body,  being  diffused  over  the  collecting  plate,  acts  induc- 
tively through  the  varnish  on  the  neutral  fluid  of  the  other  plate,  attracting 
the  opposite  electricity,  but  repelling  that  of  fike  kind.  The  two  elec- 
tricities thus  become  accumulated  on  the  two  plates  just  as  in  a 
condenser,  but  there  is  no  divergence  of  the  leaves,  for  the  opposite 
electricities  counteract  each  other.  The  finger  is  now  removed,  and  then 
the  source  of  electricity,  and  still  there  is  no  divergence  ;  but  if  the  upper 
plate  be  raised  (fig.  578)  the  neutralisation  ceases,  and  the  electricity  being 
free  to  move  diffuses  itself  over  the  rod  and  the  leaves,  which  then 
diverge  widely.  The  delicacy  of  the  apparatus  is  increased  by  adapting 
to  the  foot  of  the  apparatus  two  metal  rods,  terminating  in  knobs,  for 

y  F 


650 


Frictional  Electricity, 


[734- 


tliese  knobs,  being  excited  by  induction  from  the  gold  leaves,  react  upon 
them. 

A  still  further  degree  of  delicacy  is  attained  by  replacing  the  rods  by 
two  Bohnenberger's  dry  piles,  one  of  which  presents  its  positive  and  the 
other  its  negative  pole.  Instead  of  two  gold  leaves  there  is  only  one  ;  the 
least  trace  of  electricity  causes  it  to  oscillate  either  to  one  side  or  to  the 
other,  and  at  th'e  same  time  shows  the  kind  of  electricity. 

735.  Thomson's  electrometer. — Sir  William  Thomson  has  devised  a 
new  and  delicate  form  of  electrometer,  by  which  quantitative  measure- 
ments of  the  amount  of  electrical  charge  may  be  made.  The  principle  of 
this  instrument  may  be  understood  from  the  following  description  of  a 
model  of  it  constructed  for  lecture  purposes  by  Mr.  Becker. 

A  hght  flat  broad  aluminium  needle  hangs  by  a  very  thin  wire  from  the 
inner  coating  of  a  charged  Leyden  jar,  the  outer  coating  being  in  con- 
ducting communication  with  the 
earth.  The  whole  apparatus  is 
enclosed  within  a  glass  shade 
and  the  air  kept  dry  by  means 
of  a  dish  of  sulphuric  acid ; 
there  is,  therefore,  very  little 
loss  of  electricity  and  the  needle 
remains  at  a  virtually  constant 
charge. 

The  needle  is  suspended  over 
four  quadrantal  metal  plates 
insulated  from  each  other  and 
from  the  ground  by  resting  on 
glass  stands.  The  alternate 
quadrants  are  in  conducting 
communication  with  each  other 
by  means  of  wires.  If  now  all 
the  quadrants  are  in  the  same 
electrical  condition,  the  needle 
will  be  at  rest  when  it  is  directly 
over  one  of  the  diametrical  slits. 
But  if  the  two  pairs  of  quadrants 
^'^'  ^^^"  are  charged  with  opposite  kinds 

of  electricity,  as  when,  for  instance,  they  are  connected  with  the  two  poles 
of  an  insulated  voltaic  cell  by  means  of  the  knobs,  then  each  end  of  the 
needle  will  be  repelled  by  the  pair  of  quadrants  which  are  electrified  like 
itself,  and  will  be  attracted  by  the  other  pair.  It  will  thus  be  subject  to 
the  action  of  a  couple  tending  to  set  it  obliquely  to  the  slit. 

In  order  to  render  the  slightest  motion  of  the  needle  visible,  a  small 
silver  concave  mirror  with  a  radius  of  about  a  metre  is  fixed  above  it. 
The  light  of  a  petroleum  lamp,  not  represented  in  the  figure,  strikes 
against  this  and  is  reflected  as  a  spot  of  light  on  a  horizontal  scale.  Any 
deflection  of  the  needle  either  on  one  side  or  the  other,  is  indicated  by 
the  motion  of  the  spot  of  light  on  the  scale  (491). 


^% 


^7317/  Effects  of  the  Electric  Discharge.  651 


i 


THE   ELECTRIC   DISCHARGE.  \    ^ 

736.  Effects  of  the  electric  discbargre. — The  recombination  of  the 
two  electricities  which  constitutes  the  electrical  discharge  may  be  either 
continuous  or  sudden ;  continuous,  or  of  the  nature  of  a  current,  as  when 
the  two  conductors  of  a  cylinder  machine  are  joined  by  a  chain  or  a  wire ; 
and  sudden,  as  when  the  opposite  electricities  accumulate  on  the  surface 
of  two  adjacent  conductors,  till  their  mutual  attraction  is  strong  enough 
to  overcome  the  intervening  resistances,  whatever  they  may  be.  But  the 
difference  between  a  sudden  and  a  continuous  discharge  is  one  of  degree, 
and  not  of  kind,  for  there  is  no  such  thing  as  an  absolute  non-conductor,  r\  ^ 
and  the  very  best  conductors,  the  metals,  offer  an  appreciable  resistance 
to  the  passage  of  electricity.  Still,  the  difference  at  the  two  extremes  of 
the  scale  is  sufficiently  great  to  give  rise  to  a  wide  range  of  phenomena.  ^  xp 

Riess  has  shown  that  the  discharge  of  a  battery  does  not  consist  in  a^^^ 
simple  union  of  the  positive  and  negative  electricities,  but  that  it  consists 
of  a  series  of  successive  partial  discharges.  The  direction  of  the  discharge 
depends  mainly  on  the  length  and  nature  of  the  circuit.  By  observations 
of  the  image  of  the  spark  in  a  rotating  mirror,  and  of  the  luminous 
phenomena  at  the  positive  and  negative  poles  when  the  discharge  takes 
place  in  highly  rarefied  gases,  as  well  as  by  the  manner  in  which  a  magnet 
affects  the  phenomena  of  discharge,  Feddersen  and  Paalzow  have  shown 
that  the  discharge  consists  of  a  series  of  oscillating  currents  alternately 
in  opposite  directions.  As  the  resistance  of  the  circuit  increases,  the 
number  of  these  alternating  discharges  decreases,  but  at  the  same  time 
their  duration  is  greater.  With  very  great  resistance,  as  for  instance 
when  a  wet  thread  is  interposed,  the  alternating  discharge  becomes  a 
single  one. 

The  phenomena  of  the  discharge  are  usually  divided  into  Xki^  physio- 
logical, luminous,  mechanical,  magnetical,  and  chemical  effects, 

'j'i^'].  Physiolog^ical  effects. — The  physiological  effects  are  tliose  pro- 
duced on  living  beings,  or  on  those  recently  deprived  of  life.  In  the  first 
case  they  consist  of  a  violent  excitement  which  the  electricity  exerts 
on  the  sensibility  and  contractibihty  of  the  organic  tissues  through  which 
it  passes ;  and  in  the  latter,  of  violent  muscular  convulsions  which  re- 
semble a  return  to  life. 

The  shock  from  the  electrical  machine  has  been  already  noticed  ('717). 
The  shock  taken  from  a  charged  Leyden  jar  by  grasping  the  outer 
coating  with  one  hand  and  touching  the  inner  with  the  other,  is  much 
more  violent,  and  has  a  peculiar  character.  With  a  small  jar  the  shock 
is  felt  in  the  elbow ;  with  a  jar  of  about  a  quart  capacity  it  is  felt  across 
the  chest ;  and  w4th  jars  of  still  larger  dimensions  in  the  stomach. 

A  shock  may  be  given  to  a  large  number  of  persons  simultaneously 
by  means  of  the  Leyden  jar.  For  this  purpose  they  must  form  a  chain  by 
joining  hands.  If  then  the  first  touches  the  outside  coating  of  a  charged 
jar,  while  the  last  at  the  same  time  touches  the  knob,  all  receive  a  simul- 
taneous shock,  the  intensity  of  which  depends  on  the  charge,  and  on  the 


652  Frictional  Electricity.  [737- 

number  of  persons  receiving-  it.  Those  in  the  centre  of  the  chain  are 
found  to  receive  a  less  violent  shock  than  those  near  the  extremities. 
The  Abbe  Nollet  discharged  a  Leyden  jar  through  an  entire  regiment 
of  1,500  men,  who  all  received  a  violent  shock  in  the  arms  and  shoulders. 
With  large  Leyden  jars  and  batteries  the  shock  is  sometimes  very 
dangerous.  Priestley  killed  rats  with  batteries  of  7  square  feet  coated 
surface,  and  cats  with  a  battery  of  about  4|-  square  yards  coating. 

738.  ]Luxninous  effects. — The  recombination  of  two  electricities  of 
high  potential  (752)  is  always  accompanied  by  a  disengagement  of  light,  as 
is  seen  when  sparks  are  taken  from  a  machine,  or  when  a  Leyden  jar  is 
discharged.  The  better  the  conductors  on  which  the  electricities  are 
accumulated,  the  more  brilliant  is  the  spark ;  its  colour  varies  not  only 
with  the  nature  of  the  bodies,  but  also  with  the  nature  of  the  surrounding 
medium  and  with  the  pressure.  The  spark  between  two  charcoal  points 
is  yellow,  between  two  balls  of  silvered  copper  it  is  green,  between  knobs 
of  wood  or  ivory  it  is  crimson.  In  atmospheric  air  at  the  ordinary  pres- 
sure the  electric  spark  is  white  and  brilliant ;  in  rarefied  air  it  is  reddish ; 
and  in  vacuo  it  is  violet.  In  oxygen,  as  in  air,  the  spark  is  white;  in 
hydrogen  it  is  reddish ;  and  green  in  the  vapour  of  mercury,  in  carbonic 
acid  it  is  also  green,  while  in  nitrogen  it  is  blue  or  purple,  and  accom- 
panied by  a  peculiar  sound.  Generally  speaking,  the  higher  the  potential 
the  greater  is  the  lustre  of  the  spark.  It  is  asserted  by  Fusinieri  that  in 
the  electric  spark  there  is  always  a  transfer  of  material  particles  in  a  state 
of  extreme  tenuity,  in  which  case  the  modifications  in  colour  must  be  due 
to  the  transport  of  ponderable  matter. 

When  the  spark  is  viewed  through  a  prism,  the  spectrum  obtained  is 
full  of  dark  lines  (539),  the  number  and  arrangement  of  which  depend  on 
the  nature  of  the  poles. 

739.  Spark  and  brush  discharg:e. — The  shapes  which  luminous 
electric  phenomena  assume  may  be  classed  under  two  heads — the  spark 
and  the  brush.  The  brush  forms  when  the  electricity  leaves  the  con- 
ductor ifi  a  continuous  flow;  the  spark,  when  the  discharge  is  discon- 
tinuous. The  fonnation  of  one  or  the  jother  of  these  depends  on  the 
nature  of  the  conductor  and  on  the  nature  of  the  conductor  in  its  vicinity ; 
and  small  alterations  in  the  position  of  the  surrounding  conductors  trans- 
form the  one  into  the  other. 

The  spark  which  at  short  distances  appears  straight,  at  longer  distances 
has  a  zigzag-shape  with  diverging  branches.  Its  length  depends  on 
the  density  at  the  part  of  the  conductor  from  which  it  is  taken ;  and  to 
obtain  the  longest  sparks  the  electricity  must  be  of  as  high  density  as 
possible,  but  not  so  high  as  to  discharge  spontaneously.  With  long 
sparks  the  luminosity  is  different  in  different  parts  of  the  spark. 

The  brush  derives  its  name  from  the  radiating  divergent  arrangement 
of  the  light,  and  presents  the  appearance  of  a  luminous  cone,  whose  apex 
touches  the  conductor.  Its  size  and  colour  differ  with  the  nature  and 
form  of  the  conductor;  it  is  accompanied  by  a  peculiar  hissing  noise, 
very  different  from  the  sharp  crack  of  the  spark.  Its  luminosity  is  far 
less  than  that  of  the  spark,  for  while  the  latter  can  easily  be  seen  by 


-741] 


The  Electric  Egg. 


653 


daylight,  the  former  is  only  visible  in  a  darkened  room.  The  brush 
discharge  may  be  obtained  by  placing  on  the  conductor  a  wire  filed  round 
at  the  end,  or,  with  a  powerful  machine,  by  placing  a  small  bullet  on  the 
conductor.  The  brush  fiom  a  negative  conductor  is  less  than  from  a 
positive  conductor;  the  cause  of  this  difference  has  not  been  satis- 
factorily made  out,  but  may  originate  in  the  fact,  which  Faraday  has 
observed,  that  negative  electricity  discharges  into  the  air  at  a  some- 
what lower  density  than  positive  electricity ;  so  that  a  negatively  charged 
knob  sooner  attains  that  density  at  which  spontaneous  discharge  takes 
place  than  does  a  positively  charged  one,  and  therefore  discharges  the 
electricity  at  smaller  intervals  and  in  less  quantities. 

When  electricity,  in  virtue  of  its  high  density,  issues  from  a  conductor, 
no  other  conductor  being  near,  the  discharge  takes  place  without  noise, 
and  at  the  places  at  which  it  appears  there  is  a  pale  blue  luminosity, 
called  the  electrical  glow,  or  on  points,  a  star-like  centre  of  light.  It  is 
seen  in  the  dark  by  placing  a  point  on  the  conductor  of  the  machine. 

740.  Electric  eggr. — The  influence  of  the 
pressure  of  the  air  on  the  electric  Hght  may  be 
studied  by  means  of  the  electric  egg.  This 
consists  of  an  ellipsoidal  glass  vessel  (fig.  580), 
with  metal  caps  at  each  end.  The  lower  cap 
is  provided  with  a  stopcock,  so  that  it  can  be 
screwed  into  an  air  pump,  and  also  into  a  heavy 
metal  foot.  The  upper  metal  rod  moves  up 
and  down  in  a  leather  stuffing  box;  the  lower 
one  is  fixed  to  the  cap.  A  vacuum  having  been 
made,  the  stopcock  is  turned,  and  the  vessel 
screwed  into  its  foot;  the  upper  part  is  then 
connected  with  a  powerful  electrical  machine, 
and  the  lower  one  with  the  ground.  On  work- 
ing the  machine,  the  globe  becomes  filled  with 
a  feeble  violet  light  continuous  from  one  end 
to  the  other,  and  resulting  from  the  recomposi- 
tion  of  the  positive  fluid  of  the  upper  cap  with 
the  negative  of  the  lower.  If  the  air  be  gradu- 
ally allowed  to  enter  by  opening  the  stopcock, 
the  light  now  appears  white  and  brilliant, 
and  is  only  seen  as  an  ordinary  intermittent 
spark.  Fig.  580. 

Some  beautiful  effects  of  the  electric  light  are  obtained  by  means  of 
Geissler's  tubes,  which  will  be  noticed  under  Dynamical  Electricity. 

741.  ]Luminous  tube,  square,  and  bottle. — The  luminous  tube 
(fig.  581)  is  a  glass  tube  about  a  yard  long,  round  which  are  arranged  in 
a  spiral  form  a  series  of  lozenge-shaped  pieces  of  tin  foil,  between  which 
are  very  short  intervals.  There  is  a  brass  cap  with  hooks  at  each  end, 
in  which  the  spiral  terminates.  If  one  end  be  presented  to  a  machine  in 
action,  while  the  other  is  held  in  the  hand,  sparks  appear  simultaneously 


654 


Frictional  Electricity. 


[741 


at  each  interval,  and  produce  a  brilliant  luminous  appearance,  especially 
in  the  dark. 


# 


Fig.  581. 

The  luminous  pane  (fig.  582)  is  constructed  on  the  same  principle,  and 
consists  of  a  square  of  ordinary  glass,  on  which  is  fastened  a  narrow  strip 
of  tin  foil  folded  parallel  to  itself  for  a  great  number  of  times.  Spaces 
are  cut  out  of  this  strip  so  as  to  represent  any  figure,  a  portico  for  example- 


Fig.  582. 


The  pane  being  fixed  between  two  insulating  supports,  the  upper 
extremity  of  the  strip  is  connected  with  the  electrical  machine,  and  the 
lower  part  with  the  ground.  When  the  machine  is  in  operation,  a  spark 
appears  at  each  interval,  and  reproduces  in  luminous  flashes  the  object 
represented  on  the  glass. 

The  luminous  jar  (fig.  583)  is  a  Leyden  jar,  whose  outer  coating 
consists  of  a  layer  of  varnish  strewed  over  with  metallic  powder.  A 
strip  of  tin  fitted  on  the  bottom  is  connected  with  the  ground  by  means 
of  a  chain;  a  second  band  at  the  upper  part  of  the  coating  has  a 
projecting  part,  and  the  rod  of  the  bottle  is  curved  so  that  the  knob  is 


-742]         Calorific  Effects  of  the  Electric  Discharge. 


655 


about  f  of  an  inch  distant  from  the  projection.     This  bottle  is  suspended 
from  the  machine,  and  as  rapidly  as  this  is  worked,  large  and  brilliant 
sparks  pass  between  the  knob  and  the  outer  coating,  illuminating  the- 
outside  of  the  apparatus. 

742.  Calorific  effects. — Besides  being  luminous,  the  electric  spark 
is  a  source  of  intense  heat.  When  it  passes  through  inflammable 
liquids,  as  ether  or  alcohol,  it  inflames  them.  An  arrangement  for 
effecting  this  is  represented  in  figure  584.  It  is  a  small  glass  cup 
through  the  bottom  of  which  passes  a  metal  rod,  terminating  in  a  knob 
and  fixed  to  a  metal  foot.  A  quantity  of  liquid  sufficient  to  cover  the 
knob  is  placed  in  the  vessel.  The  outer  coating  of  the  jar  having  been 
connected  with  the  foot  by  means  of  a  chain,  the  spark  which  passes 
when  the  two  knobs  are  brought  near  each  other  inflames  the  liquid. 
With  ether  the  experiment  succeeds  very  well,  but  alcohol  requires  to  be 
first  warmed. 

Coal  gas  may  also  be  ignited  by  means  of  the  electric  spark.     A  person 


Fig.  583. 


Fig.  584. 


Standing  on  an  insulating  stool  places  one  hand  on  the  conductor  of  a 
machine  which  is  then  worked,  while  he  presents  the  other  to  the  jet  of  gas 
issuing  from  a  metallic  burner.  The  spark  which  passes  ignites  the  gas. 
When  a  battery  is  discharged  through  an  iron  or  steel  wire  it  becomes 
heated,  and  even  made  incandescent  or  melted,  if  the  discharge  is  very 
powerful. 


656  Frictioiial  Electidcity.  [742- 

The  laws  of  this  heating  effect  have  been  investigated  independently 
by  Harris  and  by  Riess  by  means  of  the  electric  thermometer.  This 
is  essentially  an  air  thermometer,  across  the  bulb  of  which  is  a  fine 
platinum  wire.  When  a  discharge  is  passed  through  the  wire  it  becomes 
heated,  expands  the  air  in  the  bulb,  and  this  expansion  is  indicated  by 
the  motion  of  the  liquid  along  the  graduated  stem  of  the  thermometer. 
In  this  way  it  has  been  found  that  the  increase  in  temperature  in  the  wire 
is  proportional  to  the  electric  density  multiplied  by ,  the  quantity  of 
electricity  ;  and  since  the  electric  density  is  equal  to  the  quantity  of 
electricity — usually  measured  by  the  number  of  discharges  of  the  unit 
jar  (732),  divided  by  the  surface,  the  heating  effect  is  proportional  to  the 

square  of  the  number  of  discharges  divided  by  the  surface ;  that  is,  h  =  ?-. 

s 

Rie?s  has  also  found  that  with  the  same  charge,  but  with  wires  of 
different  dimensions,  the  rise  of  temperature  is  inversely  as  the  fourth 
power  of  the  diameter.  Thus,  compared  with  a  given  wire  as  unity,  the 
rise  of  temperature  in  a  wire  of  double  or  treble  the  diameter  would  be  ^^ 
or  g\  as  small  ;  but  as  the  masses  of  these  wires  are  four  and  nine  times 
as  great,  the  heat  produced  v^onldi  be  respectively  \  and  |  as  great  as  in  a 
wire  of  unit  thickness. 

When  an  electric  discharge  is  sent  through  gunpowder  placed  on  the 
table  of  a  Henley's  discharger,  it  is  not  ignited,  but  is  projected  in  all 
directions.  But  if  a  wet  string  be  interposed  in  the  circuit  a  spark 
passes  which  ignites  the  powder.  This  arises  from  the  retardation 
which  electricity  experiences  in  traversing  a  semi-conductor,  such  as  a 
wet  string :  for  the  heating  effect  is  proportional  to  the  duration  of  the 
discharge. 

When  a  charge  is  passed  through  sugar,  heavy  spar,  fluorspar,  and 
other  subtances,  they  afterwards  become  phosphorescent  in  the  dark. 
Eggs,  fruit,  etc.,  may  be  made  luminous  in  the  dark  in  this  way. 

When  a  battery  is  discharged  through  a  gold  leaf,  pressed  between  two 
glass  plates  or  between  two  silk  ribbons,  the  gold  is  volatilised  in  a  violet 
powder  which  is  finely  divided  gold.  In  this  way  what  are  called  electric 
portraits  are  obtained. 

Siemens  has  shown  that  when  a  jar  is  charged  and  discharged  several 
times  in  succession  the  glass  becomes  heated.  Hence  there  must  be 
movements  of  the  molecules  of  the  glass  as  Faraday  supposed. 

743.  nxagrnetic  effects. — By  the  discharge  of  a  large  Leyden  jar  or 
battery,  a  steel  wire  may  be  magnetised  if  it  is  laid  at  right  angles  to  a 
conducting  wire  through  which  the  discharge  is  effected,  either  in  contact 
with  the  wire  or  at  some  distance.  And  even  with  less  powerful  discharges, 
a  steel  bar  or  needle  may  be  magnetised  by  placing  it  inside  a  tube  on 
which  is  coiled  a  fine  insulated  copper  wire.  On  passing  the  discharge 
through  this  wire  the  steel  becomes  magnetised. 

To  effect  a  deflection  of  the  magnetic  needle  by  the  electric  current 
produced  by  frictional  electricity  is  more  difficult.  It  may  be  accom- 
plished by  making  use  of  a  galvanometer  consisting  of  400  or  500 
turns   of  fine   silk-covered   wire,   which  is   further   insulated   by  being 


-744]        Mechanical  Effects  of  the  Electric  Discharge.         657 

coated  with  shellac  varnish,  and  by  separating  the  layers  by  means  of 
oiled  silk.     When  the  prime  conductor  of  a  machine  in  action  is  con- 
nected with  one  end  of  the  galvanometer  wire,  and  the  other  with  the_ 
ground,  a  deflection  of  the  needle  is  produced. 

744.  lUEecbanical  effects. — The  mechanical  effects  are  the  violent 
lacerations,  fractures,  and  sudden  expansions  which  ensue  when  a  power- 
ful discharge  is  passed  through  a  badly-conducting  substance.     Glass  is 


Fig-   585- 


perforated,  wood  and  stones  are  fractured,  and  gases  and  liquids  are  vio- 
lently disturbed.  The  mechanical  effects  of  the  electric  spark  may  be 
demonstrated  by  a  variety  of  experiments. 

Figure  585  represents  an  arrangement  for  perforating  a  piece  of  glass 
or  card.  It  consists  of  two  glass  columns,  with  a  horizontal  cross-piece, 
in  which  is  a  pointed  conductor,  B.  The  piece  of  glass,  A,  is  placed  on 
an  insulating  glass  support,  in  which  is  placed  a  second  conductor, 
terminating  also  in  a  point,  which  is  connected  with  the  outside  of  the 
battery,  while  the  knob  of  the  inner  coating  is  brought  near  the  knob  of 
B.  When  the  discharge  passes  between  the  two  conductors  the  glass  is 
perforated.  The  experiment  only  succeeds  with  a  single  jar  when  the 
glass  is  very  thin  ;  otherwise  a  battery  must  be  used. 

The  perturbation  and  sudden  expansion  which  the  discharge  produces 
may  be  illustrated  by  means  of  Kinnersley's  thermometer.  This  consists 
of  two  glass  tubes  (fig.  586),  which  fit  into  metallic  caps,  and  communicate 
with  each  other.  At  the  top  of  the  large  tube  is  a  rod  terminating  in  a 
knob,  and  moving  in  a  stuffing-box,  and  at  the  bottom  there  is  a  similar 
rod  with  a  knob.  The  apparatus  contains  water  up  to  the  level  of 
the  lower  knob.     When  the  electric  shock  passes  between  the  two  knobs 

F  F  3 


658 


Frictionai  Electricity. 


[744 


the  water  is  driven  out  of  the  larger  tube  and  rises  to  a  shght  extent  in 
the  small  one.  The  level  is  immediately  re-established,  and  therefore  the 
phenomenon  is  not  due  to  an  increase  of  temperature. 


Fig.  586 

For  the  production  of  mechanical  effects  the  universal  discharger, 
fig.  574,  is  of  great  service.  A  piece  of  wood,  for  instance,  placed  on  the 
table  between  the  two  conductors,  is  split  when  the  discharge  passes. 

745.  Chemical  effects. — The  chemical  effects  are  the  decompositions 
and  recombinations  effected  by  the  passage  of  the  electric  discharge. 
When  two  gases  which  act  on  each  other  are  mixed  in  the  proportions  in 
which  they  combine,  a  single  spark  is  often  sufficient  to  determine  their 
combination ;  but  when  either  of  them  is  in  great  excess,  a  succession  of 
sparks  is  necessary.  Priestley  found  that  when  a  series  of  electric  sparks 
was  passed  through  moist  air,  its  volume  diminished,  and  blue  litmus 
introduced  into  the  vessel  was  reddened.  This,  Cavendish  found,  was 
due  to  the  formation  of  nitric  acid. 

Several  compound  gases  are  decomposed  by  the  continued  action  of 
the  electric  spark.  With  olefiant  g'as,  sulphuretted  hydrogen,  and  am- 
monia, the  decomposition  is  complete  ;  while  carbonic  acid  is  partially 
decomposed  into  oxygen  and  carbonic  oxide.  The  electric  discharge  also 
by  suitable  means  can  feebly  decompose  water,  oxides,  and  salts  ;  but 
though  the  same  in  kind,  the  chemical  effects  of  statical  electricity  are  by 
no  means  so  powerful  and  varied  as  those  of  dynamical  electricity.  The 
chemical  action  of  the  spark  is  easily  demonstrated  by  means  of  a 
solution  of  iodide  of  potassium.  A  small  lozenge-shaped  piece  of  filter- 
ing paper,  impregnated  with  iodide  of  potassium,  is  placed  on  a  glass  plate, 
and  one  corner  connected  with  the  ground.     When  a  few  sparks  from  a 


-746]  Chemical  Effects  of  the  Electric  Discharge. 


659 


conductor  charged  with  positive  electricity  are  taken  at  the  other  corner, 
brown  spots  are  produced,  due  to  the  separation  of  iodine. 

Among  the  chemical  effects  must  be  enumerated  the  formatioh"~of~ 
ozone,  which  is  recognised  by  its  peculiar  odour  and  by  certain  chemical 
properties.  The  odour  is  perceived  when  electricity  issues  through  a 
series  of  points  from  a  conductor  into  the  air.  Its  true  nature  is  not 
accurately  known  ;  some  regard  it,  and  with  great  probability,  as  an 
alJotropic  modification  of  oxygen,  and  others  as  a  teroxide  of  hydrogen. 

T\vQ  electric  pistol  \'=,  2.  svtxdXS.  apparatus  which  serves  to  demonstrate 
the  chemical  effects  of  the  spark.  It  consists  of  a  brass  vessel  (fig.  587), 
in  which  is  introduced  a  detonating  mixture  of  two  volumes  of  hydrogen 
and  one  of  oxygen,  and  which  is  then  closed  with  a  cork.  In  a  tubulure 
in  the  side  there  is  a  glass  tube,  in  which  fits  a  metallic  rod,  terminated 
by  the  knobs  A  and  B.  The  knob  is  held  as  represented  in  fig.  588,  and 
brought  near  the  machine.  The  knob  A  becomes  negatively,  and  B 
positively  electrified  by  induction  from  the  machine,  and  a  spark  passes 
between  the  conductor  and  A.  Another  spark  passes  at  the  same  time 
between  the  knob  B  and  the  side :   this  determines  the  combination  of 


Fig.  587- 


Fig.  5^ 


the  gases,  which  is  accompanied  by  a  great  disengagement  of  heat,  and 
the  vapour  of  water  formed  acquires  such  an  expansive  force,  that  the 
cork  is  projected  with  a  report  like  that  of  a  pistol. 

746.  Application  of  tbe  electrical  dischargre  to  firing:  mines. — By 
the  labours  of  Prof.  Abel  in  this  country,  and  of  Baron  von  Ebner  in 
Austria,  the  electrical  discharge  has  been  applied  to  firing  mines  for 
military  purposes,  and  the  methods  have  acquired  a  high  degree  of  per- 
fection. The  principle  on  which  the  method  is  based  may  be  understood 
from  the  following  statement : 

One  end  of  an  insulated  wire  in  which  is  a  small  break  is  placed  in 
contact  with  the  outside  of  a  charged  Leyden  jar,  the  other  end  being 
placed  near  the  inner  coating.  If  now  this  end  be  brought  in  contact 
with  the  inner  coating  the  jar  is  discharged  and  a  spark  strikes  across  the 
break  ;  and  if  there  be  here  some  explosive  compound  it  is  ignited,  and 
this  ignition  may  of  course  be  communicated  to  any  gunpowder  in  which 
it  is  placed.  If  on  one  side  of  the  break,  instead  of  having  an  insulated 
wire  direct  back  to  the  outer  coating  of  the  Leyden  jar,  an  uncovered 
wire  be  led  into  the  ground,  the  outside  of  the  jar  being  also  connected 


66o 


Frictional  Electricity. 


[746 


with  the  ground,  the  result  is  unchanged,  the  earth  acting  as  a  return 
wire.  Moreover,  if  there  be  several  breaks,  the  explosion  will  still  ensue 
at  each  of  them,  provided  the  change  be  sufficiently  powerful. 

In  the  actual  application  it  is  of  course  necessary  to  have  an  arrange- 
ment for  generating  frictional  electricity  which  shall  be  simple,  portable, 
powerful,  and  capable  of  working  in  any  weather.  In  these  respects  the 
electrical  machine  devised  by  Von  Ebner  is  admirable.     Fig.  589  repre- 


Fig.  589. 

sents  a  view  of  this  instrument  as  constructed  by  Messrs.  Elliott,  part  of 
the  case  being  removed  to  show  the  internal  construction. 

It  consists  of  two  circular  plates  of  ebonite,  a,  mounted  on  an  axis  so 
that  they  are  turned  by  a  handle,  b^  between  rubbers,  which  are  so 
arranged  as  to  be  easily  removed  for  the  purposes  of  amalgamation,  etc. 
Fastened  to  a  knob  on  the  base  of  the  apparatus  and  projecting  between 
the  plates  is  a  pointed  brass  rod,  which  acts  as  a  collector  of  the 
electricity.  The  condenser  or  Leyden  jar  arrangement  is  inside  the  case, 
part  of  which  has  been  removed  to  show  the  arrangement.  It  consists  of 
India-rubber  cloth,  coated  on  each  side  with  tinfoil,  and  formed  into  a 
roll  for  the  purpose  of  greater  compactness.  By  means  of  a  metal  button 
the  knob  is  in  contact  with  one  tmfoil  coating,  which  thus  receives  the 
electricity  of  the  machine,  and  corresponds  to  the  inner  coating  of  the 
Leyden  jar.     Another  button,  connected  with  the  other  tinfoil  coating, 


-746] 


Firing  Mines  by  Electricity. 


66  r 


rests  on  a  brass  band  at  the  base  of  the  apparatus  which  is  in  metallic 
contact  with  the  cushions,  the  knob  d,  and  the  perforated  knob  in  which 
slides  a  rod  at  the  front  of  the  apparatus.  These  are  all  in  connectioiT 
with  the  earth.  The  knob  e  is  in  metallic  connection  with  a  disc  g  pro- 
vided with  a  light  arm.  By  means  of  a  flexible  chain  this  is  so  connected 
with  a  trigger  on  the  side  of  the  apparatus,  not  represented  in  the  figure, 
that  when  the  trigger  is  depressed,  the  arm,  and  therewith  the  knob  ^,  is 
brought  into  contact  with  the  inner  coating  of  the  condenser. 

On  depressing  the  trigger,  after  a  certain  number  of  turns,  a  spark 
passes  between  the  knob  e  and  the  sliding  rod,  and  the  striking  distance 
is  a  measure  of  the  working  condition  of  the  instrument. 

The  fuse  used  is  known  as  AbeVs  electrical  fuse,  and  has  the  following 
construction.  The  ends  of  two  fine  copper  wires,  fig.  591,  are  imbedded 
in  a  thin  solid  gutta  percha  rod,  parallel  to  each  other,  but  at  a  distance 
of  about  I  -5  mm.  At  the  lower  end  of  the  gutta  percha  a  small  cap  of 
paper  or  tinfoil  cc  is  fastened,  in  which  is  placed  a  small  quantity  of  the 
priming  composition,  which  consists  of  an  intimate  mixture  of  subsulphide 
of  copper,  subphosphide  of  copper,  and  chlorate  of  potassium.  The 
paper  is  fastened  down  so  that  the  exposed  ends  of  the  wires  are  pre- 
served in  close  contact  with  the  powder. 

This  is  the  actual  fuse  ;  for  service  the  capped  end  of  the  fuse  is 


Fig.  590. 


Fig-  591 


placed  in  a  perforation  in  the  rounded  head  of  a  wooden  cylinder,  so  as  to 
project  slightly  into  the  cavity^  of  the  cyhnder.  This  cavity  is  filled  with 
meal  powder  which  is  well  rammed  down,  so  that  the  fuse  is  firmly 


662  Frictional  Electricity.  [746- 

imbedded.  It  is  afterwards  closed  by  a  plug  of  gutta  percha,  and  the 
whole  is  finally  coated  with  black  varnish. 

The  free  ends  of  the  wires  a  a  are  pressed  into  small  grooves  in  the 
head  of  the  cyhnder  (fig.  591),  and  each  end  is  bent  into  one  of  the  small 
channels  with  which  the  cylinder  is  provided,  and  which  are  at  right 
angles  to  the  central  perforation.  They  are  wedged  in  here  by  driving  in 
small  copper  tubes,  the  ends  of  which  are  then  filed  flush  with  the  surface 
of  the  cylinder.  The  bared  ends  of  two  insulated  conducting  wires  are 
^hen  pressed  into  one  of  the  small  copper  tubes  or  eyes,  and  fixed  there 
by  bending  the  wire  round  on  to  the  wood,  as  shown  at  c. 

The  conducting  wire  used  in  firing  may  be  thin,  but  it  must  be  well 
insulated.  One  end,  which  is  bared,  having  been  pressed  into  the  hole  d 
of  the  fuse,  the  other  is  placed  in  proximity  to  the  exploder.  Into  the 
other  hole  d'  of  the  fuse  a  wire  is  placed  which  serves  as  earth  wire,  care 
being  ta:ken  that  there  is  connection  between  the  two  wires.  The  fuse 
having  been  introduced  into  the  charge  the  earth  wire  is  placed  in  good 
connection  with  the  ground.  The  knob  f  of  the  exploder  is  also  con- 
nected with  the  earth  by  leading  uncovered  wire  into  water  or  moist 
earth,  and  the  condition  of  the  machine  tested.  The  end  of  the  insulated 
wire  is  then  connected  with  the  knob  e  and  the  rod  drawn  down ;  at  the 
proper  signal  the  handle  is  turned  the  requisite  number  of  times,  and 
when  the  signal  is  given  the  trigger  is  depressed,  and  the  explosion 
ensues. 

When  a  number  of  charges  are  to  be  fired  they  are  best  placed  in  a 
single  circuit,  care  being  taken  that  the  insulation  is  good. 

747.  Duration  of  the  electric  spark. — Wheatstone  measured  the 
duration  of  the  electric  spark,  by  means  of  the  rotating  mirror  which 
he  invented  for  this  purpose.  At  some  distance  from  this  instrument, 
which  can  be  made  to  rotate  with  a  measured  velocity,  a  Leyden  jar  is  so 
arranged  that  the  spark  of  its  discharge  is  reflected  from  the  mirror. 
Now,  from  the  laws  of  reflection  (489)  the  image  of  the  luminous 
point  describes  an  arc  of  double  the  number  of  degrees  which  the 
mirror  describes,  in  the  time  in  which  the  mirror  passes  from  the 
position  in  which  the  image  is  visible  to  that  in  which  it  ceases  to  be  so. 
If  the  duration  of  the  image  were  absolutely  instantaneous  the  arc  would 
be  reduced  to  a  mere  point.  Knowing  the  number  of  turns  which  the 
mirror  makes  in  a  second,  and  measuring,  by  means  of  a  divided  circle, 
the  number  of  degrees  occupied  by  the  image,  the  duration  of  the  spark 
would  be  determined.  In  one  experiment  Wheatstone  found  that  this 
arc  was  24°;  Now,  in  the  time  in  which  the  mirror  traverses  360°  the 
image  traverses  720° ;  but  in  the  experiment  the  mirror  made  800  turns 
in  a  second,  ancj  therefore  the  image  traversed  576,000°  in  this  time;  and 
as  the  arc  was  24°,  the  image  must  have  lasted  the  time  expressed  by 
i?!^  or  24^00  of  a  second.  Thus  the  discharge  is  not  instantaneous,  but 
has  a  certain  duration,  which,  however,  is  excessively  short. 

Feddersen  found  that  when  greater  resistances  were  interposed  in  the 
circuit  through  which  the  discharge  was  effected,  that  the  duration  of  the 
spark  was  increased.  With  a  tube  of  water  9  mm.  in  length,  the  spark 
lasted  0-0014  second;  and  with  one  of  180  mm.  its  duration  was  0-0183 


-747]  Duration  of  the  Electric  Spark.  66^ 

second.  The  duration  increased  also  with  the  striking  distance,  and 
with  the  dimensions  of  the  battery.  _ 

To  determine  the  duration  of  the  electric  spark  MM.  Lucas  and 
Cazin  have  used  a  most  accurate  method,  by  which  it  may  be  measured 
in  millionths  of  a  second.  The  method 
is  an  application  of  the  vernier.  A 
disc  of  mica  15  centimetres  in  dia- 
meter is  blackened  on  one  face,  and  at 
the  edge  are  traced  180  equal  divisions 
in  very  fine  transparent  lines.  The  disc  Fig.  592. 

is  mounted  on  a  horizontal  axis,  and  by 

means  of  a  gas  engine  a  velocity  of  100  to  300  turns  in  a  second  may  be 
imparted  to  it.  A  second  disc  of  silvered  glass  of  the  same  radius  is 
mounted;  on  the  same  axis  as  the  other  and  very  close  to  it  at  its  upper 
edge  six  equidistant  transparent  lines  are  traced  forming  a  vernier  with 
the  lines  on  the  mica.  For  this,  the  distance  between  two  consecutive 
lines  on  the  two  discs  is  such  that  five  divisions  of  the  mica  disc  DC, 
correspond  to  six  divisions  of  the  glass  disc  AB  as  seen  in  the  figure  592. 
Thus  the  vernier  gives  the  sixths  of  a  division  of  the  mica  disc  (10).  In 
the  apparatus  the  hnes  AB  are  not  above  the  lines  CD,  but  are  at  the 
same  distance  from  the  axis,  so  that  the  latter  coincide  successively  with 
the  former. 

The  mica  disc  is  contained  in  a  brass  box  D  (fig.  593)  on  the  hinder 
face  of  which  is  fixed  the  vernier.  In  the  front  face  is  a  glass  window  O, 
through  which  the  coincidence  of  the  two  sets  of  lines  can  be  observed 
by  means  of  a  magnifying  lens  L. 

The  source  of  electricity  is  a  battery  of  2  to  8  jars,  each  having 
a  coated  surface  of  1243  square  centimetres  and  charged  continu- 
ously by  a  Holtz's  machine.  The  sparks  strike  between  two  metal 
bulbs  a  and  b^  1 1  millimetres  in  diameter.  Their  distance  can  be  varied, 
and  at  the  same  time  measured,  by  means  of  a  micrometric  screw  r. 
The  two  opposite  electricities  arrive  by  wires  in  and  ;/,  and  the  sparks 
strike  at  the  principal  focus  of  a  condensing  lens  placed  in  the  collimator 
C,  so  that  the  rays  which  fall  on  the  vernier  are  parallel. 

The  motion  is  transmitted  to  the  toothed  wheels  and  to  the  mica  disc 
by  means  of  an  endless  band,  which  can  be  placed  on  any  one  of  three 
pullies  P.  so  that  the  velocity  may  be  varied.  At  the  end  of  the  axis  of 
the  pullies  is  a  bent  wire  which  moves  a  counter,  V,  that  marks  on  three 
dials,  the  number  of  turns  of  the  disc. 

These  details  being  premised,  suppose  the  velocity  of  the  disc  is  400 
turns  in  a  second.  In  each  second  400  x  180  or  72,000  lines  pass  before 
the  observer's  eye  in  each  second ;  hence  an  interval  of  -^^^  of  a  second 
elapses  between  two  consecutive  lines.  But  as  the  spark  is  only  seen 
when  one  of  the  lines  of  the  disc  coincides  with  one  of  the  six  lines  of  the 
vernier  ;  and  as  this  gives  sixths  of  a  division  of  the  movable  disc,  when 
the  latter  has  turned  through  a  sixth  of  a  division,  a  second  coincidence 
is  produced;  so  that  the  interval  between  two  successive  coincidences  is 

\ =  0-0000023  of  a  second. 

72000  X  6 


664 


Frictioital  Electricity. 


[747- 


That  being  the  case,  let  the  duration  of  a  spark  be  something  between 
23  and  46  ten  millionths  of  a  second ;  if  it  strikes  exactly  at  the  moment 
of  a  coincidence,  it  will  last  until  the  next  coincidence ;  and  owing  to  the 
persistence  of  impressions  on  the  retina  (588)  the  observer  will  see  two 


Fig.  593. 

luminous  lines.  But  if  the  spark  strikes  between  two  coincidences  and 
has  ceased  when  the  third  is  produced  only  one  brilliant  line  is  seen. 
Thus,  if  with  the  above  velocity  sometimes  i  and  sometimes  2  bright 
lines  are  seen,  the  duration  of  the  spark  is  comprised  between  23  and  46 
ten  millionths  of  a  second. 

By  experiments  of  this  kind,  with  a  sl:riking  distance  of  5  millimetres 
between  the  bulbs  a  and  b,  and  varying  the  number  of  the  jars,  MM, 
Lucas  and  Cazin  obtained  the  following  results  : 


Number  of  jars. 

2 
4 

6 


Duration  in 

millionths  of 

a  second. 

26 

47 
55 


.-748]  Velocity  of  Electricity.  66  S 

It  will  thus  be  seen  that  the  duration  of  the  spark  increases  with  the 
number  of  jars  It  also  increases  with  the  striking  distance;  but  it  is 
independent  of  the  diameter  of  the  bulbs  between  which  the  spark 
strikes. 

The  spark  of  electrical  machines  has  so  short  a  duration  that  it  could 
not  be  measured  with  the  chronoscope. 

748.  Velocity  of  electricity. — To  determine  the  velocity  of  electri- 
city, Wheatstone  constructed  an  apparatus  the  principle  of  which  will  be 
understood  from  fig.  594 :  six  insulating  metal  knobs  were  arranged  in  a 
horizontal  line  on  a  piece  of  wood  called  a  spar^  board;  of  these  the  knob 
I  was  connected  with  the  outer,  while  6  could  be  connected  with  the 
inner  coating  of  a  charged  Leyden  jar ;  the  knob 

1  was  a  tenth  of  an  inch  distant  from  the  knob 

2  ;  while  between  2  and  3  a  quarter  of  a  mile  of 
insulated  wire  was  interposed:  3  was  hkewise  a 
tenth  of  an  inch  from  4,  and  there  was  a  quarter 
of  a  mile  of  wire  between  4  and  5  ;  lastly,  5  was 
a  tenth  of  an  inch  from  6,  from  which  a  wire  led 
directly  to  the  inner  coating  of  the  Leyden  jar. 
Hence,  when  the  jar  was  discharged  by  con- 
necting the  wire  from  6  with  the  inner  coating  _<<n~>>__ 
of  the  jar,  sparks  would  pass  between  i  and  2, 

between  3  and  4,  and  between  5  and  6.      Thus  ^'^"  ^^'^' 

the  discharge,  supposing  it  to  proceed  from  the  inner  coating,  has  to  pass 

in  its  course  through  a  quarter  of  a  mile  of  wire  between  the  first  and 

second  spark,  and  through  the  same  distance  between  the  second  and 

third. 

The  spark  board  was  arranged  at  a  distance  of  10  feet  from  the  rota- 
ting mirror,  and  at  the  same  height,  both  being  horizontal;  and  the 
observer  looked  down  on  the  mirfor.  Thus  the  sparks  were  visible  when 
the  mirror  made  an  angle  of  45°  with  the  horizon. 

Now,  if  the  mirror  were  at  rest  or  had  only  a  small  velocity,  the  images 
of  the  three  sparks  would  be  seen  as  three  dots  • ,  but  when  the  mirror 
had  a  certain  velocity  these  dots  appeared  as  lines,  which  were  longer  as 
the  rotation  was  more  rapid.  The  greatest  length  observed  was  24°, 
which,  with  800  revolutions  in  a  second,  can  be  shown  to  correspond  to  a 
duration  of  24^00  of  a  second.  With  a  slow  rotation  the  lines  present  the 
appearance  ^^^~  ;  they  are  quite  parallel,  and  the  ends  in  the  same 
line.  But  with  greater  velocity,  and  when  the  rotation  took  place  from 
left  to  right  they  presented  the  appearance  ^~'.  and  when  it  turned 

from  right  to  left  the  appearance     — --  ,  because  the  image  of  the 

centre  spark  was  formed  after  the  lateral  ones.  Wheatstone  found  that 
this  displacement  amounted  to  half  a  degree  before  or  behind  the  others. 

This  arc  corresponds  to  a  duration  of ^       or  -^^Act^kt,  of  a  second  : 

2x720x800        11^2000 

the  space  traversed  in  this  time  being  a  quarter  of  a  mile,  gives  for  the 
velocity  of  electricity,  288,000  miles  in  a  second,  which  is  greater  than 
that  of  light.     The  velocity  of  dynamical  electricity  is  far  less ;  and  owing 


666  Frictional  Electricity.  [748- 

to  induction,  the  transmission  of  a  current  through  submarine  wires  is 
comparatively  slow. 

In  the  above  experiment  the  images  of  the  two  outer  sparks  appear 
simultaneously  in  the  mirror,  from  which  it  follows  that  the' electric 
current  issues  simultaneously  from  the  two  coatings  of  the  Leyden  jar. 

From  certain  theoretical  considerations  based  upon  measurements  of 
constant  electrical  currents,  Kirchhoff  has  concluded  that  the  motion  of 
electricity  in  a  wire  in  which  it  meets  with  no  resistance  is  like  that  of  a 
wave  on  a  stretched  string,  and  has  the  velocity  192,924  miles  in  a  second, 
which  is  about  that  of  light  in  vacuo  (477). 

According  to  Walker,  the  velocity  of  electricity  is  18,400  miles,  and 
according  to  Fizeau  and  Gounelle,  it  is  62,100  miles  in  iron,  and  111,780 
in  copper  wire.  These  measurements,  however,  were  made  with  telegraph 
wires,  which  induce  opposite  electricities  in  the  surrounding  media : 
there  is  thus  produced  a  resistance  which  diminishes  the  velocity.  The 
velocity  is  less  therefore  in  water  than  in  air.  The  nature  of  the  con- 
ductor appears  to  have  some  influence  on  the  velocity;  but  not  the 
thickness  of  the  wire,  nor  the  potential  of  the  electricity. 

For  atmospheric  electricity,  reference  must  be  made  to  the  chapter  on 
Meteorology. 


-749] 


Galvani's  Experiment. 


667 


BOOK    X. 

DYNAMICAL   ELECTRICITV. 


CHAPTER   I. 

VOLTAIC    PILE.      ITS   MODIFICATIONS. 

749.  Galvani's  experiment  and  tbeory. — The  fundamental  experi- 
ment which  led  to  the  discovery  of  dynamical  electricity  is  due  to  Galvani, 
professor  of  anatomy  in  Bologna.  Occupied  with  investigations  on  the  in- 
fluence of  electricity  on  the  nervous  excitability  of  animals,  and  especially 

« 


Fig.  595. 

of  the  frog,  he  observed  that  when  the  lumbar  nerves  of  a  dead  frog  were 
connected  with  the  crural  muscles  by  a  metallic  circuit,  the  latter  became 
briskly  contracted. 

To  repeat  this  celebrated  experiment,  the  legs  of  a  recently  killed  frog 
are  prepared,  and  the  lumbar  nerves  on  each  side  of  the  vertebral  column 


66S  Dynamical  Electricity.  [749- 

are  exposed  in  the  form  of  white  threads.  A  metal  conductor,  composed 
of  zinc  and  copper,  is  then  taken  (fig.  595),  and  one  end  introduced  be- 
tween the  nerves  and  the  vertebral  column,  while  the  other  touches  one 
of  the  muscles  of  the  thighs  or  legs  ;  at  each  contact  a  smart  contraction 
of  the  muscles  ensues. 

Galvani  had  some  time  before  observed  that  the  electricity  of  machines 
produced  in  dead  frogs  analogous  contractions,  and  he  attributed  the 
phenomena  first  described  to  an  electricity  inherent  in  the  animal.  He 
assumed  that  this  electricity,  which  he  called  vital  Jiidd,  passed  from  the 
nerves  to  the  muscles  by  the  metallic  arc,  and  v/as  thus  the  cause  of  con- 
traction. This  theory  met  with  great  support,  especially  among  physiolo- 
gists, but  it  was  not  without  opponents.  The  most  considerable  of  these 
was  Alexander  Volta,  professor  of  physics  in  Pavia. 

750.  Volta's  fundamental  experiment. — Galvani's  attention  had  been 
exclusively  devoted  to  the  nerves  and  muscles  of  the  frog ;  Volta's  was 
directed  upon  the  connecting  metal.  Resting  on  the  observation,  which 
Galvani  had  also  made,  that  the  contraction  is  more  energetic  when  the 
connecting  arc  is  composed  of  two  metals  than  when  there  is  only  one, 
Volta  attributed  to  the  metals  the  active  part  in  the  phenomenon  of  con- 
traction. He  assumed  that  the  disengagement  of  electricity  was  due  to 
their  contact,  and  that  the  animal  parts  only  officiated  as  conductors,  and 
at  the  same  time  as  a  very  sensitive  electroscope. 

By  means  of  the  condensing  electroscope,  which  he  had  then  recently 
invented,  Volta  devised  several  modes  of  showing  the  disengagement  of 
electricity  on  the  contact  of  metals,  of- which  the  following  is  the  easiest 
to  perform  : 

The  moistened  finger  being  placed  on  the  upper  plate  of  a  condensing 
electroscope  (fig.  577),  the  lower  plate  is  touched  with  a  plate  of  copper,  r, 
soldered  to  a  plate  of  zinc,  z^  whicli  is  held  in  the  other  hand.  On 
breaking  the  connection  and  lifting  the  upper  plate  (fig.  578),  the  gold 
leaves  diverge,  and,  as  may  be  proved,  with  negative  electricity.  Hence, 
when  soldered  together,  the  copper  is  charged  with  negative  electricity, 
and  the  zinc  with  positive  electricity.  The  electricity  could  not  be 
due  either  to  friction  or  pressure  ;  for  if  the  condensing  plate,  which 
is  of  copper,  is  touched  with  the  zinc  plate  2^  the  copper  plate  to 
which  it  is  soldered  being  held  in  the  hand,  no  trace  of  electricity  is 
observed. 

A  memorable  controversy  arose  between  Galvani  and  Volta.  The 
latter  was  led  to  give  greater  extension  to  his  contact  theory,  and  pro- 
pounded the  principle  that  when  two  heterogeneous  substances  are  placed 
in  cofztact,  one  of  them  always  assumes  the  positive  and  the  other  the 
negative  electrical  condition.  In  this  form  Volta's  theory  obtained  the 
assent  of  the  principal  philosophers  of  his  time.  Galvani,  however,  made 
a  number  of  highly  interesting  experiments  with  animal  tissues.  In  some 
of  these  he  obtained  indications  of  contraction,  even  though  the  sub- 
stances in  contact  were  quite  homogeneous. 

751.  Disengragrement  of  electricity  in  chemical  actions. — The 
contact  theory  which  Volta  had  propounded,  and  by  which  he  explained 


-751]    Disengagement  of  Electricity  in  Chemical  Actions.     669 

the  action  of  the  pile,  soon  encountered  objectors.     Fabroni,  a  country- 
man of  Volta,  having  observed  that  in  the  pile  the  discs  of  zinc  became 
oxidised  in  contact  with  the  acidulated  water,  thought  that  this  oxidation" 
was  the  principal  cause  of  the  disengagement  of  electricity.     In  England  , 
Wollaston  soon  advanced  the  same  opinion,  and  Davy  supported  it  by 
many  ingenious  experiments. 

It  is  true  that  in  the  fundamental  experiment  of  the  contact  theory  (750) 
Volta  obtained  signs  of  electricity.  But  De  la  Rive  has  shown  that  if 
the  zinc  be  held  in  a  wooden  clamp,  all  signs  of  electricity  disappear,  and 
that  the  same  is  the  case  if  the  zinc  be  placed  in  gases,  such  as  hydrogen 
or  nitrogen,  which  exert  upon  it  no  chemical  action.  De  la  Rive  has  ac- 
cordingly concluded  that  in  Volta's  original  experiment  the  disengage- 
ment of  electricity  is  due  to  the  chemical  actions  which  result  from  the 
perspiration  and  from  the  oxygen  of  the  atmosphere. 

The  development  of  electricity  in  chemical  actions  may  be  demon- 
strated in  the  following  manner  by  means  of  the  condensing  electroscope 
(734).  A  disc  of  moistened  paper  is  placed  on  the  upper  plate  of  the 
condenser,  and  on  this  a  zinc  capsule,  in  which  some  dilute  sulphuric  acid 
is  poured.  A  platinum  wire,  communicating  with  the  ground,  but  insu- 
lated from  the  sides  of  the  vessel,  is  immersed  in  the  liquid,  and  at  the 
same  time  the  lower  plate  of  the  condenser  is  also  connected  with  the 
'ground  by  touching  it  with  the  moistened  finger.  On  breaking  contact 
and  removing  the  upper  plate,  the  gold  leaves  are  found  to  be  positively 
electrified,  proving  that  the  upper  plate  has  received  a  charge  of  negative 
electricity. 

By  a  variety  of  analogous  experiments  it  may  be  shown  that  various 
chemical  actions  are  accompanied  by  a  disturbance  of  the  electrical  equi- 
librium ;  though  of  all  chemical  actions  those  between  metals  and  liquids 
are  the  most  productive  of  electricity.  All  the  various  resultant  effects 
are  in  accordance  with  the  general  rule,  that  when  a  liquid  acts  chemi- 
cally on  a  metal  the  liquid  assumes  the  positive,  and  the  metal  the  nega- 
tive condition.  In  the  above  experiment  the  sulphuric  acid,  by  its  action 
on  zinc  becomes  positively  electrified,  and  its  electricity  passes  off  through 
the  platinum  wire  into  the  ground,  while  the  negative  electricity  excited 
in  the  zinc  acts  on  the  condenser  just  as  an  excited  rod  of  sealing-wax 
would  do. 

In  many  cases  the  electrical  indications  accompanying  chemical 
actions  are  but  feeble,  and  require  the  use  of  a  very  delicate  electroscope 
to  render  them  apparent.  Thus,  one  of  the  most  energetic  chemical 
actions,  that  of  sulphuric  acid  upon  zinc,  gives  no  more  free  electricity 
than  water  alone  does  with  zinc. 

Opinion,  which  in  this  country  at  least,  had  mainly  by  the  influence  of 
Faraday's  experiments  tended  in  favour  of  the  purely  chemical  origin  of 
the  electricity  produced  in  voltaic  action,  has  of  late  inclined  more 
towards  the  contact  theory.  The  following  experiments  due  to  Sir  W. 
Thomson  {Papers  on  Electrostatics,  Macmillan  &  Co.,  p.  317),  afford  per- 
haps the  most  conclusive  arguments  hitherto  adduced  in  favour  of  the  latter 
view. 


6/0  Dynamical  Electricity.  [751- 

A  very  light  metal  bar  was  suspended  by  a  fine  wire  so  as  to  be 
movable  about  an  axis,  perpendicular  to  the  plane  of  a  ring  made  up  of 
two  halves,  one  of  copper  and  the  other  of  zinc.  When  the  two  halves  of 
the  ring  were  in  contact,  or  were  soldered  together,  the  light  bar  turned 
from  the  copper  to  the  zinc  when  it  was  negatively  electrified,  and  from 
the  zinc  to  the  copper  when  it  was  positively  electrified,  thus  showing 
that  the  contact  of  the  two  metals  causes  them  to  assume  different 
electrical  conditions,  the  zinc  taking  the  positive,  and  the  copper  the 
negative  electricity. 

When  however,  the  two  halves  instead  of  being  in  metallic  contact 
were  connected  by  a  drop  of  water,  no  change  was  produced  in  the 
position  of  the  bar  by  altering  its  electrification,  provided  it  hung  quite 
symmetrically  relative  to  the  two  halves  of  the  ring.  This  result  shows 
that  under  the  circumstances  mentioned,  no  difference  is  produced  in  the 
electrical  condition  of  the  two  metals.  Hence  the  conclusion  has  been 
drawn  by  Sir  W.  Thomson  and  others,  that  the  movement  of  electricity 
in  the  galvanic  circuit  is  entirely  due  to  the  electrical  difference  produced 
at  the  surfaces  of  contact  of  the  dissimilar  metals. 

There  are,  however,  other  facts  which  are  not  easily  harmonised  with 
this  view  ;  and  indeed  the  last  mentioned  experiment  can  hardly  be 
regarded  as  proving  that  in  all  cases  two  different  metals  connected  by 
an  electrolytic  (772)  liquid,  assume  the  same  electrical  condition.  It  may' 
therefore  still  be  regarded  as  possible,  or  even  probable,  that  the  contact 
between  the  metals  and  the  liquids  of  a  cell  contribute  at  least  in  some 
cases  to  the  production  of  the  current. 

An  instructive  discussion  of  this  question  with  some  additional  experi- 
mental evidence  in  favour  of  the  chemical  theory,  will  be  found  in  a 
paper  by  Mr.  J,  A.  Fleming  published  in  the  proceedings  of  the  Physical 
Society  (Taylor  and  Francis). 

752.  Potential. — It  may  be  convenient  to  explain  here  what  is  meant 
by  the  term  potential,  which  has  of  late  come  into  extended  use  in  speak- 
ing of  electrical  phenomena,  to  express  the  conditon  of  an  electrified  body 
and  of  the  space  in  its  neighbourhood.  It  may  be  taken  to  represent 
what  has  been  frequently  called  tension,  though  that  word  has  been  often 
used  to  express  two  different  things. 

Introduced  originally  into  electrical  science  by  Green,  out  of  con- 
siderations arising  from  the  mathematical  treatment  of  the  subject,  the 
use  of  the  terrn  potential  is  justified  and  recommended  by  the  clearness 
with  which  it  brings  out  the  relations  of  electricity  to  work. 

We  have  already  seen,  that  in  order  to  lift  a  certain  mass  against  the 
attraction  of  gravitation  (56-59)  there  must  be  a  definite  expenditure  of 
work,  and  the  equivalent  of  this  work  is  met  with  in  the  energy  which 
the  lifted  mass  retains,  or  what  is  called  the  potential  energy  of  posi- 
tion. 

Let  us  now  suppose  that  we  have  a  large  insulated  metal  sphere 
charged  with  positive  electricity,  and  at  a  distance  which  is  very  great 
in  comparison  with  the  size  of  the  sphere,  a  small  insulated  sphere  charged 


-752]  Potential.  671 

with  the  same  kind  of  electricity.  If  now  we  move  the  small  sphere  to 
any  given  point  nearer  the  larger  one,  we  must  do  a  certain  amount  ot 
work  upon  it  to  overcome  the  repulsion  of  the  two  electricities. 

The  work  required  to  be  done  against  electrical  forces,  in  order  to 
move  the  unit  of  positive  electricity  from  an  infinite  distance  to  a  given 
point  in  the  neighbourhood  of  an  electrified  conductor  is  called  the 
potential  at  this  point. 

If,  in  the  above  case,  the  larger  sphere  were  charged  with  negative 
electricity,  then  instead  of  its  being  needful  to  do  work  in  order  to  bring 
a  unit  of  positive  electricity  towards  it,  work  would  be  done  by  electrical 
attraction,  and  the  potential  of  the  point  near  the  charged  sphere  would 
thus  be  negative.  The  potential  at  any  point  may  also  be  said  to  be  the 
work  done  against  electrical  force,  in  moving  unit  charge  of  negative 
electricity  from  that  point. 

The  amount  of  work  required  to  move  the  unit  of  positive  electricity 
against  electrical  force,  from  any  one  position  to  any  other  is  equal  to  the 
excess  of  the  electrical  potential  of  the  second  position  over  the  electrical 
potential  of  the  first.  This  is,  in  effect,  the  same  as  what  has  been  said 
above,  for  at  an  infinite  distance  the  potential  is  zero. 

We  cannot  speak  of  potential  in  the  abstract,  any  more  than  we  can 
speak  of  any  particular  height,  without  at  least  some  tacit  reference  to  a 
standard  of  level.  Thus,  if  we  say  that  such  and  such  a  place  is  300  feet 
high,  we  usually  imply  that  this  height  is  measured  in  reference  to  the 
level  of  the  sea.  So  too  we  cannot  speak  of  the  potential  of  a  mass  of 
electricity  without,  at  least,  an  impHed  reference  to  a  standard  of  potential. 
This  standard  is  usually  the  earth,  which  is  taken  at  zero  potential.  If  we 
speak  of  the  potential  at  a  given  point,  the  difference  between  the  potential 
of  this  point  and  the  earth  is  referred  to. 

If  in  the  imaginary  experiment  described  above,  we  move  the  small 
sphere  round  the  large  electrified  one  always  at  the  same  distance,  we 
shall  do  no  work  upon  it  for  the  purpose  of  overcoming  or  of  yield- 
ing to  electrical  attractions  or  repulsions,  just  as  if  we  move  a  body  at  a 
certain  constant  level  above  the  earth's  surface,  we  do  no  work  upon  it  as 
respects  gravitation.  An  imaginary  surface  drawn  in  the  neighbourhood 
of  an  electrified  body,  such,  that  a  given  charge  of  electricity  can  be 
moved  from  any  one  point  of  it  to  any  other,  without  any  work  being 
done  either  by  or  against  electrical  force  is  said  to  be  an  equipotetitial 
surface.  Such  a  surface  may  be  described  as  having  everywhere 
the  same  electrical  level ;  and  the  notion  of  bodies  at  different  electrical 
levels  in  reference  to  a  particular  standard  is  the  same  as  that  of  bodies  at 
different  potentials. 

As  water  only  flows  from  places  at  a  higher  to  places  at  a  lower  level, 
so  also  electricity  only  passes  from  places  at  a  higher  to  places  at  a  lower 
potential.  If  an  electrified  body  is  placed  in  conducting  communication 
with  the  earth,  electricity  will  flow  from  the  body  to  the  earth  if  the  body 
is  at  a  higher  potential  than  the  earth  ;  and  from  the  earth  to  the  body, 
if  the  body  is  at  a  lower  potential.     If  the  potential  of  a  body  is  higher 


6^2     ■  Dynamical  Electricity.  [752- 

than  that  of  the  earth,  it  is  said  to  have  a  positive  potential  ;  and  if  at  a 
lower  potential,  a  negative  potential.  A  body  charged  v^'ith  free  negative 
electricity  is  one  at  a  lower  potential  than  the  earth  ;  one  charged 
\i\t\i  free  positive  electricity  is  at  a  higher  potential. 

The  sense  in  which  electrical  potential  is  to  be  understood  may  be 
further  illustrated  by  reference  to  heat.  In  the  interchange  of  heat  between 
bodies  of  different  temperatures,  the  final  result  is  that  heat  only  passes 
from  bodies  at  a  higher  to  bodies  at  a  lower  temperature.  Potential  is,  as 
regards  electricity,  what  temperature  is,  as  regards  heat.  We  may  have 
a  small  quantity  of  heat  at  a  very  high  temperature.  Thus  a  short  thin 
platinum  wire  heated  to  incandescence  has  a  far  higher  heat  potential  or 
temperature,  than  a  cup  full  of  warm  water  ;  but  the  latter  will  have  a  far 
larger  quantity.  A  flash  of  lightning  represents  electricity  at  a  very  high 
potential,  but  the  quantity  is  small. 

On  an  insulated  sphere  charged  with  electricity,  the  potential  as  well 
as  the  electrical  density  (694),  are  everywhere  the  same.  On  an  ellipsoid, 
on  the  other  hand,  the  density  is  different  in  different  parts,  while  the 
potential  is  everywhere  the  same.  That  is  to  say,  that  if  a  small  in- 
sulated test  sphere  were  applied  to  various  parts  of  the  ellipsoid,  and 
each  time  brought  in  contact  with  the  fixed  ball  of  the  torsion  balance,  a 
different  degree  of  repulsion  would  be  shown  each  time.  If  however,  the 
small  sphere  were  placed  at  a  sufficient  distance  from  the  ellipsoid  and 
were  connected  by  it  with  a  thin  wire,  then  Avherever  the  wire  touched 
the  ellipsoid,  the  proof  sphere  when  afterwards  applied  to  the  torsion 
balance  would  in  all  cases  produce  the  same  repulsion. 

The  relation  between  electrical  potential  and  density  may  be  further 
illustrated  by  reference  to  the  head  of  water  in  a  reservoir.  The  pressure 
is  proportional  to  the  depth  ;  the  potential  is  everywhere  the  same.  For 
suppose  we  want  to  introduce  an  additional  pound  of  water  into  the 
reservoir,  the  same  amount  of  work  is  required  whether  the  water  be 
forced  in  at  the  bottom  or  be  poured  in  at  the  top. 

If  a  hole  be  made  very  near  the  top  of  the  reservoir,  a  quantity  of 
water  in  falling  to  the  ground  would  generate  an  amount  of  heat  propor- 
tional to  the  fall.  If  the  same  quantity  escaped  through  a  hole  near  the 
bottom,  it  would  not  produce  so  much  heat  by  direct  fall ;  but  it  will 
possess  a  certain  horizontal  velocity,  the  destruction  of  which  will  produce 
a  quantity  of  heat,  which,  added  to  that  produced  by  the  fall,  will  give 
exactly  as  much  as  the  other. 

753.  Current  electricity,--  When  a  plate  of  zinc  and  a  plate  of  copper 
are  partially  immersed  in  dilute  sulphuric  acid,  no  electrical  or  chemical 
change  is  apparent  beyond  perhaps  a  slight  disengagement  of  hydrogen 
from  the  surface  of  the  zinc  plate.  If  now  the  plates  are  placed  in  direct 
contact,  or,  more  conveniently,  are  connected  by  a  metal  wire,  the 
chemical  action  sets  in,  a  large  quantity  of  hydrogen  is  disengaged,  but 
this  hydrogen  is  no  longer  disengaged  at  the  surface  of  the  zinc,  but  at 
the  surface  of  the  copper  plate.  Here  then  we  have  to  deal  with  some- 
thing more  than  mere  chemical  action,  for  chemical  action  would  be  un- 
able to  explain  either  the  increase  in  the  quantity  of  hydrogen  disengaged 


753] 


Current  Electricity. 


^71> 


Fig.  596. 


when  the  metals  touch,  or  the  fact  that  this  hydrogen  is  now  given  off  at 
the  surface  of  the  copper  plate.  At  the  same  time,  if  the  wire  is  examined, 
it  will  be  found  to  possess  many  remarkable 
thermal  magnetic  and  other  properties  which 
will  be  afterwards  described. 

In  order  to  understand  what  here  takes 
place,  let  us  suppose  that  we  have  two  insu- 
lated metal  spheres,  and  that  one  is  charged 
with  positive  and  the  other  with  negative 
electricity,  and  that  they  are  momentarily 
connected  by  means  of  a  wire.  Electricity 
will  pass  from  a  place  of  higher  to  a  place 
of  lower  potential,  that  is,  from  the  positive 
along  the  wire  to  the  negative,  and  the  po- 
tentials become  equal.  This  is,  indeed 
nothing  more  than  an  electrical  discharge  taking  place  through  the  wire ; 
and  during  the  infinitely  short  time  in  which  this  is  accomplished,  it  can 
be  shown  that  the  wire  exhibits  certain  heating  and  magnetising  effects, 
of  which  the  increase  of  temperature  is  perhaps  the  easiest  to  observe. 
If  now  we  can  imagine  some  agency  by  which  the  different  electrical 
conditions  of  the  two  spheres  are  renewed  as  fast  as  they  are  discharged, 
which  is  what  very  nearly  takes  place  when  the  two  spheres  are  respec- 
tively connected  with  the  two  conductors  r  and  r^,  of  a  Holtz's  machine 
(figs.  55 1,  552),  this  equaUsation  of  potentials,  thus  taking  place,  is  virtually 
continuous,  and  the  phenomena  above  mentioned  are  also  continuous. 

Now  this  is  what  takes  place  when  the  two  metals  are  in  contact  in  a 
liquid  which  acts  upon  them  unequally.  This  is  independent  of  hypo- 
thesis as  to  the  cause  of  the  phenomena;  whether  the  electrical  difference 
is  only  produced  at  the  moment  of  contact  of  the  metals,  or  whether  it 
is  due  to  the  chemical  action,  or  tendency  to  chemical  action  between 
the  metal  and  the  liquid.  The  rapidly,  succeeding  series  of  equalisations 
of  potential  which  takes  place  in  the  wire  being  continuous,  so  long  as 
the  chemical  action  continues,  is  what  is  ordinarily  spoken  of  as  the 
electrical  ciin-eiit. 

If  we  represent  by  -^  e  the  potential  of  the  copper  plate,  and  by  -^ 
the  potential  of  the  zinc,  then  the  electrical  difference,  that  is  the  differ- 
ence of  potentials,  is  ^- e-{  — e)  =  '2e.  And  this  is  general — the  essential 
point  of  any  such  combination  as  the  above  is  that  it  maintains,  or  tends 
to  maintain,  a  difference  of  potentials,  which  difference  is  constant.  If, 
for  instance,  the  zinc  plate  be  connected  with  the  earth  which  is  at  zero 
potential,  its  potential  also  becomes  zero ;  and  since  the  electrical 
difference  remains  constant  we  have  for  the  potential  of  the  copper  plate 
+  2e.  Similarly,  if  the  copper  be  connected  with  the  earth  the  potential 
of  the  zinc  plate  is  negative  and  is  —  7.e. 

The  conditions  under  which  a  current  of  electricity  is  formed  in  the 
above  experiment  may  be  further  illustrated  by  reference  to  the  condi- 
tions-which  determine  the  flow  of  water  between  two  reservoirs  contain- 
ing water  at  different  levels.     If  they  are  connected  by  a  pipe,  water  will 

G  G 


6/4         •  Dynamical  Electricity.  [753- 

flow  from  the  one  at  a  higher  level  to  the  one  at  a  lower  level  until  the 
water  in  the  two  is  at  the  same  level  in  both,  when  of  course  the  flow 
ceases.  If  we  imagine  the  lower  reservoir  so  large  that  any  water  added 
to  it  would  not  affect  its  level — if  it  were  the  sea  for  example— that  would 
represent  zero  level,  and  if  the  higher  reservoir  could  be  kept  at  a 
constant  level  there  would  be  a  constant  flow  in  the  pipe. 

We  must  here  be  careful  not  to  dwell  too  much  on  this  analogy.  It 
is  not  to  be  supposed  that  in  speaking  of  current  of  electricity  we  mean 
that  any  thing  actually  flows,  that  there  is  any  actual  transfer  of  matter. 
We  say  electricity  flows,  or  a  current  is  produced,  in  much  the  same  sense 
as  that  in  which  we  say  sound  or  light  travels. 

754-  Voltaic  couple.  Electromotive  series. — The  arrangement  just 
described,  consisting  of  two  metals  in  metalHc  contact,  and  a  conducting 
liquid  in  which  they  are  placed,  constitutes  a  simple  voltaic  element  or 
couple.  So  long  as  the  metals  are  not  in  contact,  the  couple  is  said  to  be 
open,  and  when  connected  it  is  closed. 

According  to  the  chemical  view  to  which  we  shall  for  the  present 
provisionally  adhere,  it  is  not  necessary  that,  for  the  production  of  a 
current,  one  of  the  metals  be  unaffected  by  the  liquid,  but  merely  that 
the  chejnical  action  upon  the  one.  be  greater  than  upon  the  other.  For 
then  we  may  assume  that  the  current  produced  would  be  due  to  the 
difference  between  the  differences  of  potential  which  each  of  the  metals 
separately  produces  by  its  contact  with  the  liquid.  If  the  differences  of 
potentials  were  absolutely  equal — a  condition,  however,  impossible  of 
realisation  with  two  distinct  metals — we  must  assume  that  when  the  metals 
are  joined  no  current  would  be  produced.  The  metal  which  is  most 
attacked  is  called  the  positive  or  generating  plate,  and  that  which  is  least 
attacked  the  negative  or  collecting  plate.  The  positive  metal  determines 
the  direction  of  the  current,  which  proceeds  in  the  liquid  from  the  positive 
to  the  negative  plate,  and  out  of  the  liquid  through  the  connecting  wire 
from  the  negative  to  the  positive  plate. 

In  the  fundamental  experiment,  not  only  the  connecting  wire  but  also 
the  liquid  and  the  plates  are  traversed  by  the  electrical  currents — are  the 
scene  of  electrical  actions. 

In  speaking  of  the  directio7i  of  the  current  iho.  direction  of  the  positive 
electricity  is  always  understood. 

The  mere  immersion  of  two  different  metals  in  a  liquid  is  not  alone 
sufficient  to  produce  a  current,  there  must  be  chemical  action.  When  a 
platinum  and  a  gold  plate  are  connected  with  a  delicate  galvanometer 
and  immersed  in  pure  nitric  acid  no  current  is  produced ;  but  on  adding 
a  drop  of  hydrochloric  acid  a  strong  current  is  excited,  which  proceeds  in 
the  liquid  from  the  gold  to  the  platinum,  because  the  gold  is  attacked  by 
the  nitro-hydrochloric  acid,  while  the  platinum  is  less  so,  if  at  all. 

As  a  voltaic  current  is  produced  whenever  two  metals  are  placed  in 
metallic  contact  in  a  liquid  which  acts  more  powerfully  upon  one  than 
upon  the  other,  there  is  a  great  choice  in  the  mode  of  producing  such 
currents.  In  reference  to  their  electrical  deportment,  the  metals 'have 
been  arranged  in  what  is  called  an  electromotive  series,  in  which  the  most 


-755]       .  Electromotive  Force.  675 

elt'ctropositive  are  at  one  end,  and  the  most  elcctronegath'e  at  the  other. 
Hence  when  any  two  of  these  are  placed  in  contact  in  dilute  acid,  the 
current  in  the  connecting  wire  proceeds  from  the  one  lower  in  the  list4^- 
the  one  higher.     The  principal  metals  are  as  follows  : — 


I. 

Zinc 

6.  Nickel 

11.  Gold 

2. 

Cadmium 

7.  Bismuth 

12.  Platinum 

3. 

Tin 

8.  Antimony 

13.  Graphite 

4- 

Lead 

9.  Copper 

5. 

Iron 

10.  Silver 

It  will  be  seen  that  the  electrical  deportment  of  any  metal  depends  on 
the  metal  with  which  it  is  associated.  Iron,  for  example,  in  dilute  sul- 
phuric acid  is  electronegative  towards  zinc,  but  is  electropositive  towards 
copper;  copper  in  turn  is  electronegative  towards  iron  and  zinc,  but  is 
electropositive  towards  silver,  platinum,  or  graphite. 

755.  Electromotive  force. — The  force  in  virtue  of  which  continuous 
electrical  effects  are  produced  throughout  a  circuit  consisting  of  two  ; 
metals  in  metallic  contact  in  a  liquid  which  acts  unequally  upon  them,  is  'A 
usually  called  the  elect7'oi7iotive  force.  Electromotive  force  and  difference-y. 
of  potentials  are  commonly  used  in  the  same  sense.  It  is  however  more, 
correct  to  regard  difference  of  potentials  as  a  particular  case  of  electro- 
motive force ;  for  as  we  shall  afterwards  see,  there  are  cases  in  which 
electrical  currents  are  produced  without  the  occurrence  of  that  particular 
condition  which  we  have  called  difference  of  potentials.  The  electro- 
motive force  is  greater  in  proportion  to  the  distance  of  the  two  metals 
from  one  another  in  the  series.  That  is  to  say,  it  is  greater  the  greater 
the  difference  between  the  chemical  action  upon  the  two  metals  immersed. 
Thus  the  electromotive  force  between  zinc  and  platinum  is  greater  than 
that  between  zinc  and  iron,  or  between  zinc  and  copper.  The  law  esta- 
blished by  experiment  is,  that  the  electromotive  force  betweefi  any  two 
metals  is  equal  to  the  sum  of  the  electromotive  forces  betweeji  all  the 
interve7iing  metals.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  equal  to  the  sum  of  the  electromotive  forces  between  zinc 
and  iron,  iron  and  copper,  and  copper  and  platinum. 

The  electromotive  force  is  influenced  by  the  condition  of  the  metal ; 
rolled  zinc,  for  instance,  is  negative  towards  cast  zinc.  It  also  depends 
on  the  degree  of  concentration  of  the  liquid  ;  in  dilute  nitric  acid  zinc  is 
positive  towards  tin,  and  mercury  positive  towards  lead ;  while  in  con- 
centrated nitric  acid  the  reverse  is  the  case,  mercury  and  zinc  being 
respectively  electronegative  towards  lead  and  tin. 

The  nature  of  the  liquid  also  influences  the  direction  of  the  current. 
If  two  plates,  one  of  copper  and  one  of  iron,  are  immersed  in  dilute  sul- 
phuric acid,  a  current  is  set  up  proceeding  through  the  liquid  from  the 
iron  to  the  copper :  but  if  the  plates,  after  being  washed,  are  placed  in 
solution  of  sulphide  of  potassium,  a  current  is  produced  in  the  opposite 
direction,  the  copper  is  now  the  positive  metal.  Other  examples  may  be 
drawn  from  the  following  table,  which  shows  the  electric  deportment  of 
the  principal  metals  with  three  different  liquids.     It  is  arranged  like  the 


e-jG 


Dynamical  Electricity 


.      [755 


preceding  one ;  each  metal  being  electropositive  towards  any  one  low 
in  the  list,  and  electronegative  towards  any  one  higher  : — 


Caustic  potass 

Hydrochloric  acid 

Sulphide  of 
potassium 

Zinc 

Zinc 

Zinc 

Tin 

Cadmium 

Copper 

Cadmium 

Tin 

Cadmium 

Antimony 

Lead 

Tin 

Lead 

Iron 

Silver 

Bismuth 

Copper 

Antimony 

Iron 

Bismuth 

Lead 

Copper 

Nickel 

Bismuth 

Nickel    • 

Silver 

Nickel 

Silver 

Antimony 

Iron 

A  voltaic  current  may  also  be  produced  by  means  of  two  liquids  and 
one  metal.  This  may  be  shown  by  the  following  experiment:  In  a 
beaker  containing  strong  nitric  acid  is  placed  a  small  porous  cylinder 
closed  at  one  end,  and  containing  strong  solution  of  caustic  potass.  If 
now  two  platinum  wires  connected  with  the  two  ends  of  a  galvanometer 
(773)  3-re  immersed  respectively  in  the  alkali  and  in  the  acid,  a  voltaic 
current  is  produced,  proceeding  in  the  wire  from  the  nitric  acid  to  the 
potass,  which  thus  correspond  respectively  to  the  negative  and  positive 
plates  in  ordinary  couples. 

A  metal  which  is  acted  upon  by  a  liquid  can  be  protected  from  solution 
by  placing  in  contact  with  it  a  more  electropositive  metal,  and  thus  form- 
ing a  simple  voltaic  circuit.  This  principle  is  the  basis  of  Davy's  pro- 
posal to  protect  the  copper  sheathing  of  ships,  which  are  rapidly  acted 
upon  by  sea  water.  If  zinc  or  iron  be  connected  with  the  copper,  these 
metals  are  dissolved  and  the  copper  protected.  Davy  found  that  a  piece 
of  zinc  the  size  of  a  nail  was  sufficient  to  protect  a  surface  of  forty  or  fifty 
square  inches  ;  unfortunately  the  proposal  has  not  been  of  practical 
value,  for  the  copper  must  be  attacked  to  a  certain  extent  to  prevent  the 
adherence  of  marine  plants  and  shellfish. 

756.  Poles  and  electrodes. — If  the  wire  connecting  the  two  terminal 
plates  of  a  voltaic  couple  be  cut,  it  is  clear,  from  what  has  been  said 
about  the  origin  and  direction  of  the  current,  that  positive  electricity  will 
tend  to  accumulate  at  the  end  of  the  wire  attached  to  the  copper  or 
negative  plate,  and  negative  electricity  on  the  wire  attached  to  the  zinc  or 
positive  plate.  These  terminals  have  been  called  the  poles  of  the  battery. 
For  experimental  purposes,  more  especially  in  the  decomposition  of  salts, 
plates  of  platinum  are  attached  to  the  ends  of  the  wires.  Instead  of  the 
term  poles  the, word  electrode  {t'lXtKrpov  and  oroc  a  way)  is  now  commonly 
used;  for  these  are  the  ways  through  which  the  respective  electricities 
emerge.  It  is  important  not  to  confound  the  positive  plate  with  the 
positive  pole  or  electrode.  The  positive  electrode  is  that  connected  with 
the  negative  plate,  while  the  negative  electrode  is  connected  with  the 
positive  plate. 


-757] 


Voltaic  Pile.      Voltaic  Battery. 


677 


757.  Voltaic  pile.  Voltaic  battery.— When  a  series  of  voltaic  ele- 
ments or  pairs  are  arranged  so  that  the  zinc  of  one  element  is  connected 

with  the  copper  of  another;  the  zinc  of  this  with  the  cop)per  of  another^ 

and  so  on,  the  arrangement  is  called  a  voltaic  battery;  and  by  its  means 

the  effects   produced  by  a  single  element  are 

capable  of  being  very  greatly  increased. 

The  earliest  of  these  arrangements  was  de- 
vised by  Volta  himself.     It  consists  (fig.  597)  of 

a  series  of  discs  piled  one  over  the  other  in  the 

following  order :  at  the  bottom,  on  a  frame  of 

wood,  is  a  disc  of  copper,  then  a  disc  of  cloth 

moistened  by  acidulated  water,  or  by  brine,  then 

a  disc  of  zinc;  on  this  a  disc  of  copper,  and 

another  disc  of  moistened  cloth,  to  which  again 

follow  as  many  sets  of  zinc-cloth-copper,  always 

in  the  same  order,  as  may  be  convenient,  the 

highest  disc  being  of  zinc.     The  discs  are  kept 

in  vertical  positions  by  glass  rods. 

It  will  be  readily  seen  that  we  have  here  a 

series  of  simple  voltaic  couples,  the  moisture  in 

the  cloth  acting  as  the  liquid  in  the  cases  already 

mentioned,  and  that  the  terminal  zinc  is  the 

negative  and  the  terminal  copper  the  positive 

pole.     From  the  mode  of  its  arrangement,  and 

from  its  discoverer,  the  apparatus  is  known  as 

the  voltaic  pile,  a  term  applied  to  all  apparatus  of 
this  kind  for  accumulating  the  effects  of  dyna- 
mical electricity. 

The  distribution  of  electricity  in  the  pile 
varies  according  as  it  is  in  connection  with  the 
ground  by  one  of  its  extremities,  or  as  it  is 
insulated  by  being  placed  on  a  nonconducting 
cake  of  resin  or  glass. 

In  the  former  case,  the  end  in  contact  with  the  ground  is  neutral,  and 
the  rest  of  the  apparatus  contains  only  one  kind  of  electricity ;  this  is 
negative  if  the  copper  disc,  and  positive  if  the  zinc  disc  is  in  contact  with 
the  ground. 

In  the  insulated  pile  the  electricity  is  not  uniformly  distributed.  By 
means  of  the  proof-plane  and  the  electroscope  it  may  be  demonstrated 
that  the  middle  part  is  in  a  neutral  state,  and  that  one  half  is  charged 
with  positive  and  the  other  with  negative  electricity,  the  potential  increas- 
ing from  the  middle  to  the  ends.  The  half  terminated  by  a  zinc  is 
charged  with  negative  electricity,  and  that  by  a  copper  with  positive 
electricity.  The  pile  is  thus  similar  to  a  charged  Leyden  jar ;  with  this 
difference,  however,  that  when  the  jar  has  been  discharged  by  connecting 
its  two  coatings,  the  electrical  effects  cease;  while  in  the  case  of  the  pile, 
the  cause  which  originally  brought  about  the  distribution  of  electricity 
restores  this  state  of  charge  after  the  discharge;  and  the   continuous 


fig-  597- 


ej'i 


Dynamical  Electricity. 


[757 


succession  of  charges  and  discharges  form  the  current.  The  effects  of  the 
pile  will  be  discussed  in  other  places. 

758.  'WoUePston's  battery. — The  original  form  of  the  voltaic  pile  has 
a  great  many  inconveniences,  and  possesses  now  only  an  historical 
interest.  It  has  received  a  great  many  improvements,  the  principal 
object  of  which  has  been  to  facili«:ate  manipulation,  and  to  produce 
greater  electromotive  force. 

One  of  the  earliest  of  these  modifications  was  the  crown  of  cups,  or 
coiiroufie  des  tasses,  invented  by  Volta  himself;  an  improved  form  of  this 
is  known  as  IVollaston's  battery  (fig.  598)  ;  it  is  arranged  so  that  when 
the  current  is  not  wanted,  the  action  of  the  battery  can  be  stopped. 


Fig.  598. 


The  plates  Z  are  of  thick  rolled  zinc,  and  usually  about  eight  inches 
in  length  by  six  in  breadth.  The  copper  plates  C  are  of  thin  sheet,  and 
bent  so  as  to  surround  the  zincs  without  touching  them  :  contact  being 
prevented  by  small  pieces  of  cork.  To  each  copper  plate  a  narrow  strip 
of  copper,  (?,  is  soldered,  which  is  bent  twice  at  right  angles  and  is 
soldered  to  the  zinc  plate  ;  and  the  first  zinc  Z  is  surrounded  by  the  first 
copper  C  ;  these  two  constitute  a  couple,  and  each  couple  is  immersed  in 
a  glass  vessel,  containing  acidulated  water.  The  copper  C  is  soldered  to 
the  second  zinc  by  the  strip  o,  and  this  zinc  is  in  turn  surrounded  by  a 
second  copper,  and  so  on. 

Figure  598  represents  a  pile  of  sixteen  couples  united  in  two  parallel 
series  of  eight  each.  All  these  couples  are  fixed  to  a  cross  frame  pf 
wood,  by  which  they  can  be  raised  or  lowered  at  pleasure.  When  the 
battery  is  not  wanted,  the  couples  are  lifted  out  of  the  liquid.  The  water  in 
these  vessels  is  usually  acidulated  with  ^,\  sulphuric  and  ^^  of  nitric  acid. 

Hare's  deflagrator.     This  is  a  simple  voltaic  arrangement,  consisting 


-759]  Secondary  Ciir rents.  679 

of  two  large  sheets  of  copper  and  zinc  rolled  together  in  a  spiral,  but 
preserved  from  direct  contact  by  bands  of  leather  or  horsehair.  The 
whole  is  immersed  in  a  vessel  containing  acidulated  water,  and  the  two 
plates  are  connected  outside  the  liquid  by  a  conducting  wire. 

759.  Enfeeblement  of  the  current  in  batteries.  Secondary  cur> 
rents.  Polarity. — The  various  batteries  already  described,  Volta's, 
Wollaston's,  and  Hare's  which  consist  essentially  of  two  metals  and  one 
liquid,  labour  under  the  objection  that  the  currents  produced  rapidly 
diminish  in  strength. 

This  is  principally  due  to  three  causes ;  the  first  is  the  decrease  in  the 
chemical  action  owing  to  the  neutralisation  of  the  sulphuric  acid  by  its 
combination  with  the  zinc.  This  is  a  necessary  action,  for  upon  it  depends 
the  current ;  it  therefore  occurs  in  all  batteries,  and  is  without  remedy 
except  by  replacement  of  acid  and  zinc.  The  second  is  due  to  what  is 
called  local  action ;  that  is,  the  production  of  small  closed  circuits  in  the 
active  metal,  owing  to  the  impurities  it  contains.  These  local  currents 
rapidly  wear  away  the  active  plate,  without  contributing  anything  to 
the  continuance  of  the  general  current.  They  are  remedied  by  amalga- 
mating the  zinc  with  mercury,  by  which  chemical  action  is  prevented 
until  the  circuit  is  closed,  as  will  be  more  fully  explained  (768).  The 
third  arises  from  the  production  of  an  inverse  electromotive  force,  which 
tends  to  produce  a  current  in  a  contrary  direction  to  the  principal  current, 
and  therefore  to  destroy  it  either  totally  or  partially.  In  the  fundamental 
experiment  (fig.  596),  when  the  circuit  is  closed,  sulphate  of  zinc  is  formed, 
which  dissolves  in  the  liquid,  and  at  the  same  time  a  layer  of  hydrogen 
gas  is  gradually  formed  on  the  surface  of  the  copper  plate.  This  dimi- 
nishes the  activity  of  the  combination  in  more  than  one  way.  In  the 
first  place  it  interferes  with  the  contact  between  the  ijietal  and  the 
liquid ;  in  the  second  place  in  proportion  as  the  copper  becomes  coated 
with  hydrogen,  we  h'ave  virtually  a  plate  of  hydrogen  instead  of  a  plate 
of  copper  opposed  to  the  zinc,  and  in  addition,  the  hydrogen,  by  reacting 
on  the  sulphate  of  zinc  which  accumulates  in  the  liquid,  gradually  causes 
a  deposition  of  zinc  on  the  surface  of  the  copper;  hence,  instead  of  having 
two  different  metals  unequally  attacked,  the  two  metals  become  gradually 
less  different,  and,  consecjuently,  the  total  effect,  and  the  current,  become 
weaker  and  weaker. 

ThQ  polarisation  of  the  plate  (as  this  phenomenon  is  termed)  may  be 
destroyed  by  breaking  the  circuit  and  exposing  the  copper  plate  to  the 
air;  the  deposited  hydrogen  is  thus  more  or  less ,  completely  got  rid  of, 
and  on  again  closing  the  circuit  the  current  has  nearly  its  original 
strength.  The  same  result  is  obtained  when  the  current  of  another 
battery  is  transmitted  through  the  battery  in  a  direction  opposite  to  that 
of  the  first. 

De  la  Rive  found  that  when  the  platinum  electrodes  which  had  been 
used  in  decomposing  a  liquid  were  removed  from  this  Hquid  and  placed 
in  distilled  water,  they  produced  a  current  when  connected  in  a  direction 
opposite  to  that  which  they  had  at  first  transmitted.  He  calls  this  the 
polarisation  of  the  electrodes.     Becquerel  and  Faraday  have  shown  that 


68o 


Dynamical  Electricity. 


[759- 


this  polarity  of  the  metals  results  from  the  deposits  caused  by  the  passage 
of  the  current. 

Even  when  platinum  electrodes  are  used  to  decompose  pure  water, 
polarisation  takes  place  in  consequence.  This  phenomenon,  as  Mat- 
teucci  has  shown,  arises  from  a  deposit  of  hydrogen  on  the  one,  and  of 
oxygen  on  the,  other  electrode. 

CONSTANT   CURRENTS. 

760.  Constant  currents. — With  few  exceptions,  batteries  composed 
of  elements  with  a  single  liquid  have  almost  gone  out  of  use,  in  con- 
sequence of  the  rapid  enfeeblement  of  the  current  produced.  They 
have  been  replaced  by  batteries  with  two  liquids,  which  are  called  co?istant 


considerable  period  of  time.  The  essential  point  to  be  attended  to  in 
securing  a  constant  current  is  to  prevent  the  polarisation  of  the  inactive 
metal ;  in  other  words,  to  hinder  any  permanent  deposition  of  hydrogen 
on  its  surface.  This  is  effected  by  placing  the  inactive  metal  in  a  liquid 
upon  which  the  deposited  hydrogen  can  act  chemically. 

761.  Daniell's  battery. —  This  was  the  first  form  of  the  constant 
battery,  and  was  invented  by  Daniell  in  the 
year  1836.  As  regards  the  constancy  of  its 
action,  it  is  perhaps  still  the  best  of  all  con- 
stant batteries.  Fig.  599  represents  a  single 
element.  A  glass  or  porcelain  vessel,  V,  con- 
tains a  saturated  solution  of  sulphate  of 
copper,  in  which  is  immersed  a  copper 
cylinder,  G,  open  at  both  ends,  and  per- 
forated by  holes.  At  the  upper  part  of  this 
cylinder  there  is  an  arlnular  shelf,  C,  also 
perforated  by  small  holes,  and  below  the 
level  of- the  solution;  this  is  intended  to 
support  crystals  of  sulphate  of  copper  to 
replace  that  decomposed  as  the  electrical 
action  proceeds.  Inside  the  cylinder  is  a 
^'s-  599-  thin   porous   vessel,    P,   of  unglazed   earth- 

enware. This  contains  either  water  or  solution  of  common  salt  or  dilute 
sulphuric  acid,  in  which  is  placed  the  cylinder  of  amalgamated  zinc,  Z. 
Two  thin  strips  of  copper,  p  and  n,  fixed  by  binding  screws  to  the  copper 
and  to  the  zinc,  serve  for  connecting  the  elements  in  series. 

When  a  Daniell's  element  is  closed',  the  hydrogen  resulting  from 
the  action  of  the  dilute  acid  on  the  zinc  is  liberated  on  the  surface  of  the 
copper  plate,  but  meets  there  the  sulphate  of  copper,  which  is  reduced, 
forming  sulphuric  acid  and  metallic  copper,  which  is  deposited  on  the 
surface  of  the  copper  plate.  In  this  way  sulphate  of  copper  in  solution  is 
taken  up,  and  if  it  were  all  consumed,  hydrogen  would  be  deposited  on 
the  copper,  and  the  current  would  lose  its  constancy.  This  is  prevented 
by  the  crystals  of  sulphate  of  copper  which  keep  the  solution  saturated. 


763] 


Biinseiis  Battery. 


6Z 


The  sulphuric  acid  produced  by  the  decomposition  of  the  sulphate  per- 
meates the  porous  cylinder,  and  tends  to  replace  the  acid  used  up  by  its 
action  on  the  zinc  ;  and  as  the  quantity  of  sulphuric  acid  formed  in  the- 
solution  of  sulphate  of  copper  is  regular,  and  proportional  to  the  acid  used 
in  dissolving  the  zinc,  the  action  of  this  acid  on  the  zinc  is  regular  also, 
and  thus  a  constant  current  is  produced. 

In  order  to  join  together  several  of  these  elements  to  form  a  battery, 
the  zinc  of  one  is  connected  either  by  a  copper  wire  or  strip  with  the 
copper  of  the  next,  and  so  on,  from  one  element  to  another,  as  shown 
in  fig.  603,  for  another  kind  of  battery. 

Instead  of  a  porous  earthenware  vessel  a  bag  of  sailcloth  may  be  used 
for  the  diaphragm  separating  the  two  liquids.  The  effect  is  at  first  more 
powerful,  but  the  two  solutions  mix  more  rapidly,  which  weakens  the 
current.  The  object  of  the  diaphragm  is  to  allow  the  current  to  pass,  but 
to  prevent  as  much  as  possible  the  mixture  of  the  two  liquids. 

The  current  produced  by  a  Daniell's  battery  is  constant  for  some  hours; 
its  action  is  stronger  when  it  is  placed  in  hot  water. 

762.  G-rove's  battery. — In  this  battery  the  sulphate  of  copper  solution 
is  replaced  by  nitric  acid,  and  the  copper  by  platinum,  by  which  greater 
electromotive  force  is  obtained.  Fig.  609  represents  one  of  the  forms  of  a 
couple  of  this  battery.  It  consists  of  a  glass  vessel.  A,  partially  filled  with 
dilute  sulphuric  acid  (i  :  8) ;  of  a  cylinder  of  zinc,  Z,  open  at  both  ends ; 
of  a  vessel,  V,  made  of  porous 
pipeclay,  and  containing  ordi- 
nary nitric  acid ;  of  a  plate  of 
platinum,  P  (fig.  601),  bent  in 
the  form  of  an  S,  and  fixed  to 
a  cover,  r,  which  rests  on  the 
porous  vessel.  The  platinum 
is  connected  with  a  binding 
screw,  b^  and  there  is  a  similar 
binding  screw  on  the  zinc.  In 
this  battery  the  hydrogen,  which 
would  be  disengaged  on  the 
platinum,  meeting  the  nitric 
acid,  decomposes  it,  forming 
hyponitrous  acid,  which  dis- 
solves or  is  disengaged  as 
nitrous  fumes.  Grove's  battery  is  the  most  convenient  and  one  of  the 
most  powerful  of  the  two-fluid  batteries.  It  is,  however,  the  most  expen- 
sive, owing  to  the  high  price  of  platinum ;  besides  which  the  platinum  is 
liable,  after  some  time,  to  become  brittle  and  break  very  easily.  But  as 
the  platinum  is  not  consumed,  it  retains  most  of  its  value  ;  and  when  the 
plates  which  have  been  used  in  a  battery  are  heated  to  redness,  they 
retain  their  elasticity. 

763.  Bunsen's  battery. — Bunsen's  battery^  also  known  as  the  zinc 
^<?r<^^;?  battery,  was  invented  in  1843;  it  is  nothing  more  than  Grove's 
battery,  in  which  the  sheet  of  platinum  is  replaced  by  a  cylinder  of  car- 

GG  3 


Fig.  600. 


Fig.  601. 


esa 


Dynamical  Electricity, 


[763- 


bon.  This  is  made  either  of  the  graphitoidal  carbon  deposited  in  gas 
retorts,  or  by  calcining  in  an  iron  mould  an  intimate  mixture  of  coke  and 
bituminous  coal»  finely  powdered  and  strongly  compressed.  Both  these 
modifications  of  carbon  are  good  conductors.  Each  element  consists  of 
the  following  parts :  i.  a  vessel,  F  (fig,  602),  either  of  stoneware  or  of 
glass,  containing  dilute  sulphuric  acid ;  2.  a  hollow  cylinder,  Z,  of  amal- 
gamated line ;  5.  a  porous  vessel,  V,  in  which  is  ordinary  nitric  acid  ; 


Figs  6>s>j^. 

4.  a  cylinder  of  carbon,  C,  prepared  in  the  abox-e  manner.  In  the  vessel 
F  the  nnc  is  first  placed,  and  in  it  the  carbon  C  in  the  porous  vessel  V  as 
seen  in  P.  To  the  carbon  is  fixed  a  binding  screw,  wl,  to  which  a  copper 
wire  is  attached,  forming  the  positive  pole.  The  linc  is  provided  with  a 
similar  binding  screw, «,  and  wire,  which  is  thus  a  n^;ative  pole. 

The  elements  are  arranged  to  form  a  battery  by  connecting  each  carbon 
to  the  tine  of  the  following  one  by  means  of  the  clamps  wm  and  a  strip  of 
copper  €  represented  in  the  top  of  the  figure.  The  copper  is  pressed  at 
one  «ad  between  the  carbon  and  the  clamp,  and  at  the  other  it  is  soldered 
to  the  damp  «  which  is  fitted  on  the  rinc  of  the  following  element,  and  so 
forth.  The  clamp  of  the  first  carbon  and  that  of  the  last  xinc  are  alone 
provided  with  binding  screws  to  which  are  attached  the  wires. 

The  chemical  action  of  Bunsen's  battery  is  the  same  as  that  of  Grovels, 
and  bang  equally  powerful,  while  less  costly,  is  almost  uni\^ersally  used 
on  the  Continent.  But  though  its  first  cost  is  less  than  that  of  Gro\-e'^s 
battery,  it  is  more  expensive  to  work,  and  is  not  so  convenient  to  mani> 
polate^ 

OUlmis  itUitry  is  a  modified  form  of  Grovels.  Instead  of  xinc  and 
plakinum,  zinc  and  platinised  lead  are  used,  and  instead  of  pure  nitric  add 
CaUan  used  a  mixture  of  sulphuric  add,  nitric  add,  and  saturated  solution 
of  nitre.  The  battery  is  said  to  be  equal  in  its  action  to  Grove's,  and  is 
much  dieaper. 

CaUan  has  also  constructed  a  battery  in  which  zinc  in  dilute  sulphuric 
add  fonns  the  positive  plate,  and  cast  iron  in  strong  nitric  add  the  nega- 
tive. Under  these  circumstances  the  iron  becomes  passive;  it  isstrongly 
etectroncgative,  and  does  not  dissolve.  If,  however,  the  nitric  add  becomes 


764] 


Snucs  Battery, 


6Sl 


too  weak,  the  iron  is  dissolved  with  simuhaneous  disengagement  of  nitrous 
fumes. 

After  being  in  use  some  time,  all  the  batteries  in  which  the  polarisatmn- 
is  prevented  by  nitric  acid  disengage  nitrous  fumes  in  large  quantities, 
and  this  is  a  serious  objection  to  their  use,  especially  in  closed  rooms.  Tq 
prevent  this,  nitric  acid  is  frequently  replaced  by  chromic  acid,  or  better, 
by  a  mixture  of  4  parts  bichromate  of  potassium,  4  parts  sulphuric  acid, 


Fig.  603. 

and  18  water.  The  liberated  hydrogen  reduces  the  chromic  acid  to  the 
state  of  oxide  of  chromium,  which  remains  dissolved  in  sulphuric  acid. 
With  the  same  view,  sesquichloride  of  iron  is  sometimes  substituted  for 
nitric  acid ;  it  becomes  reduced  to  protochloride.  But  the  action  of  the 
elements  thus  modified  is  considerably  less  than  when  nitric  acid  is  used, 
owing  to  the  increased  resistance. 

764.  Smee's  battery. — In  this  battery  the  polarisation  of  the  negative 
plate  is  prevented  by  mechanical  means.  Each  element  consists  of-a 
sheet  of  platinum  placed  between  two  vertical  plates  of  zinc,  as  in  Grove's 
battery ;  but  as  there  is  only  a  single  liquid,  dilute  sulphuric  acid,  the  ele- 
ments have  much  the  form  of  those  in  Wollaston  s  battery.  The  adherence 
of  hydrogen  to  the  negative  plate  is  prevented  by  covering  the  platinum 
with  a  deposit  of  finely  divided  platinum.  In  this  manner  the  surface  is 
roughened,  which  facilitates  the  disengagement  of  hydrogen  to  a  remark- 
able extent,  and,  consequently,  diminishes  the  resistance  of  the  couple. 
Instead  of  platinum,  silver  covered  with  a  deposit  of  finely  divided  pla- 
tinum is  frequently  substituted,  as  being  cheaper. 

Walters  battery. — This  resembles  Smee's  battery,  but  the  electro- 
negative plate  is  either  gas  graphite  or  platinised  graphite  ;  it  is  excited 
by  dilute  sulphuric  acid.  This  battery  is  used  in  all  the  stations  of  the 
South  Eastern  Railway,  and  promises  to  come  into  more  extensive  use, 
for  it  has  considerable  electromotive  force  ;  it  is  convenient  and  econo- 
mical in  manipulation,  and  large- sized  elements  can  be  constructed  at  a 
cheap  rate. 


684 


Dynamical  Electricity. 


[765- 


765.  Recent  batteries. — The  sulphate  0/ pierctiry  hzXiery  (fig,  604)  de- 
vised by  M.  Marie  Davy,  is  essentially  a  zinc-carbon  element,  but  of  smaller 
dimensions  than  those  elements  usually  are.  In  the  outer  vessel  V  ordinary 
M^ater  or  brine  is  placed,  and  in  the  porous  vessel  sulphate  of  mercury. 
This  salt  is  agitated  with  about  three  times  its  volume  of  water,  in  which 
it  is  difficultly  soluble,  and  the  liquid  poured  off  from  the  pasty  mass.    The 


A     r 

\ 

r 

L 

\ 

\^_ 

— ^ 

~ 

^^ 

R 

Fig.  604. 


Fig.  605. 


Fitr.  606. 


carbon  being  placed  in  the  porous  vessel  the  spaces  are  filled  with  the 
residue  and  then  the  decanted  hquid  poured  into  it. 

Chemical  action  takes  place  only  when  the  pile  is  closed.  The  zinc 
then  decomposes  the  water,  liberating  hydrogen,  which  traversing  the 
porous  vessel  reduces  the  sulphate  of  mercury,  forming  metallic  mercury, 
which  collects  at  the  bottom  of  the  vessel,  while  the  sulphuric  acid  formed 
at  the  same  time  traverses  the  diaphragm  to  act  on  the  zinc  and  thus  in- 
creases the  action.  The  mercury  which  is  deposited  may  be  used  to  pre- 
pare a  quantity  of  sulphate  equal  to  that  which  has  been  consumed.  A 
small  quantity  of  the  solution  of  sulphate  of  mercury  may  also  pass  through 
the  diaphragm  ;  but  this  is  rather  advantageous,  as  its  effect  is  to  amalga- 
mate the  zinc. 

The  electromotive  force  of  this  element  is  about  a  quarter  greater  than 
that  of  Daniell's  element,  but  it  has  greater  resistance ;  it  is  rapidly  ex- 
hausted when  continuously  worked,  though  it  appears  well  suited  for  dis- 
continuous work,  as  with  the  telegraph,  and  with  alarums. 

Gravity  batteries.  The  use  of  porous  vessels  is  liable  to  many  objec- 
tions, more  especially  in  the  case  of  Daniell's  battery,  in  which  they 
gradually  become  encrusted  with  copper,  which  destroys  them.  A  kind  of 
battery  has  been  devised  in  which  the  porous  vessel  is  entirely  dispensed 
with,  and  the  separation  of  the  liquids  is  effected  by  the  difference  of 
density.  Such  batteries  are  called  gravity  batteries  ;  the  one  in  use  at  the 
telegraphic  establishment  of  the  Royal  Engineers  at  Chatham  is  based  on 
this  principle. 

Figure  605  represents  a  form  devised  by  M.  Callaud  of  Nantes.  V  is  a 
glass  or  earthenware  vessel  in  which  is  a  copper  plate  soldered  to  a  wire 
insulated  by  gutta  percha.     On  the  plate  is  a  layer  of  crystals  of  sulphate 


—767]  Electromotive  Force  of  different  Elements.  685 

of  copper  C  ;  the  whole  is  then  tilled  with  water,  and  the  zinc  cylinder  Z  is 
immersed  in  it.     The  lower  part  of  the  liquid  becomes  saturated  with  sul- 
phate of  copper  ;  the  action  of  the  battery  is  that  of  a  Daniell,  and  the  sul-_ 
phate  of  zinc  which  gradually  forms  floats  on  the  solution  of  sulphate  of 
copper  owing  to  its  lower  density. 

This  battery  is  easily  manipulated,  the  consumption  of  sulphate  of 
copper  is  economical,  and  when  not  agitated  it  works  constantly  for 
some  months,  provided  care  be  taken  to  replace  the  water  lost  by 
evaporation. 

Minottd's  battery. — This  may  be  described  as  a  Daniell's  element,  in 
which  the  porous  vessel  is  replaced  by  a  layer  of  sawdust  or  of  sand.  At 
the  bottom  of  an  earthenware  vessel  (fig.  606)  is  placed  a  layer  of  coarsely- 
powdered  sulphate  of  copper  a^  and  on  this  a  copper  plate  provided  w4th 
an  insulated  copper  wire  /.  On  this  there  is  a  layer  of  sand  or  of  sawdust 
be,  and  then  the  whole  is  filled  with  water  in  which  rests  a  zinc  cylinder  Z. 
The  action  is  just  that  of  a  Daniell  ;  the  sawdust  prevents  the  mixture  of 
the  liquids  but  it  also  offers  great  resistance,  which  increases  with  its 
thickness. 

From  its  simplicity  and  economy,  and*  the  facility  with  which  it  is 
constructed,  this  battery  merits  increased  attention. 

Leclanches  elements  consist  of  a  rod  of  carbon  placed  in  a  porous  pot, 
which  is  then  tightly  packed  with  a  mixture  of  pyrolusite  (peroxide  of 
manganese)  and  coke.  The  porous  pot  is  contained  in  an  outer  vessel  in 
which  is  the  electropositive  element  the  zinc.  The  exciting  liquid  is  a 
solution  of  sal  ammoniac  ;  it  is  advantageous  not  to  fill  the  v^essel  more 
than  one-third  with  the  liquid.  The  battery  is  coming  into  very  extended 
use  ;  its  electromotive  force  is  about  {^  that  of  a  Daniell,  "and  its  resist- 
ance about  1 1  of  a  British  Association  unit. 

766.  Electromotive  force  of  different  elements. — The  following 
numbers  represent  the  electromotive  force  of  some  of  the  elements  most 
frequently  used,  compared  with  that  of  an  ordinary  Daniell's  cell  charged 
as  above  described  ;  they  are  the  means  of  many  careful  determina- 
tions. 

Daniell's    clement  set  up  with  water  .         .         .         .     i  -co 
„  „         pure  zinc  and    pure  water,  with 

pure  copper  and  pure  saturated 
solution  of  sulphate  of  copper   .     i-02 

Leclanche's     .,         zinc    in    saturated    solution     of 

chloride  of  ammonium       .         .1-32 

Marie  Davy's  „ 1*41 

Bunsen's  ,,         carbon  in  nitric  acid      .         .         .177 

„  „         carbon  in  chromic  acid  .         .1-87 

Grove's  „         platinum  in  nitric  acid .         .         .1-82 

767.  Comparison  of  the  voltaic  battery  with  a  frictional  electrical 
machine. — Except  in  the  case  of  batteries  consisting  of  a  very  large 
number  of  couples,  the  difference  of  potentials  between  the  terminals  is 
far  weaker  than  in  electrical  machines,  and  is  insufficient  to  give  any 


686  Dynamical  Electricity.  [767- 

visible  spark.  Gassiott's  great  battery,  however,  which  consisted  of  3,-52o 
zinc  and  copper  elements  with  poles  ^-^  of  an  inch  apart,  gave  a  series  of 
sparks  across  this  interval  which  lasted  for  weeks. 

In  the  case  of  a  small  battery  or  of  a  single  cell,  very  delicate  tests 
are  required  to  detect  any  signs  of  electrification.  But  by  means  of  a 
delicate  condensing  electroscope,  and  by  extremely  careful  insulation  it 
can  be  shown  that  one  pole  possesses  a  positive  and  the  other  a  negative 
charge. 

For  this  purpose  one  of  the  plates  of  the  electroscope  is  connected 
with  one  end  of  the  pile,  and  the  other  with  the  other  end  or  with  the 
ground.  The  electroscope  thus  becomes  charged,  and  on  breaking  the 
communications  electroscopic  indications  are  observed.  A  Leyden  jar 
may  even  be  charged  when  the  interior  coating  is  connected  with  one  end 
of  the  pile,  and  the  external  coating  with  the  other;  but  this  charge  is 
far  smaller  than  that  furnished  by  an  electrical  machine. 

On  the  other  hand  the  strength  of  a  current  which  a  voltaic  element 
can  produce  in  a  good  conductor,  is  much  greater  than  that  which  can  be 
produced  by  a  machine.  Faraday  immersed  two  wires,  one  of.  zinc,  and 
the  other  of  platinum,  each  ^^  of  an  inch  in  diameter,  in  acidulated  water 
for  ~  of  a  second.  The  effect  thus  produced  on  a  magnetic  needle  in  this 
short  time  was  greater  than  that  produced  by  23  turns  of  the  large  elec- 
trical machine  of  the  Royal  Institution. 

Rossetti  concludes  from  some  experiments  that  the  electromotive 
force  of  the  current  of  a  Holtz's  machine  is  upwards  of  50,000  times  that 
of  a  Daniell's  cell. 

768.  Amalg^amated  zinc.  Iiocal  currents. — De  la  Rive  observed 
that  perfectly  pure  distilled  zinc  was  not  attacked  by  dilute  sulphuric 
acid,  but  became  so  when  immersed  in  that  liquid  in  contact  with  a  plate 
of  copper  or  of  platinum.  Ordinary  commercial  zinc,  on  the  contrary,  is 
rapidly  dissolved  by  dilute  acid.  This,  doubtless,  arises  from  the  impurity 
of  the  zinc,  which  always  contains  traces  either  of  iron  or  lead.  Being 
electro-negative  towards  zinc  they  tend  to  produce  local  electrical  currents., 
which  accelerate  the  chemical  action  without  increasing  the  quantity  of 
electricity  in  the  connecting  wire. 

Zinc,  when  amalgamated,  acquires  the  properties  of  perfectly  pure 
zinc  and  is  unaltered  by  dilute  acid,  so  long  as  it  is  not  in  contact 
with  a  copper  or  platinum  plate  immersed  in  the  same  liquid.  To 
amalgamate  a  zinc  plate,  it  is  first  immersed  in  dilute  sulphuric  or 
hydrochloric  acid  so  as  to  obtain  a  clean  surface,  and  then  a  drop  of 
mercury  is  placed  on  the  plate  and  spread  over  it  with  a  brush.  The 
amalgamation  takes  place  immediately,  and  the  plate  has  the  brilliant 
aspect  of  mercury. 

Zinc  as  well  as  other  metals  are  readily  amalgamated  by  dipping  them 
in  an  amalgam  of  one  part  sodium  and  200  parts  of  mercury. 

Zinc  plates  may  also  be  amalgamated  by  dipping  them  in  a  solution 
of  mercury  prepared  by  dissolving  at  a  gentle  heat  one  pound  of  mercury 
in  five  pounds  of  aqua  regia  (one  part  of  nitric  to  three  of  hydrochloric 
acid),  and  then  adding  five  parts  more  of  hydrochloric  acid. 


-770]  Bohnenbergcr s  Electroscope.  68^'^ 

The  amalgamation  of  the  zinc  removes  from  its  surface  all  the  im- 
purities, especially  the  iron.  The  mercury  effects  a  solution  of  pure  zinc, 
which  covers  the  surface  of  the  plate,  as  with  a  liquid  layer.  _: 

The  amalgamation  of  zinc  was  first  applied  to  electrical  batteries  by 
Kemp.  Amalgamated  zinc  is  not  attacked  so  long  as  the  circuit  is  not 
closed,  that  is,  when  there  is  no  current.  With  amalgamated  zinc  the 
current  is  more  regular,  and  at  the  same  time  more  intense,  for  the  same 
quantity  of  metal  dissolved. 

769.  Bry  piles. — In  dry  piles  the  liquid  is  replaced  by  a  solid  hygro- 
metric  substance,  such  as  paper  or  leather.  They  are  of  various  kinds  ; 
in  Zamboni's,  which  is  most  extensively  used,  the  electromotors  are  tin  or 
silver,  and  binoxide  of  manganese.  To  construct  one  of  these  a  piece  of 
paper  silvered  or  tinned  on  one  side  is  taken ;  the  other  side  of  the  paper 
is  coated  with  finely-powdered  binoxide  of  manganese  by  slightly  moisten- 
ing it,  and  rubbing  the  powder  on  with  a  cork.  Having  placed  together 
seven  or  eight  of  these  sheets,  they  are  cut  by  means  of  a  punch  into  discs 
an  inch  in  diameter.  These  discs  are  then  arranged  in  the  same  order, 
so  that  the  tin  or  silver  of  each  disc  is  in  contact  with  the  manganese  of 
the  next.  Having  piled  up,  1,200  to  1,800  couples,  they  are  placed  in  a 
glass  tube,  which  is  provided  with  a  brass  cap  at  each  end.  In  each  cap 
there  is  a  rod  and  knob,  by  which  the  leaves  can  be  pressed  together,  so 
as  to  produce  better  contact.  The  knob  in  contact  with  the  manganese 
corresponds  to  the  positive  pole,  while  that  at  the  other  end,  which  is  in 
contact  with  the  silver  or  tin,  is  the  negative  pole. 

The  dry  piles  are  remarkable  for  the  permanence  of  their  action,  which 
may  continue  for  several  years.  Their  action  depends  greatly  on  the 
temperature  and  on  the  hygrometric  state  of  the  air.  It  is  stronger  in 
summer  than  in  winter,  and  the  action  of  a  strong  heat  revives  it  when  it 
appears  extinct.  A  Zamboni's  pile  of  2,000  couples  gives  neither  shock 
nor  spark,  but  can  charge  a  Leyden  jar  and  other  condensers.  A  certain 
time  is  however  necessary,  for  electricity  only  moves  slowly  in  the 
interior. 

770.  Bolinenbergrer's  electroscope. — Bohnenbergcr  has  constructed   ^  ' 
a  dry-pile  electroscope  of  gieat  delicacy.     It  is  a  condensing  electroscope 
(fig.  577),  from  the  rod  of  which  is  suspended  a  single  gold  leaf.     This  is 

at  an  equal  distance  from  the  opposite  poles  of  two  dry  piles  placed 
vertically,  inside  the  bell  jar,  on  the  plate  of  the  apparatus.  As  soon  as 
the  gold  leaf  possesses  any  free  electricity  it  is  attracted  by  one  of  the 
poles  and  repelled  by  the  other,  and  its  electricity  is  obviously  contrary 
to  that  of  the  pole  towards  which  it  moves. 


6SS 


Dynamical  Electricity. 


[771- 


CHAPTER   II. 


DETECTION   AND   MEASUREMENT   OF  VOLTAIC   CURRENTS. 


771.  Detection  and  measurement  of  voltaic  currents. — The  remark- 
able phenomena  of  the  voltaic  battery  may  be  classed  under  the  heads 
physiological,  chemical,  mechanical,  and  physical  effects;  and  these 
latter  may  be  again  subdivided  into  the  thermal,  luminous,  and  magnetic 
effects.  For  ascertaining  the  existence  and  measuring  the  intensity  of 
voltaic  currents,  the  magnetic  effects  are  more  suitable  than  any  of  the 
others,  and,  accordingly,  the  fundamental  magnetic  phenomena  will  be 
described  here,  and  the  description  of  the  rest  postponed  to  a  special 
chapter  on  electro-magnetism. 

772.  Oersted's  experiment. — Oersted  published  in  18 19  a  discovery 
which  connected  magnetism  and  electricity  in  a  most  intimate  man- 
ner, and  became,  in  the  hands  of  Ampere  and  of  Faraday,  the  source 
of  a  new  branch  of  physics.  The  fact  discovered  by  Oersted  is  the 
directive  action  which  a  fixed  current  exerts  at  a  distance  on  a  magnetic 
needle. 

To  make  this  experiment  a  copper  wire  is  suspended  horizontally  in 

the  direction  of  the  magnetic 
meridian  over  a  movable  mag- 
netic needle,  as  represented  in 
fig.  607.  So  long  as  the  wire  is 
not  traversed  by  a  current  the 
needle  remains  parallel  to  it,  but 
as  soon  as  the  ends  of  the  wire 
are  respectively  connected  with 
the  poles  of  a  battery  or  of  a 
single  element,  the  needle  is  de- 
flected, and  tends  to  take  a  posi- 
tion which  is  the  more  nearly  at 
right  angles  to  the  magnetic  metidian  in  proportion  as  the  cicrretit  is 
stronger. 

In  reference  to  the  direction  in  which  the  poles  are  deflected,  there  are 
several  cases  which  may,  however,  be  referred  to  a  single  principle.  Re- 
membering our  assumption  as  to  the  direction  of  the  current  in  the 
connecting  wire  (754)  the  preceding  experiment  presents  the  following  four 
cases  :— 

i.  If  the  current  passes  above  the  needle,  and  goes  from  south  to  north, 
the  north  pole  of  the  magnet  is  deflected  towards  the  west ;  this  arrange- 
ment is  represented  in  the  above  figure. 

ii.  If  the  current  passes  below  the  needle,  also  from  south  to  north,  the 
north  pole  is  deflected  towards  the  east. 

iii.  When  the  current  passes  above  the  needle,  but  from  north  to  south, 
the  north  pole  is  deflected  towards  the  east. 


Fig.  607. 


-773] 


Galvanometer. 


689 


iv.  Lastly,  the  deflection  is  towards  the  west  when  the  current  goes 
from  north  to  south  below  the  needle. 

Ampere  has  given  the  following  meinoria  technica  by  which  all  the_ 
various  directions  of  the  needle  under  the  influence  of  a  current  may  be 
remembered.  If  we  imagine  an  observer  placed  in  the  connecting  wire 
in  such  a  manner  that  the  current  entering  by  his  feet  issues  by  his  head, 
and  that  his  face  is  always  turned  towards  the  needle,  we  shall  see  that 
^n  the  above  four  positions  the  north  pole  is  always  deflected  towards  the 
left  of  the  observer.  By  thus  personifying  the  current,  the  different  cases 
may  be  comprised  in  this  general  principle  :  In  the  directii'e  actioji  of 
currents  on  magnets,  the  north  pole  is  always  deflected  towards  the  left  of 
the  current. 

yjT,.  Galvanometer  or  multiplier.— The  name  galvanometer,  or 
sometimes  multiplier  or  rheometer,  is  given  to  a  very  delicate  apparatus 
by  which  the  existence,  direction,  and  intensity  of  currents  may  be 
determined.  It  was  invented  by  Schweigger  in  Germany  a  short  time 
after  Oersted's  discovery. 


h 

[ 

^^..-'^^ 

71 

^^.-'-^ 

!-            0 

If 

^^^  u. 

1  ^^- 

111)        -    ^ 

Fig.  609. 

In  order  to  understand  its  principle,  let  us  suppose  a  magnetic  needle 
suspended  by  a  filament  of  silk  (fig.  608),  and  surrounded  in  the  plane  of 
the  magnetic  meridian  by  a  copper  wire  ninopg,  forming  a  complete  circuit 
round  the  needle  in  the  direction  of  its  length.  When  this  wire  is  tra- 
versed by  a  current,  it  follows,  from  what  has  been  said  in  the  previous 
paragraph,  that  in  every  part  of  the  circuit  an  observer  lying  in  the  wire 
in  the  direction  of  the  arrows,  and  looking  at  the  needle  ab,  would  have 
his  left  always  turned  towards  the  same  point  of  the  horizon,  and  con- 
sequently, that  the  action  of  the  current  in  every  part  would  tend  to  turn 
the  north  pole  in  the  same  direction  :  that  is  to  say,  that  the  actions  of 
the  four  branches  of  the  circuit  concur  to  give  the  north  pole  the  same 
direction.  By  coiling  the  copper  wire  in  the  direction  of  the  needle,  as 
represented  in  the  figure,  the  action  of  the  current  has  been  multiplied. 
If  instead  of  a  single  one,  there  are  several  circuits,  provided  they  are 
insulated,  the  action  becomes  still  more  multiplied,  and  the  deflection  of 
the  needle  increases.  Nevertheless,  the  action  of  the  current  cannot  be 
multiplied  indefinitely  by  increasing  the  number  of  windings,  for,  as  we 
shall  presently  see,  the  intensity  of  a  current  diminishes  as  the  length  of 
the  circuit  is  increased. 


690 


Dynamical  Electricity. 


[773 


A5  the  directive  action  of  the  earth  continually  tends  to  keep  the  needle 
in  the  magnetic  meridian,  and  thus  opposes  the  action  of  the  current,  the 
effect  of  the  latter  is  increased  by  using  an  astatic  system  of  two  needles, 
as  shown  in  fig.  609.  The  action  of  the  earth  on  the  needle  is  then  very 
feeble,  and,  further,  the  actions  of  the  current  on  the  two  needles  become 
accumulated.  In  fact,  the  action  of  the  circuit,  from  the  direction  of  the 
current  indicated  by  the  arrows,  tends  to  deflect  the  north  pole  of  the 
lower  needle  towards  the  west.  The  upper  needle  a'b',  is  subjected  to  the 
action  of  two  contrary  currents  no  and  qp,  but  as  the  first  is  nearer,  its 
action  preponderates.  Now  this  current  passing,  below  the  needle,  evi- 
dently tends  to  turn  the  pole  a'  towards  the  ea?t,  and,  consequently,  the 
pole  b'  towards  the  west  :  that  is  to  say,  in  the  same  direction  as  the  pole 
a  of  the  other  needle. 

From  these  principles  it  will  be  easy  to  understand  the  theory  of  the 
multiplier.  The  apparatus  represented  in  fig.  610  consists  of  a  thick 
brass  plate,  D,  resting  on  levelling  screws  ;  on  this  is  a  rotatory  plate,  P, 
of  the  same  metal,  to  which  is  fixed  a  copper  frame,  the  breadth  of  wh'ch 


Fig.  61 


is  almost  equal  to  the  length  of  the  needles.  On  this  Is  coiled  a  great 
number  of  turns  of  wire  covered  with  silk.  The  two  ends  terminate  in 
binding  screws,  i  and  <?,     Above  the  frame  is  a  graduated  circle,  C,  with  a 


-774]  Marine  Galvanometer.  691 

central  slit  parallel  to  the  direction  in  which  the  wire  is  coiled.  The  zero 
corresponds  to  the  position  of  this  sht,  and  there  are  two  graduations  on 
the  scale,  the  one  on  the  right  and  the  other  on  the  left  of  zero,  but  they- 
only  extend  to  90°.  By  means  of  a  very  fine  filament  of  silk,  an  astatic 
system  is  suspended  ;  it  consists  of  two  needles,  ab  and  a'b',  one  above 
the  scale,  and  the  other  within  the  circuit  itself.  These  needles,  which 
are  joined  together  by  a  copper  wire,  like  those  in  fig.  521  and  fig.  609 
and  cannot  move  separately,  must  not  have  exactly  the  same  magnetic 
intensity  ;  for  if  they  are  exactly  equal,  every  current,  strong  or  weak, 
would  always  put  them  at  right  angles  with  itself. 

In  using  this  instrument,  the  diameter,  to  which  corresponds  the  zero 
of  the  graduation,  is  brought  into  the  magnetic  meridian  by  turning  the  plate 
P  until  the  end  of  the  needle  ab  corresponds  to  zero.  The  instrument  is 
fixed  in  this  position  by  means  of  the  screw  clamp  T. 

The  length  and  diameter  of  the  wire  vary  with  the, purpose  for  which 
the  galvanometer  is  intended.  *  For  one  which  is  to  be  used  in  observing 
the  currents  due  to  chemical  actions,  a  wire  about  ^  millimetre  in  diameter, 
and  making  about  800  turns,  is  well  adapted.  Those  for  thermo-electric 
currents,  which  have  low  intensity,  require  a  thicker  and  shorter  wire,  for 
example,  thirty  turns  of  a  wire  §  millimetre  in  diameter.  For  very  delicate 
experiments,  as  in  physiological  investigations,  galvanometers  with  as 
many  as  30,000  turns  have  been  used. 

By  means  of  a  delicate  galvanometer  consisting  of  2,000  or  3,000  turns 
of  fine  wire,  the  coils  of  which  are  carefully  insulated  by  means  of  silk 
and  shellac,  currents  of  high  potential,  as  those  of  the  electrical  machine, 
may  be  shown.  One  end  of  the  galvanometer  is  connected  with  the  con- 
ductor, and  the  other  with  the  ground,  and  on  working  the  machine  the 
needle  is  deflected  ;  affording  thus  an  illustration  of  the  identity  of  statical 
with  dynamical  electricity. 

The  deflection  of  the  needle  increases  with  the  intensity  of  the  current ; 
the  relation  between  the  two  is,  however,  so  complex,  that  it  cannot  well 
be  deduced  from  theoretical  considerations,  but  requires  to  be  determined 
experimentally  for  each  instrument.  And  in  the  majority  of  cases  the 
instrument  is  used  rather  as  ?igalvanoscope  or  rheoscope,  that  is,  to  ascer- 
tain the  presence  and  direction  of  currents,  than  as  a  galvanometer  or 
rheometer  in  the  strict  sense,  that  is,  as  a  measurer  of  their  intensity. 
The  latter  term  galvanometer  is,  however,  commonly  used. 

The  differential  galvanometer  consists  of  a  needle,  as  in  an  ordinary 
galvanometer,  but  round  the  frame  of  which  are  coiled  two  wires  of  the 
same  kind  and  dimensions,  carefully  insulated  from  each  other,  and  pro- 
vided with  suitable  binding  screws,  so  that  separate  currents  can  be  passed 
through  each  of  them.  If  the  currents  are  of  the  same  intensity  but  in 
different  directions,  no  deflection  is  produced ;  where  the  needle  is 
deflected  one  of  the  currents  differs  from  the  other.  Hence  the  apparatus 
is  used  to  ascertain  a  difference  in  intensity  of  two  currents  and  to  this 
circumstance  owes  its  name. 

774.  Sir  "W.  Tlioiuson's  marine  gralvanometer. — In  laying  submarine 
cables  the  want  was  felt  of  a  galvanometer  sufficiently  sensitive  to  test 


bg: 


Dynamical  Electricity. 


[774- 


insulation,  which  at  the  same  time  was  not  effected  by  the  pitching  and 
roHing  of  the  ship.  For  this  purpose,  Sir  W.  Thomson  invented  his 
marine  galvanometer.  Fig.  6ii  is  from  a  drawing  of  this  instrument 
by  Messrs.  ElHotts,  by  whom  it  is  made.  B  represents  a  coil  of  many 
thousand  turns  of  the  finest  copper  wire,  carefully  insulated  throughout, 
terminating  in  the  binding  screws  EE.  In  the  centre  of  this  coil  is  a 
slide,  which  carries  the  magnet,  the  arrangement  of  which  is  represented 
on  a  larger  scale  in  D.  The  magnet  itself  is  made  of  a  piece  of  fine 
watch  spring  about  f  of  an  inch  in  length,  and  does  not  weigh  more 
than  a  grain  ;  it  is  attached  to  a  small  and  very  slightly  concave  mirror 
of  very  thin  silvered  glass.  A  single  fibre  of  silk  is  stretched  across 
the  slide,  and  the  mirror  and  magnet  are  attached  to  it  in  such  a  manner 


Fig.  61 1. 

that  the  fibre  exactly  passes  through  the  centre  of  gravity  in  every 
'position.  As  the  mirror  and  magnet  weigh  only  a  few  grains,  they 
retain  their  position  respecting  the  instrument,  however  the  ship  may 
pitch  and  roll.  The  slide  fits  in  a  groove  in  the  coil,  and  the  whole 
is  enclosed  within  a  wrought  iron  case  with  an  aperture  in  front,  and 
a  wrought-iron  lid  on  the  top.  The  object  of  this  is  to  counteract 
the  influence  of  the  terrestrial  magnetism  when  the  ship  changes  its 
course. 

Underneath  the  coil  is  a  large  curved  steel  magnet  N,  which  compen- 
sates the  earth's  directive  action  upon  the  magnet  D,  and  in  the  side  of 
the  case,  and  on  a  level  with  D,  a  pair  of  magnets  are  placed  with  oppo- 
site poles  together.  By  a  screw,  suitably  adjusted,  the  poles  of  the  magnets 
may  be  brought  together;  in  which  case  they  quite  neutralise  each  other, 
and  thus  exert  no  action  on  the  suspended  niagnet,  or  they  may  be  slid 
apart  from  each  other  in  such  a  manner  that  the  action  of  either  pole  on 
D  preponderates  to  any  desired  extent.  This  small  magnet  is  thus 
capable  of  very  dehcate  adjustment.     The  large  magnet  N,  and  the  pair 


-^775] 


Tangent  Galvanometer. 


693 


of  magnets  C,  are  analogous  to  the  coarse  and  fine  adjustment  of  a 
microscope. 

At  a  distance  of  about  three  feet,  there  is  a  scale  with  the  zero  in  the  - 
centre  and  the  graduation  extending  on  each  side.  Underneath  this  zero 
point  is  a  narrow  slit,  through  which  passes  the  light  of  a  paraffine  lamp, 
and  which  traversing  the  window  is  reflected  from  the  curved  mirror 
against  the  graduated  scale.  By  means  of  the  adjusting  magnets  the 
image  of  the  slit  is  made  to  fall  on  the  centre  of  the  graduation. 

Thisbeing  the  case,  if  any  arrangement  for  producing  a  current  however 
weak  be  connected  with  the  terminals,  the  spot  of  light  is  deflected  either 
to  one  side  or  the  other,  according  to  the  direction  of  the  current ;  the 
stronger  the  current  the  greater  the  deflection  of  the  spot ;  and  if  the 
current  remains  of  constant  strength  for  any  length  of  time,  the  spot  is 
stationary  in  a  corresponding  position. 

The  movement  on  a  screen  of  a  spot  of  hght  reflected  from  a  body  is 
the  most  delicate  and  convenient  means  of  observing  motions  which  of 
themselves  are  too  small  for  direct  measurement  or  observation.  Hence  this 
principle  is  frequently  apphed  in  experimental  investigation  and  in  lecture 
illustration  (491).  It  is  used  in  observing  the  motion,  of  vibrating  bodies 
in  measuring  the  variations  of  magnetism,  in  determining  the  expansion 
of  solids,  &c. 

It  will  be  seen  from  the  article  on  the  Electric  Telegraph,  how  alter- 
nate deflections  of  the  spot  of  light  may  be  utiUsed  in  forming  a  code  of 
signals. 

775.  Tangrent  compass,  or  tang-entgralvanoxneter. — When  a  magnetic 


Fig.  612. 


needle  is  suspended  in  the  centre  of  a  voltaic  current  in  the  plane  of  the 
magnetic  meridian,  it  can  be  proved  that  the  intensity  of  a  current  is 


694 


Dynamical  Electricity. 


[775 


directly  proportional  to  the  tangent  of  the  angle  of  deflection,  provided 
the  dimensions  of  the  needle  are  sufficiently  small  as  compared  with  the 
diameter  of  the  circuit.  An  instrument  based  on  this  principle  is  called 
the  tangent  galvanometer,  or  tangent  compass.  It  consists  of  a  copper 
ring,  12  inches  in  diameter,  and  about  an  inch  in  breadth,  mounted 
vertically  on  a  stand ;  the  lower  half  of  the  ring  is  generally  fitted  in  a 
semicircular  frame  of  wood  to  keep  it  steady.  In  the  centre  of  the  ring 
is  suspended  a  delicate  magnetic  needle  whose  length  must  not  exceed 
~  or  ^-^  of  the  diameter  of  the  circle.  Underneath  the  needle  there  is 
a  graduated  circle.  The  ends  of  the  ring  are  prolonged  in  copper  wires, 
fitted  with  mercury  cups,  ab,  by  which  it  can  be  connected  with  a  battery 
or  element.  The  circle  is  placed  in  the  plane  of  the  magnetic  meridian, 
and  the  deflection  of  the  needle  is  directly  read  off"  on  the  circle,  and  its 
corresponding  value  obtained  from  a  table  of  tangents. 

On  account  of  its  small  resistance,  the  tangent  compass  is  well  adapted 
for  currents  of  low  tension,  but  in  which  a  considerable  quantity  of  elec- 
tricity is  set  in  motion.  For  currents  which  can  overcome  great  resist- 
ance, but  have  only  a  small  quantity  of  electricity,  the  multiplier  is  best 
fitted. 

To  prove  that  the  intensities  of  various  currents  are  proportional  to 
the  tangents  of  the  corresponding  angles  of  deflection,  let  NS  represent 
the  wire  of  the  galvanometer  and  ns  the  needle,  and 
let  0  be  the  angle  of  deflection  produced  when  a 
current  C  is  passed.  Two  forces  now  act  upon  the 
needle — the  force  of  the  earth's  magnetism,  which  we 
will  denote  by  T,  which  tends  to  place  the  needle  in 
the  magnetic  meridian,  and  the  strength  of  the  current 
C,  which  strives  to  place  it  at  right  angles  to  the  mag- 
netic meridian.  Let  the  magnitudes  of  these  forces 
be  represented  by  the  corresponding  lines  an  and  bn. 
Now  the  whole  intensities  of  these  forces  do  not  act 
so  as  to  turn  the  point  of  the  needle  round,  but  only 
those  components  which  are  at  right  angles  to  the 
needle.  Resolving  them,  we  have  ng  and  ;{/"  as  the 
forces  acting  in  opposite  directions  on  the  needle ; 
and  since  the  needle  is  at  rest  these  forces  must  be 
e«iual. 

The  angle  nag  is  equal  to  the  angle  (/,  and  therefore  ng  =  an  sin  </> ; 
and  in  like  manner  the  angle  bnf  is  equal  to  0  and  ;{/"=  bn  cos  ^ ;  and 

therefore  since  ;//=  nsr,  bn  cos  <p  =  an  sin    ,  or  bn  =  an  '-    =  an  tan  <p, 

■^       ^'  cos  ,> 

that  is,  C  =  T  tan  <■. 

If  any  other  currenc  be  passed  through  the  galvanometer  we  shall 
have  similarly  C  =  T  tan  <j> ;  and  since  the  earth's  magnetism  does  not 
alter  in  one  and  the  same  place  C  :  C  =  tan  fp  :  tan    '. 

In  this  reasoning  it  has  been  assumed  that  the  action  of  the  current 
on  the  needle  is  the  same  whatever  be  the  angle  by  which  it  is  deflected. 
This  is  only  the  case  when  the  dimensions  of  the  needle  are' small  corn- 


Fig.  613. 


-776] 


Si7ie  Compass. 


695 


pared  with  the  diameter  of  the  ring ;  it  should  not  be  more  than  \  or  ^^^ 
the  diameter.  In  order  to  measure  with  accuracy  the  deflections  a  hght 
index  is  placed  at  right  angles  to  the  needle.  ~^    ~ 

776.  Sine  compass. — This  is  another  form  of  galvanometer  for 
measuring  powerful  currents.  Round  the  circular  frame,  M,  fig.  614, 
several  turns  of  stout  insulated  copper  wire  are  coiled,  the  two  ends  of 
which,  /,  terminate  in  the  binding  screws  at  E.  On  a  table  in  the  centre 
of  the  ring  there  is  a  magnetic  needle,  in ;  a  second  light  needle,  ?/,  fixed 


Fig.  614. 


to  the  first,  serves  as  pointer  along  the  graduated  circle,  N.  Two  copper 
wires,  ab,  from  the  sources  of  electricity  to  be  measured,  are  connected 
with  E.  The  circles  M  and  N  are  supported  on  a  foot  O  which  can 
move  about  a  vertical  axis  passing  through  the  centre  of  a  fixed  horizontal 
circle  H. 

The  circle  M  being  then  placed  in  the  magnetic  meridian,  and  there- 
fore in  the  same  plane  as  the  needle,  the  current  is  allowed  to  pass.  The 
needles  being  deflected,  the  circuit  M  is  turned  until  it  coincides  with 
the  vertical  plane  passing  through  the  magnetic  needle  m.  The  directive 
action  of  the  current  is  now  e.xerted  perpendicularly  to  the  direction  of 
the  magnetic  needle,  and  it  may  be  shown  that  the  intensity  of  the 
current  is  proportional  to  the  sine  of  the  angle  of  deflection ;  this  angle 
is.  measured  on  the  circle  H  by  means  of  a  vernier  on  the  piece  C. 


696  Dynamical  Electricity.  [776- 

This  piece,  C,  fixed  to  the  foot  O,  turns  it  by  means  of  a  knob,  A.     The 

angle  of  deflection,  and  hence  its  sine,  being  known,  the  intensity  of  the 

current  may  be  thus  deduced  :  let  imn^  be 

the  direction  of  the  magnetic  meridian,  d  the 

angle  of  deflection,  C   the  strength   of  the 

current,  and   T  the  directive  action  of  the 

earth.     If  the  direction  and  intensity  of  this 

latter  force  be  represented  by  ak,  it  may  be 

replaced  by  two  components,  ah  and  ac,  fig. 

609.     Now,  as   the   first    has    no   directive 

action  on  the  needle,  the  component  ac  must 

alone  counterpoise  the  force  C,  that  is,  C  =  ac. 

But   in  the  triangle,  ack,  ac  =  ak   cos    cak^ 

from  which  ac  =  T  sin.  d,  for  the  angle  cak  is 

the  complement  of  the  angle  d,  and  ak  is 

'^"    ^^'  equal  to  T  ;  hence,  lastly,  C  =  T  sin  d,  which 

was  to  be  proved.    In  like  manner  for  any  other  current  C  which  produces 

a  deflection  d,  we  shall  have  C  =  T  sin  d\  whence  C  :  C  -=  sin  ^  :  sin  d\ 

JJJ.  Olim's  law.^ — For  a  knowledge  of  the  conditions  which  regulate 

the  action  of  the  voltaic  current,  science  is  indebted  to  the  late  Professor 

Ohm.     His  results  were  at  first  deduced  from  theoretical  considerations; 

but  by  his  own  researches,  as  well  as  by  those  of   Fechner,    Pouillet, 

Daniell,  De  la  Rive,  Wheatstone,  and  others,  they  have  received  the 

fullest  confirmation,  and  their  great  theoretical  and  practical  importance 

has  been  fully  established. 

i.  The  force  or  cause  by  which  electricity  is  set  in  motion  in  the  voltaic 
circuit  is  called  the  electromotive  force.  The  quantity  of  electricity  which 
in  any  unit  of  time  flows  through  a  section  of  the  circuit  is  called  the  in- 
tejtsity  or  perhaps  better  the  strength  of  the  current.  Ohm  found  that  this 
strength  is  the  same  in  all  parts  of  one  and  the  same  circuit,  however 
heterogeneous  they  were ;  and  also  that  it  is  proportional  to  the  electro- 
motive force. 

It  has  further  been  found  that  when  the  same  current  is  passed  respec- 
tively through  a  short  and  through  a  long  wire  of  the  same  material,  its 
action  on  the  magnetic  needle  is  less  in  the  latter  case  than  in  the  former. 
Ohm  accordingly  supposed  that  in  the  latter  case  there  was  a  greater  re- 
sistance to  the  passage  of  the  current  than  in  the  former ;  and  he  proved 
that  Uhe  resistance  is  inversely  proportional  to  the  stretigth  of  the  cicrrent.' 
On  these  principles  Ohm  founded  the  celebrated  law  which  bears  his 
name,  that — 

The  strength  of  the  current  is  equal  to  the  electromotive  force  divided 
by  the  resistance. 

Which  is  expressed  by  the  simple  formula 

^     R' 

where  C  is  the  strength  of  the  current,  E  the  electromotive  force,  and  R 
the  resistance. 


-777]  Ohm's  Law.  697 

ii.  The  resistance  of  a  conductor  depends  on  three  elements  :  its  con- 
ductivity, which  is  a  constant, determined  for  each  conductor;  its  section-^ 
and  its  length.  The  resistance  is  obviously  inversely  proportional  to  the 
conductivity,  that  is,  the  less  the  conducting  power  the  greater  the  resist- 
ance. This  has  been  experimentally  shown,  and  it  has  also  been  proved 
that  the  resistance  is  inversely  as  the  sectiofz,  and  directly  as  the  length  of 
a  conductor.  If  then  k  is  the  conductivity,  w  the  section,  and  \  the  length 
of  a  conductor,  we  have 

=  —  and  C  =   -     ; 


that  is,  the  strength  of  a  current  is  inve?'sely  proportional  to  the  length  of 
the  conductor  and  directly  proportional  to  its  section  and  conductivity. 

iii.  In  a  voltaic  battery  composed  of  different  elements,  the  strength 
of  the  current  is  equal  to  the  sum  of  the  electromotive  forces  of  all  the 
elements  divided  by  the  sum  of  the  resistances.  Usually,  however,  a 
battery  is  composed  of  elements  of  the  same  kind,  each  having  the  same 
electromotive  force  and  the  same  resistance. 

In  an  ordinary  element  there  are  essentially  two  resistances  to  be  con- 
sidered :  I.  That  offered  by  the  liquid  conductor  between  the  two  plates, 
which  is  frequently  called  the  internal  or  essential  resistance  ;  and,  2. 
That  offered  by  the  interpolar  conductor  which  connects  the  two  plates 
outside  the  liquid  ;  this  conductor  may  consist  either  wholly  of  metal,  or 
may  be  partly  of  metal  and  partly  of  liquids  to  be  decomposed  :  it  is  the 
external  or  non-essential  resistance.  Calling  the  former  R  and  the  latter  r, 
Ohm's  formula  becomes 

C  =    -^. 

iv.  If  an)'  number,  ;/,  of  similar  elements  are  joined  together,  there  is 
;/  times  the  electromotive  force,  but  at  the  same  time  n  times  the  internal 

resistance,  and  the  formula  becomes  -^ If  the   resistance   in   the 

«R  +  r 

interpolar,  r,  is  very  small,  which  is  the  case,  for  instance,  when  it  is  a 
short  thick  copper  wire,  it  may  be  neglected  in  comparison  with  the  in- 
ternal resistance,  and  then  we  have 

^  _  «E  ^  E  . 
~n^     R' 

that  is,  a  battery  consisting  of  several  elements  produces  in  this  case  no 
greater  effect  than  a  single  element. 

^v.  If,  however,  the  external  resistance  is  very  great,  as  when  the  current 
has  to  produce  the  electric  light,  or  to  work  a  long  telegraphic  circuit, 
advantage  is  gained  by  using  a  larger  number  of  elements ;  for  then  we 
have  the  formula 

«E 


C  = 


«R  +  r ' 
H  H 


6gS  Dynavtical  Electricity.  [777  - 

if  r  is  very  great  as  compared  with  ;zR,  the  latter  may  be  neglected,  and 
the  expression  becomes 

r 

that  is,  that  the  strength  within  certain  limits  is  proportional  to  the 
number  of  elements. 

In  a  thermo-electric  pile,  which  consists  of  very  short  metallic  con- 
ductors, the  internal  resistance  R  is  so  small  that  it  may  be  neglected, 
and  the  strength  is  inversely  as  the  length  of  the  connecting  wire. 

vi.  If  the  plates  of  an  element  be  made  m  times  as  large,  there  is  no 
increase  in  the  electromotive  force,  for  this  depends  on  the  nature  of  the 
metals  and  of  the  hquid  (755),  but  the  resistance  is  m  times  as  small,  for 
the  section  is  m.  times  larger ;  the  expression  becomes  then 


Hence,  an  increase  in  the  size  of  the  plate,  or,  what  is  the  same  thing, 
a  decrease  in  the  internal  resistance,  does  not  increase  the  strength  to  an 
indefinite  extent;  for  ultimately  the  resistance  of  the  element  R  vanishes 
in  comparison  with  the  resistance  r,  and  the  strength  always  approximates 

to  the  value  C  =  -  . 
7- 

vii.  Ohm's  law  enables  us  to  arrange  a  battery  so  as  to  obtain  the 
greatest  effect  in  any  given  case.  For  instance,  with  a  battery  of  six 
elements  there  are  the  following  four  ways  of  arranging  them  :  i.  In  a 
single  series  (fig.  616),  in  which  the  zinc  Z  of  one  element  is  united  with 
the  copper  C  of  the  second,  the  zinc  of  this  with  the  copper  of  the  third, 
and  so  on  ;  2.  Arranged  in  a  system  of  three  double  elements,  each 
element  being  formed  by  joining  two  of  the  former  (fig.  617)  ;  3.  In  a 
system  of  two  elements,  each  of  which  consists  of  three  of  the  original 
elements  joined,  so  as  to  form  one  of  triple  the  surface  (fig.  618)  ;  4. 
Lastly,  of  one  large  element,  all  the  zincs  and  all  the  coppers  being  joined, 
so  as  to  form  a  pair  of  six  times  the  surface  (fig.  619). 

With  a  series  of  twelve  elements  there  may  be  six  different  combina- 
tions, and  so  on  for  a  larger  number. 

Now  let  us  suppose  that  in  the  particular  case  of  a  battery  of  six 
elements  the  internal  resistance  R  of  each  element  is  3,  and  the  external 
resistance  r=i2.  Then,  in  the  first  case,  where  there  are  six  elements, 
we  have  the  value, 

C=    ^?^ -_=     _^        =-^ 
6R  +  r    6x3+12      30' 

If  they  were  united  so  as  to  form  three  elements,  each  of  double  the  sur- 
face, as  in  the  second  case  (fig.  617),  the  electromotive  force  would  then  be 
the  electromotive  force  in  each  element  ;  there  would  also  be  a  resistance 


-777] 


O  J  Lin's  Lazv. 


699 


R  in  each  element,  but  this  would  only  be  half  as  great,  for  the  section  of 
the  plate  is  now  double ;  hence  the  strength  in  this  case  would  be 

C'=      3E      _     3E    _6E. 


3^  +  r 


+  12 


33 


accordingly  this  change  would  lessen  the  strength. 


Fig.  616. 


If,  with  the  same  elements,  the  resistance  in  the  connecting  wire  were 
only  r  =  2,  we  should  have  the  values  in  the  two  cases  respectively — 

6xE   ^6E 
6x3  +  2      20' 


C  = 


and  C'  = 


/_     3E 


3R 

2 


6E 
9  +  4 


6E 
13* 


The  result  in  the  latter  case  is,  therefore  more  favourable.  If  the  resist- 
ance r  were  9,  the  strength  would  be  the  same  in  both  cases.  Hence,  by 
altering  the  size  of  the  plates  or  their  arrangement,  favourable  or  unfavour- 
able results  are  obtained  according  to  the  relation  between  R  and  r. 


700  Dynamical  Electricity.  [777- 

It  can  be  shown  that  i7i  any  git' en  covibi7iation  the  maximuin  effect  is 
obtained  when  the  total  resistance  in  the  elements  is  equal  to  the  resistance 
of  the  interpolar.  Suppose  that  in  a  given  case  n  elements  are  arranged 
so  as  to  form  a  battery  of  s  couples,  each  consisting  of  /  cells,  then  n  =  st. 
Denoting  the  resistance  of  a  single  element  by  r,  the  total  resistance  of 

the  battery  thus  arranged  is  — ^.     Now,  according  to  the  above  law,  the 

/,  where  /  is  the  resistance  of  the 


interpolar.     But  /  =  -,  hence  -"^  =  /,  or  s  =     / 


in 
7' 

If  in  a  given  case  we  have  8  elements,  each  offering  a  resistance  1 5, 
and  an  interpolar  with  the  resistance  40,  we  get  s  =  4-3,  But  this  is 
an  impossible  arrangement,  for  it  is  not  a  whole  number,  and  the 
nearest  whole  number  must  be  taken.  This  is  4,  and  it  will  be  found  on 
making  a  calculation  analogous  to  that  above,  that  when  arranged  so 
as  to  form  4  elements,  each  of  double  surface,  the  greatest  effect  is 
obtained. 


CHAPTER    III. 

EFFECTS   OF  THE   CURRENT. 


778.  Physiologrical  actions. — Under  this  name  are  included  the 
effects  produced  by  the  battery-current  on  living  organisms  or  tissues. 

When  the  electrodes  of  a  strong  battery  are  held  in  the  two  hands  a 
violent  shock  is  felt,  especially  if  the  hands  are  moistened  with  acidulated 
water,  which  increases  the  conductivity^  The  violence  of  the  shock 
increases  with  the  number  of  elements  used,  and  with  a  large  number — 
as  200  Bunsen's  cells — is  even  dangerous. 

The  power  of  contracting  upon  the  application  of  a  voltaic  current 
seems  to  be  a  very  general  property  of  protoplas77i — the  physical  basis  of 
both  animal  and  vegetable  life ;  if,  for  example,  a  current  of  moderate 
strength  be  passed  through  such  a  simple  form  of  protoplasm  as  an 
Amceba,  it  immediately  withdraws  its  processes,  ceases  its  changes  of 
form,  and  contracts  into  a  rounded  ball — soon,  however,  resuming  its 
activity  upon  the  cessation  of  the  current.  Essentially  similar  effects  of 
the  current  have  been  observed  in  the  protoplasm  of  young  vegetable 
cells. 

If  a  frog's  fresh  muscle  (which  will  retain  its  vitality  for  a  considerable 
time  after  removal  from  the  body  of  the  animal)  be  introduced  into  a 
galvanic  circuit,  no  apparent  effect  will  be  observed  during  the  steady 
passage  of  the  current,  but  every  opening  or  closure  of  the  circuit  will 
cause  a  muscular  contraction,  as  will  also  any  sudden  and  considerable 
alteration  in  its  intensity.  By  very  rapidly  interrupting  the  current,  the 
muscle  can  be  thrown  into  a  state  of  uninterrupted  contraction,  or  physio- 
logical tetanus^  each  new  contraction  occurring  before  the  previous  one 


779] 


Elcctrotojius,  701 


has  passed  off.  Other  things  being  equal,  the  amount  of  shortening 
exhibited  by  the  muscle  increases,  up  to  a  certain  limit,  with  the  intensity 
of  the  current.  These  phenomena  entirely  disappear  with  the  life  of  the- 
muscle ;  hence  the  experiments  are  somewhat  more  difficult  with  warm- 
blooded animals,  the  vitality  of  whose  muscles,  after  exposure  or  removal 
from  the  body,  is  maintained  with  more  difficulty ;  but  the  results  of 
careful  experiment  are  exactly  the  same  here  as  in  the  case  of  the  frog. 

The  influence  of  an  electric  current  upon  living  nerves  is  very  remark- 
able ;  as  a  general  rule,  it  may  be  stated  that  its  effect  is  to  throw  the 
nerve  into  a  state  of  activity,  whatever  its  special  function  may  be ;  thus, 
if  the  nerve  be  one  going  to  a  muscle,  the  latter  will  be  caused  to  contract ; 
if  it  be  one  of  common  sensation,  pain  will  be  produced ;  if  one  of  special 
sense,  the  sensation  of  a  flash  of  hght,  or  of  a  taste,  etc.,  will  be  produced, 
according  to  the  nerve  irritated.  These  effects  do  not  manifest  them- 
selves during  the  even  passage  of  the  current,  but  only  when  the  circuit 
is  either  opened  or  closed,  or  both.  Of  course,  the  continuity  of  the  nerve 
with  the  organ  where  its  activity  manifests  itself  must  be  maintained 
intact.  The  changes  set  up  by  the  current  in  the  different  nerve  trunks 
are  probably  similar,  the  various  sensations,  etc.  produced  depending  on 
the  different  terminal  organs  with  which  the  nerves  are  connected. 

779.  Slectrotonus. — In  a  living  nerve,  as  will  be  stated  more  fully  in 
Chapter  X.,  certain  parts  of  the  surface  are  electropositive  to  certain  other 
parts,  so  that  if  a  pair  of  electrodes  connected  with  a  galvanometer  be  ap- 
plied to  these  two  points,  a  current  will  be  indicated ;  if  now  another  part 
of  the  nerve  be  interposed  in  a  galvanic  circuit,  it  will  be  found  that,  if 
this  extraneous  current  be  passing  in  the  same  direction  as  the  proper 
nerve  current,  the  latter  is  increased,  and  vice  versa  ;  and  this,  although 
it  has  previously  been  demonstrated  experimentally  that  none  of  the 
battery  current  escapes  down  the  nerve,  so  as  to  exert  any  influence  of 
its  own  on  the  galvanometer.  This  alteration  of  its  natural  electromotive 
condition,  produced  through  the  whole  of  a  nerve  by  the  passage  of  a 
constant  current  through  part  of  it,  is  known  as  the  electrototiic  state ;  it 
is  most  intense  near  the  extraneous,  or,  as  it  is  called,  the  exciting  current. 
It  continues  as  long  as  the  latter  is  passing,  and  is  attended  with  important 
changes  in  the  excitability  of  the  nerve,  or,  in  other  words,  the  readiness 
with  which  the  nerve  is  thrown  into  a  state  of  functional  activity  by  any 
stimulus  applied  to  it.  Pfliiger,  who  has  investigated  these  changes,  has 
named  the  part  of  the  nerve  through  which  the  exciting  current  is  passing 
the  intrapolar  region ;  the  condition  of  the  nerve  close  to  the  positive 
pole  is  called  anelectrotonus  \  that  near  the  negative  pole,  kathelectro- 
tonus.  The  excitabihty  of  the  nerve  is  diminished  in  the  anelectrotonic 
region,  so  that  with  a  motor  nerve,  for  example,  a  stronger  stimulus  than 
before  would  need  to  be  applied  at  this  part,  in  order  to  obtain  a  muscular 
contraction;  in  the  kathelectrotonic  region,  on  the  contrary,  the  ex- 
citability of  the  nerve  is  heightened.  Moreover,  with  an  exciting  current 
of  moderate  strength  the  power  of  the  nerve  to  conduct  a  stimulus  is 
lowered  in  the  anelectrotonic  region,  and  increased  in  the  kathelectro- 
tonic ;  with  strong  currents  it  is  said  to  be  diminished  in  both. 


702  Dynamical  Electricity.  [779- 

These  facts  have  to  be  taken  into  account  in  the  scientific  application 
of  galvanism  to  medical  purposes  ;  if,  for  instance,  it  is  wished  to 
diminish  the  excitability  of  the  sensory  nerves  of  any  part  of  the  body,  the 
current  should  be  passed  in  such  a  direction  as  to  throw  the  nerves  of  that 
part  into  a  state  of  anelectrotonus — and  similarly  in  other  cases. 

If  a  powerful  electric  current  be  passed  through  the  body  of  a  recently 
killed  animal,  violent  movements  are  produced,  as  the  muscles  ordinarily 
retain  their  vitality  for  a  considerable  time  after  general  systematic  death; 
by  this  means,  also,  life  has  been  re-established  in  animals  which  were 
apparently  dead — a  properly  applied  current  stimulating  the  respiratory 
muscles  to  contract. 

780.  Tnermal  effects. — When  a  voltaic  current  is  passed  through  a 
metal  wire  the  same  effects  are  produced  as  by  the  discharge  of  an 
electric  battery  (742)  ;  the  wire  becomes  heated,  and  even  incandescent  if 


Fig.  620. 

it  is  very  short  and  thin.  With  a  powerful  battery  all  metals  are  melted, 
even  iridium  and  platinum,  the  leasit  fusible  of  metals.  Carbon  is  the 
only  element  which  has  not  hitherto  been  fused  by  it.  M.  Despretz,  how- 
ever, with  a  battery  composed  of  600  Bunsen's  elements  joined  in  six 
series  {^JTJ),  has  raised  rods  of  very  pure  carbon  to  such  a  temperature 
that  they  were  softened  and  could  be  welded  together,  indicating  an 
incipient  fusion. 

A  battery  ot  30  to  40  Bunsen's  elements  is  sufficient  to  melt  and  vola- 
tilise fine  wires  of  lead,  tin,  zinc,  copper,  gold,  silver,  iron,  and  even  pla- 
tinum, with  differently  coloured  sparks.  Iron  and  platinum  burn  with  2, 
brilliant  white  light ;  lead  with  a  purple  light ;  the  light  of  tin  and  of  gold 
is  bluish  white  ;  the  light  of  zinc  is  a  mixture  of  white  and  gold  ;  finally, 
copper  and  silver  give  a  green  light. 

The  thermal  effects  of  the  voltaic  current  are  used  for  firing  mines  for 
military  purposes  and  for  blasting  operations.  The  following  arrangement 
devised  by  Colonel  Schaw,  is  adopted  in  the  English  service.     Fig.  620 


-780]  Thermal  Effects  of  the  Current.  703 

represents  a  small  wooden  box  provided  with  a  lid.  Two  moderately  stout 
copper  wires, /?'^',  insulated  by  being  covered  with  gutta-percha,  are  deprived 
of  this  coating  at  the  ends,  which  are  then  passed  through  and  through  the 
box  in  the  manner  represented  in  the  figure.  The  distance  between  them 
is  I  of  an  inch,  and  a  very  fine  platinum,  wire  (one  weighing  1-92  grains  to 
the  yard  is  the  regulation  size)  is  soldered  across.  The  object  of  arranging 
the  wires  in  this  manner  is  that  they  shall  not  be  in  contact,  and  that  the 
strain  which  they  exert  may  be  spent  on  the  box,  and  not  on  the  platinum 
wire  joining  them,  which,  being  extremely  thin,  would  be  broken  by  even  a 
very  slight  pull.  The  box  is  then  filled  with  fine-grained  powder,  and  the 
lid  tied  down.  The  wires  of  the  fuse  are  then  carefully  joined  to  the  long 
conducting  wires,  which  lead  to  the  battery ;  these  should  be  of  copper, 
and  as  thick  as  is  convenient,  so  as  to  offer  very  little  resistance :  No.  16 
gauge  copper  wire  is  a  suitable  size.  The  fuse  is  then  introduced  into 
the  charge  to  be  fired  :  if  it  is  for  a  submarine  explosion,  the  powder  is 
contained  in  a  canister,  the  neck  of  which,  after  the  introduction  of  the 
fuse,  is  carefully  fastened  by  means  of  cement,  When  contact  is  made 
with  the  battery,  which  is  .effected  through  the  intervention  of  mercury 
cups,  the  current  traversing  the  platinum  wire  renders  it  incandescent, 
which  fires  the  fuse  ;  and  thus  the  ignition  is  communicated  to  the  charge 
in  which  it  is  placed. 

The  thermal  effect  depends  more  on  the  size  than  on  the  number  of 
the  plates  of  a  battery,  for  the  resistance  in  the  connecting  wires  is  small. 
An  iron  wire  may  be  melted  by  a  single  Wollaston's  element,  the  zinc  of 
which  is  8  inches  by  6.  Hare's  battery  (758)  has  received  its  name 
defiagrator  on  account  of  its  greater  heating  effect  produced  by  the  great 
surface  of  its  plates. 

When  any  circuit  is  closed,  a  definite  amount  of  heat  is  produced 
throughout  the  entire  circuit ;  and  the  amount  of  heat  produced  in  any 
particular  part  of  the  circuit  is  greater,  the  greater  the  proportion  which 
the  resistance  of  this  part  bears  to  the  entire  circuit.  Hence  in  firing 
mines  the  wire  to  be  heated  should  be  of  as  small  section  and  of  as  small 
conductivity  as  practicable.  These  conditions  are  well  satisfied  by 
platinum,  which  has  over  iron  the  advantage  of  being  less  brittle  and  of 
not  being  liable  to  rust.  Platinum  too  has  a  low  specific  heat,  and  is  thus 
raised  to  a  higher  temperature  by  the  same  amount  of  heat  than  a  wire 
of  greater  specific  heat. 

On  the  other  hand,  the  conducting  wires  should  present  as  small  a 
resistance  as  possible,  a  condition  satisfied  by  a  stout  copper  wire  ;  and 
again,  as  the  heating  effect  of  any  circuit  is  proportional  to  the  square  of 
the  strength,  and  as  this  is  directly  as  the  electromotive  force,  and 
inversely  as  the  resistance,  a  battery  with  a  high  electromotive  force,  and 
small  resistance,  such  as  Grove's  or  Bunsen's,  should  be  selected. 

By  means  of  a  heated  platinum  wire,  parts  of  the  body  may  be  safely 
cauterised  which  could  not  be  got  at  by  a  red-hot  iron  ;  the  removal  of 
tumours  may  be  effected  by  drawing  a  loop  of  platinum  round  their  base, 
which  is  then  gradually  pulled  together.  It  has  been  observed  that  when 
the  temperature  of  the  wire  is  about  600°  C,  the  combustion  of  the  tissues 


704  Dynamical  Electricity.  [780- 

is  so  complete  that  there  is  no  haemorrhage ;  while  at  1 500°  the  action  of 
the  wire  is  Hke  that  of  a  sharp  knife. 

781.  £a-ws  of  beating:  effects.  Galvano-tbermometer. — Although 
the  thermal  effects  are  most  obvious  in  the  case  of  thin  wires,  they  are 
not  limited  to  them ;  with  thicker  wires  they  may  be  perceived  by  means 
of  delicate  thermometric  arrangements,  by  which  also  the  laws  of,  the 
heating  effect  may  be  investigated. 

Such  an  arrangement  is  called  a  galvano-therinometer.  It  consists 
essentially  of  a  glass  vessel  containing  alcohol,  in  which  is  a  delicate 
thermometer ;  the  wire  to  be  investigated  is  fitted  to  two  platinum  wires 
fused  in  the  well-ground  stopper  of  the  vessel.  The  current  is  passed 
through  the  platinum  wires,  and  its  strength  measured  by  means  of  a 
tangent  compass  interposed  in  the  circuit.  By  observing  the  increase  of 
temperature  in  the  thermometer  in  a  given  time,  and  knowing  the  weight 
of  the  alcohol,  the  mass  of  the  wire,  the  specific  heat,  and  the  calorimetric 
values  (424)  of  the  vessel,  and  of  the  thermometer,  compared  with  al- 
cohol, the  thermal  effect  .which  is  produced  by  the  current  in  a  given 
time  can  be  calculated. 

By  apparatus  of  this  kind  the  laws  of  the  thermal  effects  have  been 
investigated  by  Lenz,  Joule,  and  Becquerel.     They  are  as  follows : 

I.  The  heat  disengaged  in  a  give  ft  time  is  directly  proportional  to 
the  square  of  the  strength  of  the  current,  and  to  the  resistance. 

II.  Whatever  be  the  length  of  a  wire,  provided  its  diameter  remains 
the  same,  and  that  the  same  quantity  of  electricity  passes,  the  increase  of 
temperature  is  the  same  in  all  parts  of  the  wire. 

III.  For  the  same  quatitity  of  electricity,  the  increase  of  tefnperature 
in  different  parts  of  a  wire  is  inversely  as  the  fourth  power  of  the  dia- 
meter. 

If  the  current  passes  through  a  chain  of  platinum  and  silver  Avire  of 
equal  sizes,  the  platinum  becomes  more  heated  than  the  silver  from  its 
greater  resistance ;  and  with  a  suitable  current  the  platinum  may  become 
incandescent  while  the  silver  remains  dark.  This  experiment  was  de- 
vised by  Children.  If  a  long  thin  platinum  wire  be  raised  to  dull  redness 
by  passing  a  voltaic  current  through  it,  and  if  part  of  it  be  cooled  down 
by  ice,  the  resistance  of  the  cooled  part  is  diminished,  the  intensity  of  the 
current  increases,  and  the  rest  of  the  wire  becomes  brighter  than  before. 

If,  on  the  contrary,  a  part  of  the  feebly  incandescent  wire  be  heated  by 
a  spirit-lamp,  the  resistance  of  the  heated  part  increases,  for  the  effect 
is  the  same  as  that  of  introducing  fresh  resistance,  the  intensity  of  the 
current  diminishes,  and  the  wire  ceases  to  be  incandescent  in  the  non- 
heated  part. 

The  cooling  by  the  surrounding  medium  exercises  an  important  in- 
fluence on  the  phenomenon  of  ignition.  A  round  wire  is  more  heated  by 
the  same  current  than  the  same  wire  which  has  been  beaten  out  flat;  for 
the  latter  with  the  same  section  offers  a  greater  surface  to  the  cooling 
medium  than  the  others.  For  the  same  reason,  when  a  wire  is  stretched 
in  a  glass  tube  on  which  two  brass  caps  are  fitted  air-tight,  and  the  wire 
is  raised  to  dull  incandescence  by  the  passage  of  a  current,  the  incan- 


-782]    Representation  of  the  heating  Effects  in  a  Cirenit,     705 

descence  is  more  vivid  when  the  air  has  been  pumped  out  of  the  tube, 
because  it  now  simply  loses  heat  by  radiation,  and  not  by  communication 
to  the  surrounding  medium. 

Similarly,  a  current  which  will  melt  a  wire  in  air  will  only  raise  it  to 
dull  redness  in  ether,  and  in  oil  or  in  water  will  not  heat  it  to  redness  at 
all,  for  the  liquids  conduct  heat  away  more  readily  than  air  does. 

From  the  above  laws  it  follows  that  the  heating  effect  is  the  same  in  a 
wire  whatever  be  its  length,  provided  the  current  is  constant ;  but  it  must 
be  remembered  that  by  increasing  the  length  of  the  wire  we  increase 
the  resistance,  and  consequently  diminish  the  intensity  of  the  current ; 
further,  in  a  long  wire  there  is  a  greater  surface,  and  hence  more  heat  is 
lost  by  radiation  and  by  conduction. 

782.  Graphical  representation  of  the  heating:  effects  in  a  circuit.  — 
The  law  representing  the  production  of  heat  in  a  circuit  in  the  unit  of 
time  is  very  well  seen  by  the  following  geometrical  construction,  due  to 
Professor  Foster,  who  has  devised  several  similar  methods  of  graphically 
representing  electrical  laws. 

The  heat  H  produced  in  a  circuit  in  the  unit  of  time  is  proportional  to 
the  square  of  the  strength  of  the  current  C,  and  to  the  resistance  R  ;  that 

is,  H  =  C'^R ;  but  since  C 


E  E- 

-  ,  we  shall  have  H  =  _p. 
R  R 


Draw  a  straight  line  DAB,  and  from  any  point  A  in  it  draw  a  line 
AC,  at  right  angles  to  DAB,  and  of  a  length  proportional  to  the  electro- 
motive force  of  the  cell.  Lay  off  a  length  AB  proportional  to  the  resist- 
ance of  the  circuit.  Join  CB,  and  at  C  draw  a  line  at  right  angles  to 
EC  and  let  D  be  the  point  where  the  line  cuts  the  line  DAB.  Then  the 
length  AD  is  proportional  to  the  heat  produced  in  the  whole  circuit  in 
unit  time.     For  the  triangles  ADC  and  ACB  are  similar  and  therefore 

AD  :  AC  -=  AC  :  AB,  that  is  AD  =  ^— ,  that  is  H  =  — 
'  AB '  R  • 


Fig.  621. 

By  drawing  figures  similar  to  the  above  it  will  be  found  that  for  a  given 
electromotive  force  the  heat  is  inversely  proportional  to  the  resistance, 
and  for  a  given  resistance  directly  proportional  to  the  square  of  the 
electromotive  force.  That  is,  if  the  resistance  is  doubled,  the  heat  is  re- 
duced to  one  half;  if  the  electromotive  force  is  doubled  the  heat  is 
quadrupled. 

H    H  3 


7o6  Dynamical  Electricity.  [783- 

783.  Relation  of  beating-  effect  to  work  of  a  battery. — In  every 
closed  circuit  chemical  action  is  continuously  going  on ;  in  ordinary 
circuits,  the  most  common  action  is  the  solution  of  zinc  in  sulphuric 
acid,  which  may  be  regarded  as  an  oxidation  of  the  zinc  to  form  oxide  of 
zinc,  and  a  combination  of  this  oxide  of  zinc  with  sulphuric  acid  to  form 
water  and  zinc  sulphate.  It  is  a  true  combustion  of  zinc,  and  this  com- 
bustion serves  to  maintain  all  the  actions  which  the  circuit  can  produce, 
just  as  all  the  work  which  a  steam-engine  can  effect  has  its  origin  in  the 
combustion  of  fuel  (445). 

By  independent  experiments  it  has  been  found  that,  when  a  given 
weight  of  zinc  is  dissolved  in  sulphuric  acid,  a  certain  definite  measurable 
quantity  of  heat  is  produced,  which,  as  in  all  cases  of  chemical  action,  is 
the  same,  whatever  be  the  rapidity  with  which  the  solution  is  effected. 
If  this  solution  takes  place  while  the  zinc  is  associated  with  another 
metal  so  as  to  form  a  voltaic  couple,  the  rapidity  of  the  solution  will 
be  altered,  and  the  whole  circuit  will  become  heated — the  liquid,  the 
plates,  the  containing  vessel  as  well  as  the  connecting  wire.  But 
although  the  distribution  of  the  heat  is  thus  altered,  its  quantity  is  not. 
If  the  values  of  all  the  several  heating  effects  in  the  various  parts  of  the 
circuit  be  determined,  it  will  still  be  found  that  this  sum  is  exactly 
equivalent  to  that  produced  by  the  solution  of  a  certain  weight  of  zinc. 

If  the  couple  be  made  to  do  external  mechanical  work  the  case  is 
different.  Joule  made  the  following  remarkable  experiment.  A  small 
zinc  and  copper  couple  were  arranged  in  a  calorimeter  and  the  amount 
of  heat  determined  while  the  couple  was  closed  for  a  certain  length  of 
time  by  a  short  thick  wire.  The  couple  still  contained  in  the  calorimeter 
was  next  connected  with  a  small  electromagnetic  engine  (796),  by  which 
a  weight  was  raised.  It  was  thus  found  that  the  heat  produced  in  the 
calorimeter  in  a  given  time — while  therefore  a  certain  amount  of  zinc  was 
dissolved — was  less  while  the  couple  was  doing  work  than  when  it  was 
not ;  and  the  amount  of  this  diminution  was  the  exact  thermal  equivalent 
x>f  the  work  performed  in  raising  the  weight  (467).  . 

784.  Ibuminous  effects.— In  closing  a  voltaic  battery  a  spark  is  ob- 
tained at  the  point  of  contact,  which  is  frequently  of  great  brilliance.  A 
similar  spark  is  also  perceived  on  breaking  contact.  These  luminous 
effects  are  obtained  when  the  battery  is  sufficiently  powerful,  by  bringing 
the  two  electrodes  very  nearly  in  contact ;  a  succession  of  bright  sparks 
springs  sometimes  across  the  interval,  which  follow  each  other  with  such 
rapidity  as  to  produce  a  continuous  light.  With  eight  or  ten  of  Grove's 
elements  brilliant  luminous  sparks  are  obtained  by  connecting  one 
terminal  of  the  battery  with  a  file,  and  moving  its  point  along  the  teeth 
of  another  file  connected  with  the  other  terminal. 

The  most  beautiful  effect  of  the  electric  light  is  obtained  when,  with 
the  terminals  of  the  battery,  two  pencils  of  charcoal  are  connected  in  the 
manner  represented  in  fig.  622.  The  charcoal  b  is  fixed,  while  the  char- 
coal a  can  be  raised  and  lowered  by  means  of  a  rack  and  pinion  motion, 
c.  The  two  charcoals  being  placed  in  contact,  the  current  passes,  and 
their  ends  soon  become  incandescent.     If  they  are  then  removed  to  a 


-784] 


Luminous  Effects  of  tJie  Current, 


707 


distance  of  about  the  tenth  of  an  inch,  according  to  the  strength  of  the 
current,  a  luminous  arc  extends  between  the  two  points,  which  has  ai> 
exceedingly  brilliant  lustre,  and  is  called  the  voltaic  arc.  — 

The  length  of  this  arc  varies  with  the  fo»-ce  of  the  current.  In  air 
it  may  exceed  2  inches  with  a  battery  of  600  elements,  arranged  in 
six  series  of  100  each,  provided  the  positive  pole  is  uppermost,  as  repre- 
sented in  the  figure ;  if  it  is  undermost,  the  arc  is  about  one-third  shorter. 
In  vacuo  the  distance  of  the  charcoal  may  be  greater  than  in  air;  in  fact, 
as  the  electricity  meets  with  no  resistance,  it  springs  between  the  two 
charcoals,  even  before  they  are  in  contact.     The  voltaic  arc  can  also  be 


Fig.  622. 

produced  in  liquids,  but  it  is  then  much  shorter,  and  its  brilliancy  is 
greatly  diminished. 

The  voltaic  arc  has  the  property  that  it  is  attracted  when  a  magnet  is 
presented  to  it  ;  a  consequence  of  the  action  of  magnets  on  currents  (818). 

Some  physicists  have  considered  the  voltaic  arc  as  formed  0/  a  very 
rapid  succession  of  bright  sparks.  Its  colour  and  shape  depend  on  the 
nature  of  the  conductors  between  which  it  is  formed,  and  hence  it  is 
probable  that  it  is  due  to  the  incandescent  particles  of  the  conductor, 
which  are  volatilised  and  transported  in  the  direction  of  the  current — that 
is,  from  the  positive  to  the  negative  pole.  The  more  easily  the  electrodes 
are  disintegrated  by  the  current,  the  greater  is  the  distance  at  which  the 
electrodes  can  be  placed.  Charcoal,  which  is  a  very  friable  substance,  is 
one  of  the  bodies  which  gives  the  largest  luminous  arc. 

Recent  researches  by  Edlund  have  shown  that  this  disintegration  of 
the  terminals  by  the  voltaic  arc  gives  rise  to  an  electromotive  force 
opposed  in  direction  to  that  of  the  main  current. 


7o8 


Dynamical  Electricity. 


[784- 


Davy  first  made  the  experiment  of  the  electric  hght,  in  1 80 1,  by  means 
of  a  battery  of  2,000  plates,  each  4  inches  square.  He  used  charcoal 
points  made  of  light  wood  charcoal  which  had  been  heated  to  redness, 
and  immersed  in  a  mercury  bath  ;  the  mercury,  penetrating  into  the 
pores  of  the  charcoal,  increased  its  conductivity.  When  any  substance 
was  introduced  into  the  voltaic  arc  produced  by  this  battery,  it  became 
incandescent ;  platinum  melted  like  wax  in  the  flame  of  a  candle ; 
sapphire,  magnesia,  lime,  and  most  refractory  substances  were  fused. 
Fragments  of  diamond,  of  charcoal,  and  of  graphite  rapidly  disappeared 
without  undergoing  any  previous  fusion. 

As  charcoal  rapidly  burns  in  air,  it  was  necessary  to  operate  in  vacuo, 
and  hence  the  experiment  was  for  a  long  time  made  by  fitting  the  two 
points  in  an  electric  ^%%^  like  that  represented  in  fig.  580.    At  present  the 


electrodes  are  made  of  gas  graphite,  a  modification  of  charcoal  deposited 
in  gas  retorts  ;  this  is  hard  and  compact,  and  only  burns  slowly  in  air  : 
hence  it  is  unnecessary  to  operate  in  vacuo.  When  the  experiment  is 
made  in  vacuo,  there  is  no  combustion,  but  the  charcoal  wears  away  at 
the  positive  pole,  while  it  is  somewhat  increased  on  the  negative  pole, 
indicating  that  there  is  a  transport  of  solid  matter  from  the  positive  to  the 
negative  pole. 

785.  Foucault's  experiment. — This  consists  in  projecting  on  a  screen 
the  image  of  the  charcoal  points  produced  in  the  camera  obscura  at  the 
moment  at  which  the  electric  light  is  formed  (fig.  623).  By  means  of  this 
experiment,  which  is  made  by  the  photo-electric  microscope  already 
described  (fig.  459),  the  two  charcoals  can  be  readily  distinguished,  and 
the  positive  charcoal  is  seen  to  becom.e  somewhat  hollow  and  diminish, 
while  the  other  increases.  The  globules  represented  on  the  two  charcoals 
arise  from  the  fusion  of  a  small  quantity  of  silica  contained  in  the 
charcoal.     When  the  current  begins  to  pass,  the  negative  charcoal  first 


786] 


Regidator  of  the  Electric  L  ight. 


709 


becomes  luminous,  but  the  light  of  the  positive  charcoal  is  the  brightest  ; 
as  it  also  wears  away  the  most  rapidly,  it  ought  to  be  rather  the  larger. 

786.  Reg:ulator  of  the  electric  Ugrbt. — When  the  electric  light  is  to 
be  used  for  illumination,  it  must  be  as  continuous  as  other  modes  of 
lighting.  For  this  purpose,  not  only  must  the  current  be  constant,  but 
the  distance  of  the  charcoals  must  not  alter,  which  necessitates  the  use 


Fig.  624. 


of  some  arrangement  for  bringing  them  nearer  together  in  proportion  as 
they  wear  away.  One  of  the  best  modes  of  effecting  this  is  by  an  ap- 
paratus invented  by  M.  Duboscq. 

In  this  regulator  the  two  charcoals  are  movable,  but  with  unequal 
velocities,  which  are  virtually  proportional  to  their  waste.  The  motion  is 
transmitted  by  a  drum  placed  on  the  axis,  xy  (fig.  624).     This  turns  in 


7 1 0  Dynajnical  Electricity.  [786- 

the  direction  of  the  arrows  two  wheels,  a  and  b,  the  diameters  of  which 
are  as  i  :  2,  and  which  respectively  transmit  their  motion  to  two  rack- 
works,  Of  and  C.  C  lowers  the  positive  charcoal,  p^  by  means  of  a  rod 
sliding  in  the  tube,  H,  while  the  other  Q'  raises  the  negative  charcoal,  «, 
half  as  rapidly.  By  means  of  the  milled  head  y  the  drum  can  be  wound 
up,  and  at  the  same  time  the  positive  charcoal  moved  by  the  hand  ;  the 
milled  head  x  moves  the  negative  charcoal  also  by  the  hand,  and 
independently  of  the  first.  For  this  purpose  the  axis,  xy  consists  of  two 
parts  pressing  against  each  other  with  some  force,  so  that,  holding  the 
milled  head  x  between  the  fingers,  the  other,  jj/,  may  be  moved,  and  by 
holding  the  latter  the  former  can  be  moved.  But  the  friction  is  sufficient 
when  the  drum  works  to  move  the  two  wheels  a  and  b  and  the  two  rack- 
works. 

The  two  charcoals  being  placed  in  contact,  the  current  of  a  powerful 
battery  of  40  to  50  elements  reaches  the  apparatus  by  means  of  the  wires, 
E  and  E^  The  current  rising  in  H  descends  by  the  positive  charcoal, 
then  by  the  negative  charcoal,  and  reaches  the  apparatus,  but  without 
passing  into  the  rackwork,  C,  or  into  the  part  on  the  right  of  the  plate, 
N  ;  these  pieces  being  insulated  by  ivory  discs  placed  at  their  lower  part. 
The  current  ultimately  reaches  the  bobbin  B,  which  forms  the  foot  of  the 
regulator,  and  passes  into  the  wire,  E^  Inside  the  bobbin  is  a  bar  of 
soft  iron,  which  is  magnetised  as  long  as  the  current  passes  in  the  bobbin, 
and  demagnetised  when  it  does  not  pass,  and  this  temporary  magnet  is 
the  regulator.  For  this  purpose  it  acts  attractively  on  an  armature  of 
soft  iron,  A,  open  in  the  centre  so  as  to  allow  the  rackwork  C  to  pass, 
and  fixed  at  the  end  of  a  lever,  which  works  on  two  points,  imn^  and 
transmits  a  slight  oscillation  to  a  rod,  d,  which,  by  means  of  a  catch,  /, 
seizes  the  wheel  2",  as  is  seen  on  a  larger  scale  in  figure  625.  By  an 
endless  screw,  and  a  series  of  toothed  wheels,  the  stop  is  transmitted  to 
the  drum,  and  the  rackwork  being  fixed,  the  same  is  the  case  with  the 
carbons.  This  is  what  takes  place  so  long  as  the  magnetisation  in  the 
bobbin  is  strong  enough  to  keep  down  the  armature,  A  ;  but  in  proportion 
as  the  carbons  wear  away,  the  current  becomes  feebler,  though  the  voltaic 
arc  continues,  so  that  ultimately  the  attraction  of  the  magnet  no  longer 
counterbalances  a  spring,  r,  which  continually  tends  to  raise  the  armature. 
It  then  ascends,  the  piece  d  disengages  the  stop  i,  the  drum  works,  and 
the  carbons  come  nearer;  they  do  not,  however,  touch,  because  the 
strength  of  the  current  gains  the  upper  hand,  the  armature  A  is  attracted, 
and  the  carbons  remain  fixed.  As  their  distance  only  varies  within  very 
narrow  limits,  a  regular  and  continuous  light  is  obtained  with  this  appa- 
ratus until  the  carbons  are  quite  used. 

By  means  of  a  regulator,  M.  Duboscq  illuminates  the  photogenic 
apparatus  represented  in  fig.  459,  by  which  all  the  optical  experiments 
may  be  performed  for  which  solar  light  was  formerly  necessary. 

787.  Brownfngr's  regulator.  —  A  much  simpler  apparatus,  repre- 
sented in  fig.  626,  has  been  devised  by  Mr.  John  Browning.  It  has  the 
great  advantage  of  being  less  costly  than  the  other  lamps,  and  also  of 
requiring  a  smaller  number  of  elements  to  work  it.     The  current  enters 


— ^       V 


788] 


Properties  of  the  Electric  L  ight. 


711 


the  lamp  by  a  wire  attached  to  a  binding  screw  on  the  base  of  the 
instrument,  passing  up  the  pillar  by  the  small  electromagnet  to  the  centre 
pillar  along  the  top  of  the  horizontal 
bar,  down  the  left-hand  bar  through 
the  two  carbons,  and  away  by  a 
wire  attached  to  a  binding  screw  on 
the  left  hand.  A  tube  holding  the 
upper  carbon  slides  freely  up  and 
down  a  tube  at  the  end  of  the 
cross-piece,  and  would  by  its  own 
weight  rest  on  the  lower  carbon, 
but  the  electromagnet  is  provided 
with  a  keeper,  to  which  is  attached 
a  rest  that  encircles  the  carbon 
tube  and  grasps  it.  When  the  elec- 
tromagnet works  and  attracts  the 
keeper,  the  rest  tightens  and  there- 
by prevents  the  descent  of  the 
carbon.  When  the  keeper  is  not 
attracted  the  rest  loosens,  and  the 
carbon  holder  descends. 

When  the  two  carbons  are  at 
rest,  on  making  contact  with 'a  bat- 
tery the  current  traverses  both  car- 
bons and  no  light  is  produced.  But 
if  the  upper  carbon  be  raised  ever 
so  little,  a  brilliant  light  is  emitted. 
When  the  lamp  is  thus  once  set  to 
work,  the  rod  attached  to  the  upper 

carbon  may  be  let  go,  and  the  magnet  will  afterwards  keep  the  lamp  at 
work.  For  when  some  of  the  carbon  is  consumed,  and  the  interval  be- 
tween the  two  is  too  great  for  the  current  to  pass,  the  magnet  loses  some 
of  its  power,  the  keeper  loosens  its  hold  on  the  -carbon,  and  this  descends 
by  its  own  weight.  When  they  are  sufficiently  near,  but  before  they  are 
in  contact,  the  current  is  re-established  ;  the  magnet  again  draws  on  the 
keeper,  and  the  keeper  again  checks  the  descent  of  the  carbon,  and  so 
forth.  Thus  the  points  are  retained  at  the  right  distances  apart,  and  the 
light  is  continuous  and  brilliant. 

788.  Properties  and  intensity  of  the  electric  lisbt. — The  electric 
light  has  similar  chemical  properties  to  solar  light ;  it  effects  the  combi- 
nation of  chlorine  and  hydrogen,  acts  chemically  on  chloride  of  silver, 
and  applied  to  photography  gives  fine  impressions  remarkable  for  the 
warmth  of  its  tones  ;  it  is,  however,  inapplicable  for  taking  portraits,  as 
it  fatigues  the  sight  too  greatly. 

Passed  through  a  prism,  the  electric  light,  like  the  sun,  is  decomposed 
and  gives  a  spectrum.  WoUaston,  and  more  especially  Fraunhofer,  have 
found  that  the  spectrum  of  the  electric  light  differs  from  that  of  other 
hghts  and  of  the  sun-light  by  the  presence  of  several  very  bright  lines, 


Fig.  626. 


712  Dynamical  Electricity,  [788- 

as  has  been  already  stated.  Wheatstone  was  the  first  to  observe  that  by 
using  electrodes  of  different  metals,  the  spectrum  and  the  lines  are  modified. 

Masson  has  recently  studied  the  electric  light  in  great  detail,  and  has 
experimented  upon  the  light  of  the  electric  machine,  that  of  the  voltaic 
arc,  and  that  of  RuhmkorfPs  coil.  He  has  found  the  same  colours  in 
the  electric  spectrum  as  in  the  solar  spectrum,  but  traversed  by  very 
brilliant  luminous  bands  of  the  same  shade  as  that  of  the  colour  in  which 
they  occur.  The  number  and  position  of  these  bands  do  not  depend  on 
the  intensity  of  the  light,  but,  as  we  have  seen,  upon  the  substances 
between  which  the  voltaic  arc  is  formed. 

With  carbon  the  lines  are  remarkable  for  their  number  and  brilliancy  ; 
with  zinc  the  spectrum  is  characterised  by  a  very  marked  apple-green 
tint ;  silver  produces  a  very  intense  green  ;  with  lead  a  violet  tint  pre- 
dominates, and  so  on  with  other  metals. 

Bunsen,  in  experimenting  with  48  couples,  and  removing  the  charcoals 
to  a  distance  of  a  quarter  of  an  inch,  has  found  that  the  intensity  of  the 
electric  light  is  equal  to  that  of  572  candles. 

Fizeau  and  Foucault  have  compared  the  chemical  effects  of  the  solar 
and  the  electric  lights,  by  investigating  their  action  on  iodized  silver 
plates.  Representing  the  intensity  of  the  sun-light  at  midday  at  1000, 
these  physicists  found  that  that  of  46  Bunsen's  elements  was  235,  while 
that  of  80  elements  was  only  238.  It  follows  that  the  intensity  does 
not  increase  to  any  material  extent  with  the  number  of  the  couples  ;  but 
experiment  shows  that  it  increases  considerably  with  their  surface.  For 
with  a  battery  of  46  elements,  each  consisting  of  3  elements,  with  their 
zinc  and  copper  respectively  united  so  as  to  form  one  element  of  triple 
surface  (777),  the  intensity  was  385,  the  battery,  working  for  an  hour; 
that  is  to  say,  more  than  a  third  of  the  intensity  of  the  solar  light. 

Despretz  observes  that  too  great  precautions  cannot  be  taken  against 
the  effects  of  the  electric  light  when  they  attain  a  certain  intensity.  The. 
light  of  100  couples,  he  says,  may  produce  very  painful  affections  of  the 
eyes.  With  600,  a  single  moment's  exposure  to  the  light  is  sufficient  to 
produce  very  violent  headaches  and  pains  in  the  eye,  and  the  whole  frame 
is  affected  as  by  a  powerful  sunstroke. 

Mr.  Way  has  obtained  a  very  bright  light  by  passing  the  electric 
current  along  a  stream  of  mercury.  The  light  is  produced  by  the  incan- 
descence of  the  mercury  vapour  ;  it  has  a  somewhat  flickering  character, 
and  a  greenish  tinge. 

Attempts  have  been  made  to  apply  the  electric  light  to  the  illumination 
of  rooms,  and  even  of  streets ;  but  partly  the  cost,  and  partly  the  difficulty 
of  producing  with  it  a  uniform  illumination,  inasmuch  as  the  shadows  are 
thrown  into  too  sharp  relief,  have  hitherto  been  great  obstacles  to  its  use. 
Yet  it  is  advantageously  applied  in  special  cases,  such  as  the  photo-electric 
microscope,  illuminations  in  theatres,  etc. 

789.  nxeclianical  effects  ef  tne  battery. — Under  this  head  may  be 
included  the  motion  of  solids  and  hquids  effected  by  the  current.  An  ex- 
ample of  the  former  is  found  in  the  voltaic  arc,  in  which  there  is  a  passage 
of  the  molecules  of  carbon  from  the  positive  to  the  negative  pole  (784). 


-790]  Chemical  'Effects  of  the  Current.  7 1 3 

If,  in  a  slightly  inclined  glass  tube,  a  thread  of  liquid  be  contained 
between  two  platinum  wires  fused  in  the  glass,  and  if  a  current  of  elec- 
tricity be  passed  through  the  liquid  by  means  of  these  electrodes,  then,  if 
the  positive  electricity  moves  upwards,  the  liquid  will  be  carried  along 
with  it — it  will  become  somewhat  raised.  The  ascent  is  proportional  to 
the  intensity  of  the  current  and  to  the  section  of  the  tube.  The  pheno- 
menon is  met  with  in  alcohol  and  in  turpentine,  but  in  a  contrary  direction  ; 
the  liquid  rising  in  the  direction  of  the  negative  electricity. 

A  similar  phenomenon,  known  as  electrical  endosjuose,  is  observed  in 
the  following  experiment,  due  to  Porret.  Having  divided  a  glass  vessel 
into  two  compartments  by  a  porous  diaphragm  consisting  of  bladder,  he 
poured  water  into  the  two  compartments  to  the  same  height,  and  im- 
mersed two  electrodes  of  platinum  in  connection  with  a  battery  of  80 
elements.  As  the  water  became  decomposed,  part  of  the  liquid  was 
carried  in  the  direction  of  the  current,  through  the  diaphragm,  from  the 
positive  to  the  negative  compartment,  where  the  level  rose  above  that  in 
the  other  compartment.  A  solution  of  blue  vitriol  is  best  for  these 
experiments,  because  then  the  disturbing  influence  of  the  disengagement 
of  gas  at  the  negative  electrode  is  avoided. 

The  converse  of  these  phenomena  is  observed  when  a  liquid  is  forced 
through  a  diaphragm  by  mechanical  means  ;  electrical  currents  are 
produced,  if  on  both  sides  the  diaphragm,  metal  electrodes  of  the  same 
material  are  immersed  in  the  liquid  in  conducting  communication  with 
each  other.  Such  currents,  which  were  discovered  by  Quincke,  are 
called  diaphragm  ciirrents. 

According  to  Wertheim,  the  elasticity  of  metallic  wires  is  diminished 
by  the  current,  and  not  by  the  heat  alone,  but  by  the  electricity  ;  he 
has  also  found  that  the  cohesion  is  diminished  by  the  passage  of  a  current. 

To  the  mechanical  effects  of  the  current  may  be  assigned  the  sounds 
produced  in  soft  iron  when  submitted  to  the  magnetising  action  of  a  dis- 
continuous current— a  phenomenon  which  will  be  subsequently  described. 

790.  Cbemlcal  effects. — These  are  among  the  most  important  of 
all  the  actions,  either  of  the  simple  or  compound  circuit.  The  first 
decomposition  effected  by  the 
battery  was  that  of  water, 
obtained  in  1800  by  CarUsle 
and  Nicholson  by  means  of 
a  voltaic  pile.  Water  is 
rapidly  decomposed  by  4  or  5 
Bunsen's  cells ;  the  apparatus 
(fig.  627)  is  very  convenient 
for  the  purpose.  It  consists 
of  a  glass  vessel  fixed  on  a 
wooden  base.  In  the  bottom 
of  the  vessel  two  platinum 
electrodes,  j)  and  w,  are  fitted,  Fig.  627. 

communicating     by    means     of 
copper  wires  with  the  binding  screws.     The  vessel  is  filled  with  water  to 


714 


Dynamical  Electricity. 


[790- 


which  some  sulphuric  acid  has  been  added  to  increase  its  conductivity,  for 
pure  water  is  a  very  imperfect  conductor ;  two  glass  tubes  filled  with 
water  are  inverted  over  the  electrodes,  and  on  interposing  the  apparatus 
in  the  circuit  of  a  battery  decomposition  is  rapidly  set  up,  and  gas 
bubbles  rise  from  the  surface  of  each  pole.  The  volume  of  gas  liberated 
at  the  negative  pole  is  about  double  that  at  the  positive,  and  on  exa- 
mination the  former  gas  is  found  to  be  hydrogen  and  the  latter  gas 
oxygen.  This  experiment  accordingly  gives  at  once  the  qualitative  and 
quantitative  analysis  of  water.  The  oxygen  thus  obtained  has  the 
peculiar  and  penetrating  odour  observed  when  an  electrical  machine  is 
worked  (745),  and  which  is  due  to  ozone.  The  water  contained  at  the 
same  time  some  peroxide  of  hydrogen,  in  producing  which  some  oxygen 
is  consumed.  Moreover  oxygen  is  somewhat  more  soluble  in  water  than 
hydrogen.  Owing  to  these  causes  the  volume  of  oxygen  is  less  than  that 
required  by  the  composition  of  water,  which  is  two  volumes  of  hydrogen 
to  one  of  oxygen.  Hence  voltametric  measurements  are  most  exact 
when  the  hydrogen  alone  is  considered,  and  when  this  is  liberated  at  the 
surface  of  a  small  electrode. 

791.  Electrolysis. — To  those  substances  which,  like  water,  are  re- 
solved into  their  elements  by  the  voltaic  current,  the  term  electrolyte  has 
been  applied  by  Faraday,  to  whom  the  principal  discoveries  in  this 
subject  and  the  nomenclature  are  due.  Electrolysis  is  the  decomposition 
by  the  voltaic  battery ;  the  positive  electrode  was  by  Faraday  called  the 
a?iode,  and  the  negative  electrode  the  kathode.  The  products  of  decom- 
position are  tones ;  katione,  that  which  appears  of  the  kathode  ;  and 
anione,  that  which  appears  at  the  anode. 

By  means  of  the  battery,  the  compound  nature  of  several  substances 
which  had  previously  been  considered  as  elements  has  been  determined. 
By  means  of  a  battery  of  250  couples,  Davy,  shortly  after  the  discovery 
of  the  decomposition  of  water,  succeeded  in  decomposing  the  alkalies 
potass  and  soda,  and  proved  that  they  were  the  oxides  of  the  hitherto 


Fig.  628. 


Fig.  629. 


unknown  metals  potassium  and  sodium.  The  decomposition  of  potass 
may  be  demonstrated  with  the  aid  of  the  battery  of  4  to  6  elements  in 
the  following  manner ;  a  small  cavity  is  made  in  a  piece  of  solid  caustic 


-792]  Decomposition  of  Salts.  715 

potass,  which  is  moistened,  and  a  drop  of  mercury  placed  in  it  (fig.  628). 
The  potass  is  placed  on  a  piece  of  platinum  connected  with  the  positive 
pole  of  the  battery.  The  mercury  is  then  touched  with  the  negative 
pole.  When  the  current  passes,  the  potass  is  decomposed,  oxygen  is 
liberated  at  the  positive  pole,  while  the  potassium  liberated  at  the 
negativ^e  pole  amalgamates  with  the  mercury.  On  distilling  this  amalgam 
out  of  contact  with  air,  the  mercury  passes  off,  leaving  the  potassium. 

The  decomposition  of  binary  compounds — that  is,  bodies  containing 
two  elements — is  quite  analogous  to  that  of  water  and  of  potass ;  one  of 
the  elements  goes  to  the  positive,  and  the  other  to  the  negative  pole. 
The  bodies  separated  at  the  positive  pole  are  called  electronegative  ele- 
ments, because  at  the  moment  of  separation  they  are  considered  to  be 
charged  with  negative  electricity,  while  those  separated  at  the  negative 
pole  are  called  cledropositive  elements.  One  and  the  same  body  may  be 
electronegative  or  electropositive,  according  to  the  body  with  which  it  is 
associated.  For  instance,  sulphur  is  electronegative  towards  hydrogen, 
but  is  electropositive  towards  oxygen.  The  various  elements  may  be 
arranged  in  such  a  series  that  any  one  in  combination  is  electronegative 
to  any  following,  but  electropositive  towards  all  preceding  ones.  This  is 
called  the  electrochemical  series,  and  begins  with  oxygen  as  the  most 
electronegative  element,  terminating  with  potassium  as  the  most  electro- 
positive. 

The  decomposition  of  hydrochloric  acid  into  its  constituents,  chlorine 
and  hydrogen,  may  be  shown  by  means  of  the  apparatus  represented  in 
fig.  629.  Carbon  electrodes  must,  however,  be  substituted  for  those  of 
platinum,  which  is  attacked  by  the  liberated  chlorine ;  a  quantity  of  salt 
also  must  be  added  to  the  hydrochloric  acid,  in  order  to  diminish  the 
solubility  of  the  liberated  chlorine.  The  decomposition  of  iodide  of  po- 
tassium may  be  demonstrated  by  means  of  a  single  element.  For  this 
purpose  a  piece  of  bibulous  paper  is  soaked  with  a  solution  of  starch,  to 
which  iodide  of  potassium  is  added.  On  touching  this  paper  with  the 
electrodes,  a  blue  spot  is  produced  at  the  positive  pole,  due  to  the  action 
of  the  liberated  iodine  on  the  starch. 

792.  Decomposition  of  salts. — Ternary  salts  in  solution  are  decom- 
posed by  the  battery,  and  then  present  effects  varying  with  the  chemical 
affinities,  and  the  intensity  of  the  current.  In  all  cases  the  acid,  or  the 
body  which  is  chemically  equivalent  to  it,  is  electronegative  in  its  action 
towards  the  other  constituent.  The  decomposition  of  salts  may  be 
readily  shown  by  means  of  the  bent  tube  represented  in  fig.  629.  This  is 
nearly  filled  with  a  saturated  solution  of  a  salt,  say  sulphate  of  sodium, 
coloured  with  tincture  of  violets.  The  platinum  electrodes  of  a  battery 
of  four  Bunsen's  elements  are  then  placed  in  the  two  legs  of  the  tube. 
After  a  few  minutes  the  liquid  in  the  positive  leg,  A,  becomes  of  a 
red,  and  that  in  the  negative  leg,  B,  of  a  green  colour,  showing  that 
the  salt  has  been  resolved  into  acid  which  has  passed  to  the  positive, 
and  into  a  base  which  has  gone  to  the  negative  pole,  for  these  are  the 
effects  which  a  free  acid  and  a  free  base  respectively  produce  on  tincture 
of  violets. 


7 1 6  Dynamical  Electricity.  [792- 

In  a  solution  of  sulphate  of  copper,  free  acid  and  oxygen  gas  appear  at 
the  positive  electrode,  and  metallic  copper  is  deposited  at  the  negative 
electrode.  In  like  manner,  with  nitrate  of  silver,  metallic  silver  is  de- 
posited on  the  negative,  while  free  acid  and  oxygen  appear  at  the  positive 
electrode. 

This  decomposition  of  salts  was  formerly  explained  by  saying  that  the 
acid  was  liberated  at  the  positive  electrode  and  the  base  at  the  negative. 
Thus  sulphate  of  potassium,  K^OSOg,  was  considered  to  be  resolved  into 
sulphuric  acid,  SO3,  and  potash,  KoO.  This  view  regarded  salts  com- 
posed of  three  elements  as  different  in  their  constitution  from  binary  or 
haloid  salts.  Their  electrolytic  deportment  has  led  to  a  mode  of  regard- 
ing the  constitution  of  salts  which  brings  all  classes  of  them  under  one 
category.  In  sulphate  of  potassium,  for  instance,  the  electropositive 
element  is  potassium,'  while  the  electronegative  element  is  a  complex  of 
sulphur  and  oxygen,  which  is  regarded  as  a  single  group,  SO^,  and  to 
which  the  name  oxy-sidphion  may  be  assigned.  The  formula  of  sulphate 
of  potassium  would  thus  be  K^SO^,  and  its  decomposition  would  be  quite 
analogous  to  that  of  chloride  of  potassium,  KCl,  chloride  of  lead,  PbCl.,, 
iodide  of  potassium,  KI.  The  electronegative  group  SO^  corresponds  to 
a  molecule  of  chlorine  or  iodine.  In  the  decomposition  of  sulphate  of 
potassium  the  potassium  liberated  at  the  negative  pole  decomposes  water, 
forming  potash  and  liberating  hydrogen.  In  like  manner  the  electro- 
negative constituent  SO^,  which  cannot  exist  in  the  free  state,  decomposes 
into  oxygen  gas,  which  is  liberated,  and  into  anhydrous  sulphuric  acid, 
SO3,  which  immediately  combines  with  water  to  form  ordinary  sulphuric 
acid,  H2SO4.  In  fact,  where  the  action  of  the  battery  is  strong  these 
gases  are  liberated  at  the  corresponding  poles  ;  in  other  cases  they  com- 
bine in  the  liquid  itself,  reproducing  water.  The  constitution  of  sulphate 
of  copper,  CuSO^,  and  of  nitrate  of  silver,  AgNOg,  and  their  decomposi- 
tion, will  be  readily  understood  from  these  examples. 

793.  Transmissions  effected  by  the  current. — In  chemical  decom- 
positions effected  by  the  battery  there  is  not  merely  a  separation  of  the 
elements,  but  a  passage  of  the  one  to  the  positive  and  of  the  other  to  the 
negative  electrode.  This  phenomenon  has  been  demonstrated  by  Davy 
by  means  of  several  experiments,  of  which  the  two  following  are  ex- 
amples : — 

i.  He  placed  solution  of  sulphate  of  sodium  in  two  capsules  connected 
by  a  thread  of  asbestos  moistened  with  the  same  solution,  and  immersed 
the  positive  electrode  in  one  of  the  capsules,  and  the  negative  electrode 
in  the  other.  The  salt  was  decomposed,  and  at  the  expiration  of  some 
time  all  the  sulphuric  acid  was  found  in  the  first  capsule,  and  the  soda  in 
the  second. 

ii.  Having  taken  three  glasses,  A,  B,  and  C  (fig.  630),  he  poured  into  the 
first,  solution  of  sulphate  of  sodium,  into  the  second  dilute  syrup  of 
violets,  and  into  the  third  pure  water,  and  connected  them  by  moistened 
threads  of  asbestos.  The  current  was  then  passed  in  the  direction  from 
C  to  A.  The  sulphate  in  the  vessel  A  was  decomposed,  and  in  the  course 
of  time  there  was  nothing  but  soda  in  this  glass,  which  formed  the  nega- 
tive end,  while  all  the  acid  had  been  transported  to  the  glass  C,  which 


795] 


Laws  of  Electrolysis, 


717 


was  positive.     If,  on  the  contrary,  the  currents  passed  from  A  to  C,  the 

soda  was  found  in  C,  while  all  the  acid  remained  in  A;  but  in  both  cases 

the  remarkable  phenomenon 

was  seen  that  the  syrup  of 

violets  in  B  neither  became 

red  nor  green  by  the  passage 

of  the  acid  or  base  through 

its  mass,  a  phenomenon  the   /j 

explanation  of  which  is  based 

on     the     hypothesis     enun-  "^K: 

ciated  in  the  following  para-  -=-—-.-=^-^- =-.„==..-.-=— -  - 

graph.  Fis-  630. 

794.  Grotbiiss's  bypothesis. — Grothiiss  has  given  the  following  ex- 
planation of  the  chemical  decompositions  effected  by  the  battery. 
Adopting  the  hypothesis  that  in  every  binary  compound,  or  body  which 
acts  as  such,  one  of  the  elements  is  electropositive,  and  the  other  electro- 
negative, he  assumes  that,  under  the  influence  of  the  contrary  electricities 
of  the  electrodes,  there  is  effected,  in  the  liquid  in  which  they  are  im- 
mersed, a  series  of  successive  decompositions  and  recompositions  from 
one  pole  to  the  other.  Hence 
it  is  only  the  elements  of  the 
terminal  molecules  which  do 
not  recombine,  and  remain- 
ing free  appear  at  the  elec- 
trodes.    Water,  for  instance.  Fig.  631. 

is  formed  of  one  atom  of  oxygen  and  two  atoms  of  hydrogen,  the  first 
gas  being  electronegative,  and  the  second  electropositive.  Hence  when 
the  liquid  is  traversed  by  a  sufficiently  powerful  current,  the  molecule  a 
in  contact  with  the  positive  pole  arranges  itself  as  shown  in  fig.  631,  that 
is,  the  oxygen  is  attracted  and  the  hydrogen  repelled.  The  oxygen  of 
this  molecule  is  then  given  off  at  the  positive  electrode,  the  liberated 
hydrogen  immediately  unites  with  the  oxygen  of  the  molecule  b,  the 
hydrogen  of  this  with  the  oxygen  of  the  molecule  c,  and  so  on,  to  the 
negative  electrode,  where  the  last  atoms  of  hydrogen  become  free  and 
appear  on  the  poles.  The  same  theory  applies  to  the  metallic  oxides,  to 
the  acids  and  salts,  and  explains  why  in  the  experiment  mentioned  in 
the  preceding  paragraph  the  syrup  of  violets  in  the  vessel  B  becomes 
neither  red  nor  green.  The  reason  why,  in  the  fundamental  experiment, 
the  hydrogen  is  given  off  at  the  negative  pole  when  the  circuit  is  closed 
will  be  readily  understood  from  a  consideration  of  this  hypothesis. 

795.  Iiaws  of  electrolysis. — The  laws  of  electrolysis  were  discovered, 
by  Faraday  ;  the  most  important  of  them  are  as  follows  : — 

I.  Electrolysis  cannot  take  place  unless  the  electi'olyte  is  a  conductor. 
Hence  ice  is  not  decomposed  by  the  battery,  because  it  is  a  bad  conductor 
Other  bodies,  such  as  oxide  of  lead,  chloride  of  silver,  etc.,  are  only 
electrolysed  in  a  fused  state — that  is,  when  they  can  conduct  the  current. 

n.  The  energy  0/  the  electrolytic  action  of  the  current  is  the  same  in  all 
its  parts. 

III.   The  same  quantity  of  electricity — that  is,  the  same  electric  current 


yi8  Dynamical  ElecU'icity.  [795- 

— decomposes  chemically  eqinvalent  quantities  of  all  the  bodies  which  it 
t7'averses  ;  from  which  it  follows,  that  the  weights  of  elerneiits  separated 
in  these  electrolytes  are  to  each  other  as  their  chemical  equivalents. 

If  an  apparatus  for  decomposing  water  (fig.  628)  and  various  U-shaped 
tubes  containing  respectively  fused  oxide  of  lead  and  chloride  of  tin  are 
interposed  in  the  same  voltaic  current,  which  must  be  sufficiently  power- 
ful, these  substances  will  be  decomposed  ;  the  electronegative  elements 
will  be  separated  at  the  positive  and  the  electropositive  at  the  negative 
poles.  The  quantities  of  substances  liberated  are  in  a  certain  definite 
relation.  Thus  for  every  18  parts  of  water  decomposed  in  the  voltameter 
there  will  be  liberated  2  parts  of  hydrogen,  207  parts  of  lead,  and  117  of 
tin  at  the  respective  negative  electrodes,  and  16  parts  of  oxygen,  and  71 
(or  2  X  35*5)  parts  of  chlorine  at  the  corresponding  positive  electrode. 
Now  these  numbers  are  exactly  as  the  equivalents  (not  as  the  atomic 
weights)  of  the  bodies. 

It  will  further  be  found  that  in  each  of  the  cells  of  the  battery  65  parts 
by  weight  of  zinc  have  been  dissolved,  for  every  two  parts  by  weight  of 
hydrogen  liberated  ;  that  is,  that  for  every  equivalent  of  a  substance 
decomposed  in  the  circuit  one  equivalent  of  zinc  is  dissolved.  This  is 
the  case  whatever  be  the  number  of  cells.  An  increase  in  the  number 
only  has  the  effect  of  overcoming  the  great  resistance  which  many  eleC' 
trolytes  offer,  and  of  accelerating  the  decomposition.  It  does  not  increase 
the  quantity  of  the  eletrolyte  decomposed.  If  in  any  of  the  cells  more 
than  65  parts  of  zinc  are  dissolved  for  every  two  parts  of  hydrogen 
liberated,  this  arises  from  a  disadvantageous  succeeding  local  action  ; 
and  the  more  perfect  the  battery,  the  more  nearly  does  it  approach  this 
ratio. 

IV.  It  follows  from  the  above  law,  that  the  quantity  of  a  body  decom- 
posed in  a  givefi  time  is  proportional  to  the  strength  of  the  current.  On 
this  is  founded  the  use  of  Faraday's  voltajneter,  in  which  the  intensity  of 
a  current  is  ascertained  from  the  quantity  of  water  which  it  decomposes 
in  a  given  time.  It  consists  of  a  glass  vessel,  in  which  two  platinum 
electrodes  are  fixed.  In  the  neck  of  a  vessel  a  bent  delivery  tube  is 
fitted,  and  the  mixed  gases  are  collected  in  a  graduated  cylinder,  so  that 
their  volume  can  be  determined,  which,  reduced  to  a  constant  tempera- 
ture and  pressure,  is  a  measure  of  their  quantity. 

The  use  of  this  voltameter  appears  simple  and  convenient ;  and  hence 
some  physicists  have  proposed  as  unit  of  the  strength  of  the  current, 
that  strength  which  in  o?ie  minute  yields  a  cubic  centimetre  of  mixed  gas 
reduced  to  the  temperature  0°  and  the  pressure  760  ^nin.  Yet,  for  reasons 
mentioned  before  (790),  the  measurements  should  be  based  on  the  volume 
of  hydrogen  liberated. 

The  silver  voltameter  is  an  instrument  for  measuring  the  intensity  of 
the  current.  A  solution  of  nitrate  of  silver  of  known  strength  is  placed 
in  a  platinum  dish  which  is  connected  with  the  negative  pole ;  in  this 
solution  is  placed  the  positive  pole,  which  consists  of  a  rod  of  silver 
wrapped  round  with  muslin.  The  silver  which  separates  at  the  negative 
pole  is  washed,  dried,  and  weighed  ;  and  the  weight  thus  produced  in  a 


-796]    Tangent  Compass  compared  witJi  the  Voltameter.      'ji<^ 

given  time  is  a  measure  for  the  intensity  of  the  current.  The  silver  par- 
ticles which  become  detached  from  the  positive  pole  are  retained  in  the 
mushn. 

The  current  from  the  electrical  machine,  which  is  of  very  high  in- 
tensity, is  capable  of  traversing  any  electrolyte,  but  the  quantity  which  it 
can  decompose  is  extremely  small  as  compared  even  with  the  smallest 
voltaic  apparatus,  and  it  must  be  concluded  that  the  quantity  developed 
by  the  frictional  machine  is  very  small  as  compared  with  that  developed 
by  chemical  action. 

It  has  been  calculated  by  Weber,  that  if  the  quantity  of  positive  elec- 
tricity required  to  decompose  a  grain  of  water  were  accumulated  on  a 
cloud  at  a  distance  of  3,000  feet  from  the  earth's  surface,  it  would  exert 
an  attractive  force  upon  the  earth  of  upwards  of  1,500  tons. 

796.  Comparison  between  tbe  tangrent  compass  and  the  volta- 
meter.— There  are  several  objections  to  the  use  of  the  voltameter.  In 
the  first  place,  it  does  not  indicate  the  strength  at  any  given  moment,  for 
in  order  to  obtain  measurable  quantities  of  gas  the  current  must  be 
continued  for  some  time.  Again,  the  voltameter  gives  no  indications  of 
the  changes  which  take  place,  in  this  time,  but  only  the  mean  strength. 
It  offers  also  great  resistance,  and  can  thus  only  be  used  in  the  case  of 
strong  currents ;  for  such  currents  either  do  not  decompose  water,  or 
only  yield  quantities  too  small  for  accurate  measurement.  In  addition 
to  this,  the  indications  of  the  voltameter  depend  not  only  on  the  intensity 
of  the  current,  but  on  the  acidity  of  the  water,  and  on  the  distance  and 
size  of  the  electrodes. 

The  magnetic  measurements  are  preferable  to  the  chemical  ones. 
Not  only  are  they  more  delicate  and  offer  less  resistance,  but  they  give 
the  intensity  at  any  moment.  On  the  other  hand,  indications  furnished 
by  the  tangent  compass  hold  only  for  one  special  instriynent.  They  vary 
with  the  diameter  of  the  ring  and  the  number  of  turns ;  moreover,  one 
and  the  same  instrument  will  give  different  indications  on  different  places, 
seeing  that  the  force  of  the  earth's  magnetism  varies  from  one  place  to 
another. 

The  indications  of  the  two  instruments  may,  however,  be  readily  com- 
pared with  one  another.  For  this  purpose  the  voltameter  and  the  tangent 
compass  are  simultaneoiisly  inserted  in  the  circuit  of  a  battery,  and  the 
deflection  of  the  needle  and  the  amount  of  gas  liberated  in  a  given  time 
are  noted.  In  one  special  set  of  experiments  the  following  results  were 
obtained : — 


Number  of 
Elements. 

Deflection. 

Gas  liberated  in 
three  minutes. 

12 

8 
6 

3 
2 

28-5° 

24-8 
22-0 

1375 
6-9 

I25CC. 
106 

93 
56 
24 

720  Dynamical  Electricity.  [796- 

If  we  divide  the  tangents  of  the  angle  into  the  corresponding  volume  of 
gas  liberated  in  one  minute,  we  should  obtain  a  constant  magnitude  which 
represents  how  much  gas  is  developed  in  a  minute  by  a  current  which 
could  produce  on  the  tangent  compass  the  deflection  45°,  for  tang.  45°  =  i. 
Making  this  calculation  with  the  above  observations,  we  obtain  a  set  of 
closely  agreeing  numbers,  the  mean  of  which  is  76-5.  The  gas  was 
measured  under  a  pressure  of  737  mm.  and  at  a  temperature  of  315°,  and 
therefore  under  normal  conditions  (309)  its  volume  would  be  70  cubic 
centimetres.  That  is  to  say,  this  is  the  volume  of  gas  which  corresponds 
to  a  deflection  of  45°. 

Hence  in  chemical  measure  the  strength  C  of  a  current  which  produces 
in  this  particular  tangent  compass  a  deflection  of  6°  is 

C  =  70  tang.  ^. 

For  instance,  supposing  a  current  produced  in  this  tangent  compass  a 
deflection  of  54°,  this  current,  if  it  passed  through  a  voltameter,  would 
liberate  in  a  minute  70  x  tang.  54  =  70  x  1-376  =  96*32  cubic  centimetres 
of  gas. 

If  once  the  reduction  factor  for  a  tangent  compass  has  been  deter- 
mined, the  strength  of  any  current  may  be  readily  calculated  in  chemical 
measure  by  a  simple  reading  of  the  angle  of  deflection.  This  reduction 
factor  of  course  only  holds  for  one  special  instrument,  and  for  experi- 
ments on  the  same  place,  seeing  that  the  force  of  the  earth's  magnetism 
varies  in  different  places". 

The  indications  of  the  sine-compass  may  be  compared  with  those  of 
the  galvanometer  in  a  similar  manner. 

797.  Polarisation. — When  the  platinum  electrodes,  which  have  been 
used  in  decomposing  water,  are  disconnected  from  the  battery,  and  con- 
nected with  a  galvanometer,  the  existence  of  a  current  is  indicated  which 
has  the  opposite  direction  to  that  which  had  previously  passed.  This 
phenomenon  is  explained  by  the  fact  that  oxygen  has  been  condensed  on 
the  surface  of  the  positive  plate,  and  hydrogen  on  the  surface  of  the 
negative  plate,  analogous  to  what  has  been  already  seen  in  the  case  of 
the  non-constant  batteries  (759).  The  effect  of  this  is  to  produce  two 
different  electromotors,  which  produce  a  current  opposed  in  direction  to 
the  original  one,  and  which,  therefore,  must  weaken  it.  As  the  two 
electrodes  thus  become  the  poles  of  a  new  current,  they  are  said  to  be 
polarised^  and  the  current  is  called  a  polarisatioti-current. 

On  this  principle  batteries  may  be  constructed  of  pieces  of  metal  of  the 
same  kind — for  instance,  platinum — which  otherwise  gives  no  current.  A 
piece  of  moistened  cloth  is  interposed  between  each  pair,  and  each  end 
of  this  system  is  connected  with  the  poles  of  a  battery.  After  some  time 
the  apparatus  has  received  a  charge,  and  if  separated  from  the  battery 
can  itself  produce  all  the  effects  of  a  voltaic  battery.  Such  batteries  are 
called  secondary  batteries.  Their  action  depends  on  an  alteration  of  the 
surface  of  the  metal  produced  by  the  electric  current ;  the  constituents  of 
the  Hquid  with  which  the  cloth  is  moistened  having  become  accumulated 
on  the  opposite  plates  of  the  circuit. 


-800]  NobilVs  Rings.  721 

A  dry  pile  which  has  become  inactive  may  be  used  as  a  secondary 
battery.  When  a  current  is  passed  through  it,  in  a  direction  contrary  to 
that  which  the  active  battery  yields,  it  then  regains  its  activity. 

To  this  class  belongs  Planters  secondary  battery,  which  consists  of 
two  concentric  cylinders  of  sheet  lead,  which  do  not  touch,  and  are 
immersed  in  dilute  acid.  They  are  charged  by  being  placed  in  contact 
with  a  battery  of  two  or  three  cells,  and  there  is  an  arrangement  by  which 
they  can  be  detached  from  the  battery  and  their  current  utilised.  They 
serve  in  a  certain  sense  to  store  up  and  transform  the  power  of  the 
primary  battery,  and  produce  effects  of  great  intensity. 

798.  Grove's  gras  battery. — On  the  property,  which  metals  have,  of 
condensing  gases  on  their  surfaces.  Grove  has  constructed  h.\s  gas  battery. 
In  its  simplest  form  it  consists  of  two  glass  tubes,  in  each  of  which  is 
fused  a  platinum  electrode,  provided  on  the  outside  with  binding  screws. 
These  electrodes  are  made  more  efficient  by  being  covered  with  finely 
divided  platinum.  One  of  the  tubes  is  partially  filled  with  hydrogen, 
and  the  other  partially  with  oxygen,  and  they  are  inverted  over  dilute 
sulphuric  acid,  so  that  half  the  platinum  is  in  the  hquid  and  half  in  gas. 
On  connecting  the  electrodes  with  a  galvanometer,  the  existence  of  a 
current  is  indicated,  whose  direction  in  the  connecting  wire  is  from  the 
platinum  in  oxygen  to  that  in  hydrogen  ;  so  that  the  latter  is  negative 
towards  the  former.  As  the  current  passes  through  water  this  is  decom- 
posed ;  oxygen  is  separated  at  the  positive  plate,  and  hydrogen  at  the 
other.  These  gases  unite  with  the  gases  condensed  on  their  surface,  so 
that  the  volume  of  gas  in  the  tubes  gradually  diminishes,  but  in  the  ratio 
of  one  volume  of  oxygen  to  two  volumes  of  hydrogen.  These  elements 
can  be  formed  into  a  battery  by  joining  the  dissimilar  plates  with  one 
another  just  as  they  are  joined  in  an  ordinary  battery.  One  element  of 
such  a  battery  is  sufficient  to  decompose  iodide  of  potassium,  and  four 
will  decompose  water. 

799.  Passive  state  of  iron. — With  polarisation  is  probably  connected 
a  vei7  remarkable  chemical  phenomenon,  which  many  metals  exhibit, 
but  more  especially  iron.  When  this  is  immersed  in  concentrated 
nitric  acid  it  is  unattacked.  This  condition  of  iron  is  called  the  passive 
state,  and  upon  it  depends  the  possibility  of  the  zinc-iron  battery  (763). 
It  is  probable  that  in  the  above  experiment  a  thin  superficial  layer  of 
sesquioxide  of  iron  is  formed,  which  is  then  negative  towards  platinum. 

800.  XffoMli's  rings. — When  a  drop  of  acetate  of  copper  is  placed  on 
a  silver  plate,  and  the  silver  is  touched  in  the  middle  of  the  drop  with  a 
piece  of  zinc,  there  are  formed  around  the  point  of  contact  a  series  of 
copper  rings  alternately  dark  and  light.  These  are  Nobili's  coloured  rings. 
They  may  be  obtained  in  beautiful  iridescent  colours  by  the  following 
process  :  A  solution  of  oxide  of  lead  in  potash  is  obtained  by  boiling 
finely  powdered  litharge  in  a  solution  of  potash.  In  this  solution  is  im- 
mersed a  polished  plate  of  silver  or  of  German  silver,  which  is  connected 
with  the  positive  electrode  of  a  battery  of  eight  Bunsen's  elements.  With 
the  negative  pole  is  connected  a  fine  platinum  wire  fused  in  glass,  so  that 
only  its  point  projects  ;  and  this  is  placed  in  the  liquid  at  a  small  distance 

I  I 


722  Dynamical  Electricity.  [800- 

from  the  plate.  Around  this  point  binoxide  of  lead  is  separated  on  the 
plate  in  very  thin  concentric  layers,  the  thickness  of  which  decreases  from 
the  middle.  They  show  the  same  series  of  colours  as  Newton's  coloured 
rings  in  transmitted  light.  The  binoxide  of  lead  owes  its  origin  to  a 
secondary  decomposition ;  by  the  passage  of  the  current  some  oxide  of 
lead  is  decomposed  into  metallic  lead,  which  is  deposited  at  the  negative 
pole,  and  oxygen  which  is  liberated  at  the  positive ;  and  this  oxygen  com- 
bines with  some  oxide  of  lead  to  form  binoxide,  which  is  deposited  on  the 
positive  pole  as  the  decomposition  proceeds. 

The  effects  are  also  well  seen  if  a  solution  of  sulphate  of  copper  is 
placed  on  a  silver  plate,  which  is  touched  with  a  zinc  rod,  the  point  of 
which  is  in  the  solution;  for  then  a  current  is  formed  by  these  metals 
and  the  liquid. 

8oi.  Arbor  Saturni,  or  lead  tree.  Arbor  Dianae. — When,  in  a 
solution  of  a  salt,  is  immersed  a  metal  which  is  more  oxidisable  than  the 
metal  of  the  salt,  the  latter  is  precipitated  by  the  former,  while  the  im- 
mersed metal  is  substituted  equivalent  for  equivalent  for  the  metal  of  the 
salt.  This  precipitation  of  one  metal  by  another  is  partly  attributable  to 
the  difference  in  their  affinities,  and  partly  to  the  action  of  a  current 
which  is  set  up  as  soon  as  a  portion  of  the  less  oxidisable  metal  has  been 
deposited.  The  action  is  promoted  by  the  presence  of  a  slight  excess  of 
acid  in  the  solution. 

A  remarkable  instance  of  the  precipitation  of  one  metal  by  another  is 
the  arbor  Saturni.  This  name  is  given  to  a  series  of  brilliant  ramified 
crystalhsations  obtained  by  zinc  in  solutions  of  acetate  of  lead.  A  glass 
flask  is  filled  with  a  clear  solution  of  this  salt,  and  the  vessel  closed  with 
a  cork,  to  which  is  fixed  a  piece  of  zinc  in  contact  with  some  copper  wire. 
The  flask,  being  closed,  is  left  to  itself.  The  copper  wire  at  once  begins 
to  be  covered  with  a  moss-like  growth  of  metallic  lead,  out  of  which 
brilliant  crystallised  laminae  of  the  same  metal  continue  to  form  ;  the 
whole  phenomenon  has  great  resemblance  to  the  growth  of  vegetation, 
from  which  indeed  the  old  alchemical  name  is  derived.  For  the  same 
reason  the  name  arbor  DiaiicE  has  been  given  to  the  metallic  deposit 
produced  in  a  similar  manner  by  mercury  in  a  solution  of  nitrate  of 
silver. 

ELECTROMETALLURGY. 

802.  Electrometallurg-y-. — The  decomposition  of  salts  by  the  battery 
has  received  a  most  important  application  in  electro7netatturgy,  or 
galvanoplastics^  by  which  is  meant  the  art  of  precipitating  certain  metals 
from  their  solutions  by  the  slow  action  of  a  galvanic  current,  by  which 
means  the  salts  of  certain  metals  are  decomposed,  the  metal  being 
deposited  on  the  negative  pole,  while  the  acid  is  liberated  at  the  positive. 
The  art  was  discovered  independently  by  Spencer  in  England,  and  by 
Jacobi  in  Petersburg. 

In  order  to  obtain  a  galvanoplastic  reproduction  of  a  medal  or  any 
other  object,  a  mould  must  first  be  made,  on  which  the  layer  of  metal  is 
deposited  by  the  electric  current. 


Electrometallurgy,  723 

For  this  purpose  several  substances  are  in  use,  and  one  or  the  other  is 
preferred  according  to  circumstances.  For  medals  and  similar  objects 
Avhich  can  be  submitted  to  pressure,  gutta  percha  may  be  used  witE~ 
advantage.  The  gutta  percha  is  softened  in  hot  water,  pressed  against 
the  object  to  be  copied,  and  allowed  to  cool,  when  it  can  be  detached 
without  difficulty. 

For  the  reproduction  of  engraved  woodblocks  or  type,  wax  moulds  are 
now  commonly  used.  They  are  prepared  by  pouring  into  a  narrow  flat 
pan  a  suitable  mixture  of  wax,  tallow,  and  Venice  turpentine,  which  is 
allowed  to  set,  and  is  then  carefully  brushed  over  with  very  finely 
powdered  graphite.  While  this  composition  is  still  somewhat  soft,  the 
woodblock  or  type  is  pressed  upon  it  either  by  a  screw  press,  or,  still 
better,  by  hydraulic  pressure.  If  plaster  of  Paris  moulds  are  to  be  made 
use  of,  it  is  essential  that  they  be  first  thoroughly  saturated  with  wax  or 
tallow  so  as  to  become  impervious  to  water. 

In  all  cases,  whether  the  moulds  be  of  gutta  percha,  of  wax,  or  any 
non-conducting  substance,  it  is  of  the  highest  importance  that  their  surface 
be  brushed  over  very  carefully  with  graphite  and  so  made  a  good  con- 
ductor. The  conducting  surface  thus  prepared  must  also  be  in  metallic 
contact  with  a  wire  or  a  strip  of  copper  by  which  it  is  connected  with  the 
negative  electrode. 

Sometimes  the  moulds  are  made  of  a  fusible  alloy  (317),  which  may 
consist  of  5  parts  of  lead,  8  of  bismuth,  and  3  of  tin.  Some  of  the  melted 
alloy  is  poured  into  a  shallow  box,  and  just  as  it  begins  to  solidify  the 
medal  is  placed  horizontally  on  it  in  a  fixed  position.  When  the  alloy 
has  become  cool,  a  slight  shock  is  sufficient  to  detach  the  medal.  A 
copper  wire  is  then  bound  round  the  edge  of  the  mould,  by  which  it  can 
be  connected  with  the  negative  electrode  of  the  battery,  and  then  the 
edge  and  the  back  are  covered  with  a  thin  non-conducting  layer  of  wax, 
so  that  the  deposit  is  only  formed  on  the  mould  itself. 

The  most  suitable  arrangement  for  producing  an  electro-deposit  of 
copper  consists  of  a  trough  of  glass,  slate,  or  of  wood,  lined  with  india- 
rubber  or  coated  with  marine  glue  (fig.  632).  This  contains  an  acid  solution 
of  sulphate  of  copper,  and  across  it  are  stretched  copper  rods  B  and  D 
connected  respectively  with  the  negative  and  positive  poles  of  a  battery. 
By  their  copper  conductors  the  moulds  m  are  suspended  in  the  liquid 
from  the  negative  rod  B,  whilst  a  sheet  of  copper  C,  presenting  a  surface 
about  equal  to  that  of  the  moulds  to  be  covered,  is  suspended  from 
the  positive  rod  D,  at  a  distance  of  about  2  inches,  directly  opposite  to 
them. 

The  battery  employed  for  the  electric  deposition  of  metals  ought  to  be 
one  of  great  constancy,  and  Daniell's  and  Smee's  are  mostly  in  use.  The 
currents  of  electricity  furnished  by  magneto-electrical  machines  of  a 
special  construction  are  also  used  in  large  establishments. 

The  copper  plate  suspended  from  the  positive  pole  serves  a  double 
purpose  ;  it  not  only  closes  the  current,  but  it  keeps  the  solution  in  a  state 
of  concentration,  for  the  acid  liberated  at  the  positive  pole  dissolves  the 


724  Dynamical  Electricity.  [802- 

copper,  and  reproduces  a  quantity  of  sulphate  of  copper  equal  to  that  de- 
composed by  the  current. 

Another,  and  very  simple  process  for  producing  the  electric  deposit  of 
copper  consists  in  making  use  of  what  is  in  effect  a  Daniell's  cell.  A 
porous  pot,  or  a  glass  cylinder  covered  at  the  bottom  with  bladder,  or 
with  vegetable  parchment,  is  immersed  in  a  vessel  of  larger  capacity 
containing  a  concentrated  solution  of  sulphate  of  copper.  The  porous 
vessel  contains  acidulated  water,  and  in  it  is  suspended  a  piece  of  amal- 
gamated zinc  of  suitable  form;  and  having  a  surface  about  equal  to  that 


Fig.  632. 

of  the  mould.  The  latter  is  attached  to  an  insulated  wire  connected  with 
the  zinc  and  is  immersed  in  the  solution  of  sulphate  of  copper  in  such  a 
position  that  it  is  directly  opposite  to  the  diaphragm.  The  action  com- 
mences by  the  mould  becoming  covered  with  a  film  of  copper  commencing 
at  the  point  of  contact  with  the  conductor  and  gradually  increasing  in 
thickness  in  proportion  to  the  action  of  the  Daniell's  element  thus  formed. 
It  is  of  course  essential  in  the  process  to  keep  the  solution  of  copper  at  a 
uniform  strength  which  is  done  by  suspending  muslin  bags  filled  with 
crystals  of  sulphate  of  copper. 

How  great  is  the  delicacy  with  which  such  electric  deposits  can  attain 
appears  from  the  fact  that  galvanoplastic  copies  can  be  made  of  daguerre- 
otypes, which  are  of  the  greatest  accuracy.    • 

803.  Electrog-ilding-. — The  old  method  of  gilding  was  by  means  of 
mercury.  It  was  effected  by  an  amalgam  of  gold  and  mercury,  which 
was  applied  on  the  metal  to  be  gilt.  The  objects  thus  covered  were 
heated  in  a  furnace,  the  mercury  volatilised,  and  the  gold  remained  in 
a  very  thin  layer  on  the  objects.  The  same  process  was  used  for  silver- 
ing ;  but  they  were  expensive  and  unhealthy  methods,  and  have  now 
been  entirely  replaced  by  electrogilding  and  electrosilvering.  Electro- 
gilding  only  differs  from  the  process  described  in  the  previous  paragraph, 
in  that  the  layer  is  thinner  and  adheres  more  firmly.  Brugnatelli,  a 
pupil  .of  Volta,  appears  to  have  been  the  first,  in  1803,  to  observe  that  a 
body  could  be  gilded  by  means  of  the  battery  and  an  alkaline  solution  of 
gold ;  but  De  la  Rive  was  the  first  who  really  used  the  battery  in 
gilding.     The  methods  both  of  gilding  and  silvering  owe  their  present 


-805]  Deposition  of  Ii'on  and  Nickel.  725 

high  state  of  perfection  principally  to  the  improvements  of  Elkington, 
Ruolz,  and  others. 

The  pieces  to  be  gilt  have  to  undergo  three  processes  before  gilding. 

The  first  consists  in  heating  them  so  as  to  remove  the  fatty  matter 
which  has  adhered  to  them  in  previous  processes. 

As  the  objects  to  be  gilt  are  usually  of  what  is  called  gilding  metal 
or  red  brass,  and  which  is  a  special  kind  of  brass  rich  in  copper,  and 
their  surface  during  the  operation  of  heating  becomes  covered  with  a 
layer  of  suboxide  or  of  protoxide  of  copper,  this  is  removed  by  the  second 
operation.  For  this  purpose  the  objects^  while  still  hot,  are  immersed  in 
very  dilute  nitric  acid,  where  they  remain  until  the  oxide  is  removed. 
They  are  then  rubbed  with  a  hard  brush,  washed  in  distilled  water,  and 
dried  in  gently  heated  sawdust. 

To  remove  all  spots  they  must  undergo  the  third  process,  which  con- 
sists in  rapidly  immersing  them  in  ordinary  nitric  acid,  and  then  in  a 
mixture  of  nitric  acid,  bay  salt ,  and  soot. 

When  thus  prepared  the  objects  are  attached  to  the  negative  pole  of  a 
battery,  consisting  of  three  or  four  Bunsen's  or  Daniell's  elements.  They 
are  then  immersed  in  a  bath  of  gold,  as  previously  described.  They  remain 
in  the  bath  for  a  time  which  depends  on  the  thickness  of  the  desired  de- 
posit. There  is  great  difference  in  the  composition  of  the  baths.  That 
most  in  use  consists  of  i  part  of  chloride  of  gold.  10  parts  of  cyanide  of 
potassium,  dissolved  in  200  parts  of  water.  In  order  to  keep  the  bath  in 
a  state  of  concentration,  a  piece  of  gold  is  suspended  from  the  positive 
electrode,  which  dissolves  in  proportion  as  the  gold  dissolved  in  the  bath 
is  deposited  on  the  objects  attached  to  the  negative  pole. 

The  method  which  has  just  been  described  can  also  be  used  for  silver, 
bronze,  German  silver,  etc.  But  other  metals^  such  as  iron,  steel,  zinc, 
tin,  and  lead,  are  very  difficult  to  gild  well.  To  obtain  a  good  coating, 
they  must  first  be  covered  with  a  layer  of  copper,  by  means  of  the  battery 
and  a  bath  of  sulphate  of  copper  ;  the  copper  with  which  they  are  coated 
is  then  gilded,  as  in  the  previous  case. 

804.  Electrosllvering-. — What  has  been  said  about  gilding  applies 
exactly  to  the  process  of  electrosilvering.  The  difference  is  in  the  com- 
position of  the  bath,  which  consists  of  two  parts  of  cyanide  of  silver,  and 
two  parts  of  cyanide  of  potassium  dissolved  in  250  parts  of  water.  To  the 
positive  electrode  is  suspended  a  plate  of  silver,  which  prevents  the  bath 
from  becoming  poorer:  the  pieces  to  be  silvered,  which  must  be  well 
cleaned,  are  attached  to  the  negative  pole. 

It  may  here  be  observed  that  these  processes  succeed  best  with  hot 
solutions. 

805.  Electric  deposition  of  iron  and  nickel. — One  of  the  most 
valuable  applications  of  the  electric  deposition  of  metals  is  to  what  is 
called  the  steeling  (acierage)  of  engraved  copper  plates.  The  bath  re- 
quired for  this  purpose  is  obtained  by  suspending  a  large  sheet  of  iron, 
connected  with  the  positive  pole  of  a  battery,  in  a  trough  filled  with  a 
saturated  solution  of  sal-ammoniac ;  whilst  a  thin  strip  of  iron,  also  im- 
mersed, is  connected  with  the  negative  pole.     By  this  means  iron  from 


726  Dyjianiical  Electricity,  [805- 

the  large  plate  is  dissolved  in  the  sal-ammoniac  while  hydrogen  is  given 
off  on  the  surface  of  the  small  one.  When  the  bath  has  thus  taken  up  a 
sufficient  quantity  of  iron,  an  engraved  copper  plate  is  substituted  for 
the  small  negative  strip.  A  bright  deposit  of  iron  begins  to  form  on  it 
at  once,  and  the  plate  assumes  the  colour  of  a  polished  steel  plate.  The 
deposit  thus  obtained  in  the  course  of  half  an  hour  is  exceedingly  thin, 
and  an  impression  of  the  plate  thus  covered  does  not  seem  different  from 
an  uncovered  plate;  it  possesses  however  an  extraordinary  degree  of 
hardness,  so  that  a  very  large  number  of  impressions  can  be  taken  from 
such  a  plate  before  the  thin  coating  of  iron  is  worn  off.  When,  however, 
this  is  the  case,  the  film  of  iron  is  dissolved  off  by  dilute  nitric  acid  and 
the  plate  is  again  covered  with  the  deposit  of  iron. 

An  indefinite  number  of  perfect  impressions  may,  by  this  means,  be 
obtained  from  one  copper  plate,  without  altering  the  original  sharp  con- 
dition of  the  engraving. 

The  covering  of  metals  by  a  deposit  of  nickel  has  of  late  come  into 
use.  The  process  is  essentially  the  same  as  that  just  described.  The 
bath  used  for  the  purpose  can  however  be  made  more  directly  by  mixing, 
in  suitable  proportions,  salts  of  nickel  with  those  of  ammonia.  The 
positive  pole  consists  of  a  plate  of  pure  nickel. 

A  special  difficulty  is  met  with  in  the  electric  deposition  of  nickel 
owing  to  the  tendency  of  this  metal  to  deposit  in  an  uneven  manner; 
and  then  to  become  detached.  This  is  got  over  by  frequently  removing 
the  articles  from  the  bath,  and  submitting  them  to  a  polishing  process. 

Objects  coated  with  nickel  show  a  highly  polished  surface  of  the 
characteristic  bright  colour  of  this  metal.  The  coating  is  moreover  very 
hard  and  durable,  and  is  unaffected  either  by  the  atmosphere  or  even  by 
sulphuretted  hydrogen.  ' 


CHAPTER   IV. 


ELECTRODYNAMICS.   ATTRACTION  AND  REPULSION  OF  CURRENTS  BY 

CURRENTS. 

806.  Electrodynamics. — Under  electrodyttamics  is  understood  the  laws 
of  electricity  in  a  state  of  motion,  or  the  action  of  electric  currents  upon 
each  other  and  upon  magnets,  while  electrostatics  deals  with  the  laws  of 
electricity  in  a  state  of  rest. 

The  action  of  one  electrical  current  upon  another  was  first  investigated 
by  Ampere,  shortly  after  the  discovery  of  Oersted's  celebrated  funda- 
mental experiment  (772).  All  the  phenomena,  even  the  most  compli- 
cated^ follow  from  two  simple  laws,  which  are — 

I.  Two  cicrrents  which  are  parallel^  and  in  the  same  direction,  attract 
07ie  another. 

I I.  Two  currents  par  at  let,  but  in  contrary  directions,  repel  one  another. 
In  order  to  demonstrate  these  laws,  the  circuit  which  the  current 

traverses  must  consist  of  two  parts,  one  fixed  and  the  other  movable. 


-806] 


Elmtrodyna  in  ics. 


727 


This  is  effected  by  the  apparatus  (fig.  633),  which  is  a  modified  and  im- 
proved form  of  one  originally  devised  by  Ampere. 

It  consists  of  two  brass  columns,  A  and  D,  between  which  is  a  shorter 
one.  The  column  D  is  provided  with  a  multiplier  (773)  of  20  turns,  MN 
(fig.  633),  which  greatly  increases  the  sensitiveness  of  the  instrument.    This 


Fig.  633. 

can  be  adjusted  at  any  height  and  in  any  position  by  means  of  a  universal 
screw  clamp  (see  figs.  633,  635-638). 

The  short  column  is  hollow,  and  in  its  interior  slides  a  brass  tube  ter- 
minating in  a  mercury  cup,  ^,  which  can  be  raised  or  lowered.  On  the 
column  A  is  another  mercury  cup  represented  in  section  at  fig.  634  in  its 
natural  size.  In  the  bottom  is  a  capillary  aperture  through  which  passes 
the  point  of  a  sewing  needle  fixed  to  a  small  copper  ball.  This  point  ex- 
tends as  far  as  the  mercury,  and  turns  freely  in  the  hole.  The  movable 
part  of  the  circuit  consists  of  a  copper  wire  proceeding  from  a  small 
ball,  and  turning  in  the  direction  of  the  arrows  from  the  cup  a  to  the  cup 
c.  The  two  lower  branches  are  fixed  to  a  thin  strip  of  wood,  and  the  whole 
system  is  balanced  by  two  copper  balls  sus- 
pended to  the  ends. 

The  details  being  known,  the  current  of  a 
Bunsen's  battery  of  4  or  5  cells  ascending  by 
the  column  A  (fig.  633)  to  the  cup  a^  traverses 
the  circuit  BC,  reaches  the  cup  c,  descends 
the  central  column,  and  thence  passes  by  a 
wire,  P,   to  the  multiplier  AIN,  from   whence 


Fig.  634. 


it  returns  to  the  battery  by  the  wire  Q.     Now  if,  before  the  current  passes, 


728 


Dynamical  Electricity. 


[806 


the  movable  circuit  has  been  arranged  in  the  plane  of  the  multiplier,  with 
the  sides  B  and  M  opposite  each  other,  when  the  current  passes  the  side 
B  is  repelled,  which  demonstrates  the  second  law  ;  for  in  the  branches  B 
and  M  the  currents,  as  indicated  by  the  arrows,  are  proceeding  in  opposite 
directions. 

To  demonstrate  the  first  law  the  experiment  is  arranged  as  in  figure  635 
— that  is,  the  multiplier  is  reversed  ;  the  current  is  then  in  the  same  direc- 
tion both  in  the  multiplier  and  in  the  movable  part ;  and  when  the  latter  is 
removed  out  of  the  plane  of  the  multiplier,  so  long  as  the  current  passes 
it  tends  to  return  to  it,  proving  that  there  is  attraction  between  the  two 
parts. 

807.  Ro§ret's  vibratingr  spiral. — The  attraction  of  parallel  currents 
may  also  be  shown  by  an  experiment  known  as  that  of  Rogefs  vibrating 
spiral.  A  copper  wire  about  07  mm.  in  diameter  is  coiled  in  a  spiral  of 
about  30  coils  of  25  mm.  diameter.  At  one  end  it  is  hung  vertically  from 
a  binding  screw,  while  the  other  just  dips  in  a  mercury  cup.  On  passing 
the  current  of  a  battery  of  3  to  5  Grove's  cells  through  the  spiral  by  means 
of  the  mercury  cup  and  the  binding  screw,  its  coils  are  traversed  by  parallel 
currents  ;  they  therefore  attract  one  another,  and  rise,  and  thus  the  con- 
tact with  the  mercury  is  broken.  The  current  having  thus  ceased,  the 
coils  no  longer  attract  each  other,  they  fall  by  their  own  weight,  contact 
with  the  mercury  is  re-established,  and  the  series  of  phenomena  are  indefi- 
nitely reproduced.  The  experiment  is  still  more  striking  if  a  magnetised 
rod  the  thickness  of  a  pencil  is  introduced  into  the  interior.  This  will  be 
intelligible  if  we  consider  the  action  between  the  parallel  Amperian 
currents  of  the  magnet  and  of  the  helix. 

808.  Iiaws  of  angrular  currents. — I.  Two  rectilinear  currents,  the 
directions  of  which  form  an  ajtgle  with  each  other,  attract  one  another 
when  both  approach,  or  recede  from,  the  apex  of  the  angle. 


.  Fig.  635. 

1 1.   They  repel  one  another  if  one  approaches  and  the  other  recedes  from 
the  apex  of  the  angle. 


808] 


Laws  of  Angular  Currents. 


729 


These  two  laws  may  be  demonstrated  by  means  of  the  apparatus  above 
described,  replacing  the  movable  circuit  by  the  circuit  BC  (fig.  636).  Jii 
then  the  multiplier  is  placed  horizontally,  so  that  its  current  is  in  the  same 
direction  as  in  the  movable  current,  if  the  latter  is  removed  and  the  cur- 


Fig.  636. 

rent  passes  so  that  the  direction  is  the  same  as  in  the  movable  part,  on 
removing  the  latter  it  quickly  approaches  the  multiplier,  which  verifies  the 
first  law. 

To  prove  the  second  law,  the  multiplier  is  turned  so  that  the  currents 
are  in  opposite  directions,  and  then  repulsion  ensues  (fig.  637). 


Fig.  637. 

In  a  rectilinear  current  each  elenient  of  the  current  repels  the  succeeding 
one,  and  is  itself  repelled. 

This  is  an  important  consequence  of  Ampere's  law,  and  may  be  experi- 
mentally demonstrated  by  the  following  arrangement,  which  was  devised 
by  Faraday.  A  U-shaped  piece  of  copper  wire,  whose  ends  dip  in  two 
separate  deep  mercury  cups,  is  suspended  from  one  end  of  a  delicate 

1 13 


730 


Dynamical  Electricity. 


[808- 


balance  and  suitably  equipoised.  When  the  mercury  cups  are  connected 
with  the  two  poles  of  a  battery,  the  wire  rises  very  appreciably,  and  sinks 
again  to  its  original. position  when  the  current  ceases  to  pass.  The  current 
passes  into  the  mercury  and  into  the  wire  ;  but  from  the  construction  of 
the  apparatus  the  former  is  fixed,  while  the  latter  is  movable,  and  is  ac- 
cordingly repelled. 

809.  Kaws  of  sinuous  currents.^ 77z^  action  of  a  simtoiis  current  is 
equal  to  that  of  a  rectilifuar  current  of  the  same  length  in  projection. 
This  principle  is  demonstrated  by  arranging  the  multiplier  vertically  and 


M 


Fig.  638. 

placing  near  it  a  movable  circuit  of  insulated  wire  half  sinuous  and  half 
rectihnear  (fig.  638).  It  will  be  seen  that  there  is  neither  attraction  nor 
repulsion,  showing  that  the  action  of  the  sinuous  portion  inn  is  equalled 
by  that  of  the  rectilinear  portion. 

An  application  of  this  principle  will  presently  be  met  with  in  the  appa- 
ratus called  solenoids  (822),  which  are  formed  of  the  combination  of  a 
sinuous  with  a  rectilinear  current. 


DIRECTION   OF  CURRENTS   BY   CURRENTS. 

810.  Action  of  an  infinite  current  on  a  current  perpendicular  to 
its  direction. — From  the  action  exerted  between  two  angular  currents 
(808)  the  action  of  a  fixed  and  infinite  rectilinear  current,  PO  (fig.  639),  on 
a  movable  current,  KH,  perpendicular  to  its  direction,  can  be  determined. 
Let  OK  be  the  perpendicular  common  to  KH  and  ?(),  which  is  null  if  the 
two  lines  PQ  and  KH  meet.  The  current  PQ  flowing  from  O  to  P  in  the 
direction  of  the  arrows,  let  us  first  consider  the  case  in  which  the  current 
KH  approaches  the  current  QP.  From  the  first  law  of  angular  currents 
(808)  the  portion  QO  of  the  current  PQ  attracts  the  current  KH,  because 
they  both  flow  towards  the  summit  of  the  angle  formed  by  their  directions. 
The  portion  PO,  on  the  contrary,  will  repel  the  current  KH,  for  here  the 
two  currents  are  in  opposite  directions  at  the  summit  of  the  angle.    If  then 


810] 


Direction  of  Currents  by  Querents. 


731 


mq  and  mp  stand  for  the  two  forces,  one  attractive  and  the  other  repulsive, 
which  act  on  the  current  KH,  and  which  are  necessarily  of  the  same  in- 
tensity, since  they  are  symmetrically  arranged  in  reference  to  the  two  sides 
of  the  point  O,  these  two  forces  may  be  resolved  into  a  single  force,  w;/, 


r 


~/^ 


.'■  y 


Fig.  639. 


Fig.  640. 


which  tends  to  move  the  current  KH  parallel  to  the  current  QP,  but  in  a 
contrary  direction. 

A  little  consideration  will  show  that  when  the  current  KH  is  below 
the  current  PQ,  its  action  will  be  the  opposite  of  what  it  is  when  above. 

On  considering  the  case  in  which  the  current  KH  moves  away  from 
PO  (fig.  640),  it  will  be  readily  seen  from  similar  considerations  that  it 
moves  parallel  to  this  current,  but  in  the  same  direction. 

Hence  follows  this  general  principle  :  A  Jinite  movable  current  which 
approaches  a  fixed  infinite  current  is  acted  on  so  as  to  move  in  a  direction 
parallel  and  opposite  to  that  of  the  fixed  current;  if  the  movable  currerU 
tends  from  the  fixed  current^  it  is  acted  on  so  as  to  move  parallel  to  the 
cnrretit  and  in  the  same  direction. 

It  follows  from  this,  that  if  a  vertical  current  is  movable  about  an 
axis,  XY,  parallel  to  its  direction  (figs.  641  and  642).  any  horizontal 
current,  PO,  will  have  the  effect  of  turning  the  movable  current  about 


Fig.  641. 


Fig.  642. 


its  axis,  tmtil  the  plane  of  the  axis  and  of  the  current  have  become  parallel 
to  PQ ;  the  vertical  current  stopping,  in  reference  to  its  axis,  on  the  side 
from  which  the  current  PQ  cotJtes  (fig.  64.1),  or  on  the  side  towards  which 
it  is  directed  (fig.  642),  according  as  the  vertical  current  descends  or  ascends 
— that  is,  according  as  it  approaches  or  moves  from  the  horizontal  axis. 
It  also  follows  from  this  principle  that  a  system  of  two  vertical  cur- 
rents rotating  about  a  vertical  axis  (fig.  643  and  644)  is  directed  by  a 
horizontal  current,  PQ,  in  a  plane  parallel  to  this  current,  when  one  of  the 


732 


Dynamical  Electricity. 


[810- 


vertical  currents  is  ascending  and  the  other  descending  (fig.  643),  but 
that  if  they  are  both  ascending  or  both  descending  (fig.  644),  they  are  not 
directed. 

;         Xi 


Fig.  643. 


Fig.  644. 


811.  Action  Of  an  infinite  rectilinear  current  on  a  rectangular 
or  circular  current. — It  is  easy  to  see  that  a  horizontal  infinite  current 
exercises  the  same  directive  action  on  a  rectangular  current  movable 
about  a  vertical  axis  (fig.  645),  as  what  has  been  above  stated.  For, 
from  the  direction  of  the  currents  indicated  by  the  arrows,  the  part  OY 
acts  by  attraction  not  only  on  the  horizontal  portion  YD  {law  of  angular 
currents),  but  also  on  the  vertical  portion  AD  (laiv  of  perpetidicular 
currents).  The  same  action  evidently  takes  place  between  the  part 
PY  and  the  parts  CY  and  BC.  Hence,  the  fixed  current  PQ  teitds  to 
direct  the  movable  rectangular  current  ABCD  into  a  position  parallel  to 
PQ,  and  such  that  in  the  wires  CD  and  PQ  the  direction  of  the  two  currejits 
is  the  sa7ne. 

This  principle  is  readily  demonstrated  by  placing  the  circuit  ABCD  on 
the  apparatus  with  two  supports  (fig.  652),  so  that  at  first  it  makes  an  angle 


Fig.  645. 


Fig.  646. 


with  the  plane  of  the  supports.  On  passing  below  the  circuit,  a  somewhat 
powerful  current  in  the  same  plane  as  the  supports,  the  movable,  part 
passes  into  that  plane.  It  is  best  to  use  the  circuit  in  fig.  652,  which  is 
astatic,  while  that  of  fig.  645  is  not. 

What  has  been  said  about  the  rectangular  current  in  fig.  645  applies 
also  to  the  circular  current  of  fig.  646,  and  is  demonstrated  by  the  same 
experiments. 


-813]  Rotation  of  Currents  by  Currents.  733 


ROTATION   OF   CURRENTS   BY   CURRENTS. 

8 1 2.  Rotation  of  a  finite  horizontal  current  by  an  infinite  horizontal 

rectilinear  current. — The  attractions  and  repulsions  which  rectangular 
currents  exert  on  one  another  may  readily  be  transformed  into  a  con- 
tinuous circular  motion.  Let  OA  (fig.  647)  be  a  current  movable  about 
the  point  O  in  a  horizontal  plane,  and  let  PQ  be  a  fixed  infinite  current 
also  horizontal.     As  these  two  currents  flow  in  the  direction  of  the  arrows, 


*-    0 


k/  1 


„-'A" 


A", 
P   ./'  M: 0 

N      "        * 

Fig.  647. 

it  follows  that  in  the  position  OA,  the  movable  current  is  attracted  by  the 
current  PQ,  for  they  are  in  the  same  direction.  Having  reached  the  posi- 
tion OA',  the  movable  current  is  attracted  by  the  part  NQ  of  the  fixed 
current,  and  repelled  by  the  part  PN.  Similarly,  in  the  position  OA'^it  is 
attracted  by  MQ  and  repelled  by  PM,  and  so  on  ;  from  which  follows  a 
continuous  rotatory  motion  in  the  direction  AA'A'^A'^'.  If  the  movable 
current,  instead  of  being  directed  from  O  towards  A,  were  directed  from 
A  towards  O,  it  is  easy  to  see  that  the  rotation  would  take  place  in  the 
contrary  direction.  Hence,  by  the  action  of  a  fixed  infinite  current,  PO, 
the  movable  current  OA  tends  to  a  continuous  motion  in  a  direction 
opposite  that  of  the  fixed  current. 

If,  both  currents  being  horizontal,  the  fixed  current  were  circular 
instead  of  being  rectilinear,  its  effect  would  still  be  to  produce  a  con- 
tinuous circular  motion.  For,  let  ABC  (fig.  648)  be  a  fixed  circular 
current,  and  mn  a  rectilinear  current  movable  about  the  axis  n,  both 
currents  being  horizontal.  These  currents,  flowing  in  the  direction  of 
the  arrows,  would  attract  one  another  in  the  angle  nAC,  for  they  both 
flow  towards  the  summit  (808).  In  the  angle  «AB,  on  the  contrary, 
they  repel  one  another,  for  one  goes  towards  the  summit  and  the  other 
moves  from  it.  Both  effects  coincide  in  moving  the  wire  mn  in  the  same 
direction  ACB. 

813.  Rotation  of  a  vertical  current  by  a  horizontal  circular 
current.— A  horizontal  circular  current,  acting  on  a  rectilinear  vertical 
current  also  imparts  to  it  a  continuous  rotatory  motion.  In  order  to 
show  this,  the  apparatus  represented  in  fig.  649  is  used. 

It  consists  of  a  brass  vessel,  round  which  are  rolled  several  coils  of 
insulated  copper  wire,  through  which  a  current  passes.  In  the  centre  of 
the  vessel  is  a  brass  support,  a,  terminated  by  a  small  cup  containing 
mercury.     In  this  dips  a  pivot  supporting  a  copper  wire,  bb,  bent  at  its 


734  Dynamical  Electricity.  [813- 

ends  in  two  vertical  branches,  which  are  soldered  to  a  very  light 
copper  ring  immersed  in  acidulated  water  contained  in  the  vessel.  A 
current  entering  through  the  wire  w,  reaches  the  wire  A,  and  having 
made  several  circuits,  terminates  at  B,  which  is  connected  by  a  wire 
underneath  with  the  lower  part  of  the  column  a.  Ascending  in  this 
column,  it  passes  by  the  wires  bb  into  the  copper  ring,  into  the  acidulated 
water,  and  into  the  sides  of  the  vessel,  whence  it  returns  to  the  battery 
by  the  strip  D.  The  current  being  thus  closed,  the  circuit  bb  and  the 
ring  tend  to  turn  in  a  direction  contrary  to  that  of  the  fixed  current,  a 
motion  due  to  the  action  of  the  circular  current  on  the  current  in  the  ver- 
tical branches  bb ;  for,  as  follows  from  the  two  laws  of  angular  currents,  the 
branch  b  on  the  right  is  attracted  by  the  portion  A  of  the  fixed  current, 


Fig.  649. 

and  the  branch  b  on  the  left  is  attracted  in  the  contrary  direction  by  the 
opposite  part,  and  these  two  motions  coincide  in  giving  the  ring  a  con- 
tinuous rotatory  motion  in  the  same  direction.  The  action  of  the  circular 
current  on  the  horizontal  part  of  the  circuit  bb  would  manifestly  tend  to 
turn  it  in  the  same  direction ;  but  from  its  distance  it  may  evidently  be 
neglected. 

814.  Rotation  of  xnagrnets  by  currents.  —  Faraday  has  proved  that 
currents  impart  the  same  rotatory  motions  to  magnets  which  they  do  to 
currents.  This  may  be  shown  by  means  of  the  apparatus  represented  in 
fig.  650.  It  consists  of  a  large  glass  vessel,  almost  filled  with  mercury.  In 
the  centre  of  this  is  immersed  a  magnet  A  about  8  inches  in  length,  which 
projects  a  little  above  the  surface  of  the  mercury,  and  is  loaded  at  the 
bottom  with  a  platinum  cylinder.  At  the  top  of  the  magnet  is  a  small 
cavity  containing  mercury ;  the  current  ascending  the  column  7n  passes 
into  this  cavity  by  the  rod  C.  From  the  magnet  it  passes  by  the  mercury 
to  a  copper  ring  G,  whence  it  emerges  by  the  column  11.  When  this  takes 
place  the  magnet  begins  to  rotate  round  its  own  axis  with  a  velocity 
depending  on  its  magnetic  power  and  on  the  intensity  of  the  current. 

Instead  of  making  the  magnet  rotate  on  its  axis,  it  may  be  caused  to 
rotate  round  a  line  parallel  to  its  axis  by  arranging  the  experiment  as 
shown  in  fig.  651. 

This  rotatory  motion  is  readily  intelligible  on  Ampere's  theory  of  mag- 
netism, which  will  be  subsequently  explained  (827),  according  to  which 


-815]    Action  of  the  Earth  a? id  of  Magnets  on  Querents.     735 

magnets  are  traversed  on  their  surface  by  an  infinity  of  circular  currents 
in  the  same  direction,  in  planes  perpendicular  to  the  axis  of  the  magnet. 
At  the  moment  at  which  the  current  passes  from  the  magnet  into  the  mer- 
cury, it  is  divided  on  the  surface  of  the  mercury  into  an  infinity  of  rectilinear 
currents  proceeding  from  the  axis  of  the  magnet  to  the  circumference  of 
the  glass.  Now  each  of  these  currents  acts  on  the  currents  of  the  magnet 
in  the  same  manner  as,  in  fig.  647,  the  rectilinear  current  uui  acts  upon 
the  circular  current  CAB  ;  that  is  to  say,  that  the  circle  CAB  representing 
one  of  the  currents  of  the  magnet,  there  is  attraction  in  the  angle  ;^AC, 


Fig.  650. 


Fig.  65] 


and  repulsion  in  the  angle  «AB,  and,  consequently,  rotation  of  the  magnet 
round  its  axis.  The  action  of  the  current  merely  affects  the  upper  part  of 
the  magnet,  and  if  the  north  pole  is  uppermost,  as  in  the  figure,  the  rota- 
tion is  from  west  to  east.  If  the  north  pole  is  below,  or  the  direction 
of  the  current  be  altered,  the  rotation  of  the  magnet  is  in  the  opposite 
direction. 


ACTION  OF  THE  EARTH  AND  OF  MAGNETS  ON  CURRENTS. 

815.  Directive  action  of  mag-nets  on  currents. — Not  only  do  currents 
act  upon  magnets,  but  magnets  also  act  upon  currents.  In  Oersted's 
fundamental  experiment  (fig.  607),  the  magnet  being  movable  while  the 
current  is  fixed,  the  former  is  directed  and  sets  at  right  angles  with  the 
current.  If,  on  the  contrary,  the  magnet  is  fixed  and  the  current  mova- 
ble, the  latter  is  directed  and  sets  across  the  direction  of  the  magnet. 
This  may  be  illustrated  by  the  apparatus  represented  in  fig.  652.  This  is 
the  original  form  of  Ampere's  stand,  and  is  frequently  used  in  experimental 
demonstration.  It  needs  no  explanation.  The  circuit  which  the  current 
traverses  is  movable,  and  below  its  lower  branch  a  powerful  bar  magnet 
is  placed;  the  circuit  immediately  begins  to  turn,  and  stops  after  some 
oscillations  in  a  plane  perpendicular  to  the  axis  of  the  magnet. 


71^ 


Dynamical  Electricity. 


[815- 


For  demonstrating  the  action  of  magnets  upon  currents,  and  indeed  for 
establishing  the  fundamental  laws  of  electrodynamics,  a  small  apparatus, 
known  as  De  la  'K\v€s  fioating  battery,  is  well  adapted.  It  consists  of  a 
small  Daniell's  element,  contained  in  a  glass  tube  attached  to  a  cork,  so 
that  it  can  float  freely  on  water.     The  plates  are  connected  with  minute 


Fig.  652. 

mercury  cups  on  the  cork  float ;  and  with  these  can  be  connected  either 
circular  or  rectangular  wires,  coils,  or  solenoids  ;  they  are  then  traversed 
by  a  current,  and  can  be  subjected  to  the  action  either  of  magnets  or  of 
currents. 

816.  Rotation  of  currents  by  magrnets. — Not  merely  can  currents  be 
directed  by  magnets,  but  they  may  also  be  made  to  rotate,  as  is  seen  from 
the  following  experiment,  devised  by  Faraday,  fig.  653.  On  a  base  with 
levelling  screws,  and  resting  on  an  ivory  support,  is  a  copper  rod,  BD. 
It  is  surmounted  in  part  of  its  length  by  a  magnetised  bundle,  AB,  and 
at  the  top  is  a  rhercury  cup.  A  copper  circuit,  EF,  balanced  on  a  steel 
point,  rests  in  the  cup,  and  the  other  ends  of  the  circuit,  which  terminate 
in  steel  points,  dip  in  an  annular  reservoir  full  of  mercury. 

The  apparatus  being  thus  arranged,  the  current  from  4  or  5  Bunsen's 
elements  enters  at  the  binding  screw  b  ;  it  thence  ascends  in  the  rod  D, 
redescerjds  by  the  two  branches,  reaches  the  mercury  by  the  steel  points, 
whence  it  passes  by  the  framework,  which  is  of  copper,  to  the  battery  by 
the  binding  screw  a.  If  now  the  magnetised  bundle  be  raised,  the  circuit 
EF  rotates  either  in  one  direction  or  the  other  according  to  the  pole  by 
which  it  is  influenced.  This  rotation  is  due  to  currents  assumed  to  cir- 
culate round  magnets,  currents  which  act  on  the  vertical  branches  EF  in 
the  same  way  as  the  circular  current  on  the  arm  in  fig.  649. 

In  this  experiment  the  magnetised  bundle  may  be  replaced  by  a 
solenoid  (822)  or  by  an  electromagnet,  in  which  case  the  two  binding 


-817] 


Electrodynamic  Rotation  of  Liquids. 


717 


screws  in  the  base  of  the  apparatus  on  the  left  give  entrance  to  the  current 
which  is  to  traverse  the  solenoid  or  electromagnet. 

817.  Electrodynamic  and  electro- 
mag-netic  rotation   of  liquids. — In  the 

experiments  hitherto  discussed  rotation 
is  produced  by  causing  a  fixed  current  to 
act  upon  a  movable  linear  current.  The 
condition  of  a  linear  current  is  not  neces- 
sary. Fig.  654  represents  an  apparatus 
devised  by  M.  Bertin  to  show  the  electro- 
dynamic  and  electromagnetic  rotation  of 
liquids.  This  apparatus  consists  of  an 
annular  earthern  vessel,  VV  ;  that  is  to 
say,  it  is  open  in  the  centre  so  as  to  be 
traversed  by  a  coil,  H.  This  rests  on  a 
board  which  can  be  raised  along  two 
columns,  E  and  I,  and  which  are  fixed  by 
means  of  the  screws  KK.  Round  the 
vessel  VV  is  a  second  larger  coil,  G,  fixed 
on  the  columns  SS.  The  vessel  VV  rests 
on  the  lower  plane.  In  the  centre  of  the 
coil  there  is  a  bar  of  soft  iron,  x,  which 
makes  an  electromagnet. 

The  vessel .  VV  contains  acidulated 
water,  and  in  the  liquid  are  plunged  two 
cylindrical  copper  plates,  e  and  /,  soldered 
to  copper  wires,  e'  and  /',  which  convey 
the  current  of  a  battery  of  four  couples 
through  the  rods  E  and  I. 

The  whole  system  is  arranged  on  a  larger  base,  on  the  left  of  which  is 
a  commutator  represented  afterwards  on  a  larger  scale  (fig.  655).  With 
the  base  of  the  columns  E,  I,  S,  and  S',  are  connected  four  copper  strips, 
three  of  which  lead  to  the  commutator  and  the  fourth  to  the  binding 
screw  A,  which  receives  the  wire  from  the  positive  pole. 

These  details  being  premised,  the  following  three  effects  may  be 
obtained  with  this  apparatus: — (i),  the  action  of  the  coil  G  alone;  (2), 
the  action  of  the  electromagnet  H  alone ;  (3),  the  simultaneous  action  of 
the  coil  and  of  the  electromagnet. 

I.  Fig.  654  represents  the  apparatus  arranged  for  the  first  effect.  The 
current  coming  by  the  binding  screw  A  attains  the  column  S',  which  leads 
it  to  the  coil  G,  with  regard  to  which  it  is  left — that  is,  in  a  contrary  direction 
to  the  hands  of  a  watch.  Then  descending  by  the  column  S,  it  reaches 
the  commutator,  which  leads  it  by  the  plate  marked  centripete  to  the 
column  E  and  to  the  electrode  e'.  The  current  here  traverses  the 
liquid  from  the  circumference  to  the  centre,  attains  the  electrode  /,  the 
column  I,  and  by  the  intervention  of  the  plate  centrifuge  the  central  piece 
of  the  commutator.      This  transmits  it  finally  to  the  negative  binding 


Fig.  653. 


738 


Dynamical  Electricity. 


[817- 


screw,  which  leads  it  to  the  battery.      The  hquid  then  commences   a 
direct  rotatory  motion — that  is  to  say,  in  the  same  direction  as  the  coil. 

If  the  direction  of  the  current  in  the  liquid  is  centrifiigal — that  is,  pro- 
ceeds from  the  centre  to  the  circumference^-the  rotation  is  inverse ;  that 
is,  is  in  the  opposite  direction  to  that  of  the  coil.  In  both  cases  the 
rotations  may  be  shown  to  those  at  a  distance  by  means  of  small  flags, 


Fig.  654. 


/",/,  fixed  on  discs  of  cork  which  float  on  the  liquid,  and  which  are  coated 
with  lampblack  to  prevent  adherence  by  capillary  attraction  between  the 
discs  and  the  electrodes  e  and  i. 

II.  To  experiment  with  the  electromagnet  alone,  the  positive  wire  of 
the  battery  is  joined  with  the  binding  screw  C,  and  the  binding  screws 
D  and  B  are  joined  by  a  copper  wire.  The  current  first  passes  into  the 
electromagnet  H,  then,  reaching  the  commutator  by  the  binding  screw  B, 
passes  into  the  centripetal  plate,  whence  it  rises  in  the  column  E,  tra- 
verses the  liquid  in  the  same  direction  as  at  first,  reascends  by  the 
column  I,  and  from  thence  to  the  centre  of  the  commutator  and  the 
negative  binding  screw  which  leads  it  to  the  battery. 

If  the  north  pole  of  the  electromagnet  is  at  the  same  height  as  the 
glass  vessel,  as  in  the  figure,  the  Amperian  currents  move  in  the  opposite 
direction  to  the  hands  of  a  watch,  and  the  floats  then  move*  in  the  same 
direction  as  above ;  and  if  the  electromagnet  is  raised  until  the  neutral 
line  is  at  the  same  height  as  the  vessel,  the  floats  stop;  if  it  is  above  them, 
the  floats  mote  again,  but  in  the  opposite  direction. 

III.  To  cause  the  coil  and  the  electromagnet  to  act  simultaneously, 
the  positive  wire  of  the  battery  is  attached  at  C,  and  the  binding  screws  D 
and  A  are  connected  by  a  conductor.  Hence,  after  having  traversed  the 
coil  H,  the  current  arrives  from  D,  and  the  binding  screw  A,  whence  it 


-819]  Bertiiis  Commutator.  •  739 

traverses  exactly  the  same  circuit  as  in  the  first  experiments.  The  effects 
are  the  same,  though  more  intense ;  the  action  of  the  coil  and  the  electro- 
magnet being  in  the  same  direction. 

818.  Bertin's  commutator. — Commutators  are  apparatus  by  which 
the  direction  of  currents  may  be  changed  at  pleasure,  or  by  which  they 
may  be  opened  or  closed.  Bertin's  has  the  advantage  of  at  once  showing 
the  direction  of  the  current.  It  consists  of  a  small  base  of  hard  wood  on 
which  is  an  ebonite  plate,  which,  by  means  of  the  handle  m  (fig.  655),  is 


Fig.  655. 

turned  about  a  central  axis,  between  two  stops,  c  and  c'.  On  the  disc  are 
fixed  two  copper  plates,  one  of  which  o  is  always  positive,  being  connected 
by  the  axis  and  by  a  plate,  +  ,  with  the  binding  screw  P,  which  receives  the 
positive  electrode  of  the  battery ;  the  other,  z>,  bent  in  the  form  of  a  horse- 
shoe, is  connected  by  friction  below  the  disc  witha  plate  — which  passes  to 
the  negative  electrode  N.  On  the  opposite  side  of  the  board  are  two 
binding  screws,  b  and  b\  to  which  are  adapted  two  elastic  metal  plates,  r 
and  7''. 

These  details  being  premised,  the  disc  being  turned  as  shown  in  the 
figure,  the  current  coming  by  the  binding  screw  T  passes  into  the  piece  0, 
the  plate  r  and  the  binding  screw  b,  which  by  a  second  plate,  or  by  a 
copper  wire,  leads  it  to  the  apparatus  of  fig.  654,  or  any  other.  Then 
returning  to  the  binding  screw  ^,  the  current  attains  the  plate  r',  the  piece 
/  e,  and  ultimately  the  binding  screw  N,  which  returns  it  to  the  battery. 

If  the  disc  is  turned  so  that  the  handle  is  half  way  between  c  and  c\  the 
pieces  0  and  /  e  being  no  longer  in  contact  with  the  plates  r  and  r,  the 
current  does  not  pass.  If ;;/  is  turned  as  far  as  c,  the  plate  0  touches  r\ 
the  current  thus  passes  first  to  b'  and  returns  by  ^  ;  it  is  therefore 
reversed. 

819.  Directive  action  of  tbe  earth  on  vertical  currents. — The  earth, 
which  exercises  a  directive  action  on  magnets  (65 1),  acts  also  upon  currents, 
giving  them,  in  some  cases,  a  fixed  direction,  in  others  a  continuous 
rotatory  motion,  according  as  their  currents  are  arranged  in  a  vertical  or 
horizontal  direction. 

The  first  of  these  two  actions  may  be  thus  enunciated  :  Every  vertical 
current  movable  about  an  axis  parallel  to  itself^  places  itself  under  the 
directive  action  of  the  earth  in  a  plane  through  this  axis  perpendicular  to 


740 


Dynamical  Electricity. 


[819- 


the  magnetic  meridian^  and  stops,  after  some  oscillations,  otj  the  east  of  its 

axis  of  rotation  when  it  is  descending.,  and  on  the  west  when  it  is  ascending. 

This  may  be  demonstrated  by  means  of  the  apparatus  represented  in 

fig.  657,  which  consists  of  two  brass  vessels  of  somewhat  different  diameters. 


i-'ig.  656. 


Fig.  657. 


The  larger,  a,  about  13  inches  in  diameter,  has  an  aperture  in  the  centre, 
through  which  passes  a  brass  support,  b,  insulated  from  the  vessel  a,  but 
communicating  with  the  vessel  K.  This  column  terminates  in  a  small 
cup,  in  which  a  light  wooden  rod  rests  on  a  pivot.  At  one  end  of  this  rod 
a  fine  wire  is  coiled,  each  end  of  which  dips  in  acidulated  water,  with 
which  the  two  vessels  are  respectively  filled. 

The  current  arriving  by  the  wire  m  passes  to  a  strip  of  copper,  which  is 
connected  underneath  the  base  of  the  apparatus  with  the  bottom  of  the 
column  b.  Ascending  in  this  column,  the  current  reaches  the  vessel  K, 
and  the  acidulated  water  which  it  contains  ;  it  ascends  from  thence  in  the 
wire  c,  redescends  by  the  wire  e,  and  traversing  the  acidulated  water,  it 
reaches  the  sides  of  the  vessel  a,  and  so  back  to  the  battery  through  the 
wire  n. 

The  current  being  thus  closed,  the  wire  e  moves  round  the  column  b, 
and  stops  to  the  east  of  it,  when  it  descends,  as  is  the  case  in  the  figure  ; 
but  if  it  ascends,  which  is  effected  by  transmitting  the  current  by  the  wire 
n,  the  wire  e  stops  to  the  west  of  the  column  b,  in  a  position  directly 
opposite  to  that  which  it  assumes  when  it  is  descending. 

If  the  rod  with  a  single  wire,  in  fig.  657,  be  replaced  by  one  with  two 
wires,  as  in  fig.  656,  the  rod  will  not  move,  for  as  each  wire  tends  to  place 
itself  on  the  east  of  the  column  b,  two  equal  and  contrary  effects  are 
produced,  which. counterbalance  one  another. 

820.  Action  of  tbe  eartb  on  horizontal  currents  movable  about  a 
vertical  axis. — The  action  of  the  earth  on  horizontal  currents,  is  not 
directive,  h\it  gives  them  a  continuous  rotatory  motion  frotn  the  east  to  the 
west  when  the  horizotital  current  moves  away  font  the  axis  of  rotatioji. 
and  frotn  the  west  to  the  east  when  it  is  directed  towards  this  axis. 


821] 


Action  of  the  Earth  on  Closed  Currents. 


741 


This  may  be  illustrated  by  means  of  the  apparatus  represented  in  fig. 
658,  which  only  differs  from  tha^  of  fig.  657  in  having  but  one  vessel.  The- 
current  ascending  by  the  column  a,  traverses  the  two  wires  cc,  and  descends 
by  the  wires  bb,  from  which  it  regains  the  pile  ;  the  circuit  bccb  then  begins 
a  continuous  rotation,  either  from  the  east  to  the  west,  or  from  the  west  to 
the  east,  according  as  in  the  wires  cc  the  current  goes  from  the  centre,  as 
is  the  case  in  the  figure  ;  or  according  as  it  goes  towards  it,  which  is  the 
case  when  the  current  enters  by  the  wire  in  instead  of  by  11.  But  we  have 
seen  (819)  that  the  action  of  the  earth  on  the  vertical  wires  bb  is  destroyed  : 
hence  the  rotation   is  that  produced  by  the  action  on   the   horizontal 


Fig.  658. 

branches  cc.  This  rotatory  action  of  the  terrestrial  current  on  horizontal 
currents  is  a  consequence  of  the  rotation  of  a  finite  horizontal  by  an  infinite 
horizontal  current  (812). 

821.  Directive  action  of  the  eartb  on  closed  currents  movable 
about  a  vertical  axis. — If  the  current  on  which  the  earth  acts  is  closed, 
whether  it  be  rectangular  or  circular,  the  result  is  not  a  continuous  rotation, 
but  a  directive  action,  as  in  the  case  of  vertical  currents  (819),  in  virtue  ot 
which  the  current  places  itself  in  a  plane  perpe?idiciilar  to  the  magnetic 
ineridiajt,  so  that,  for  an  observer  looking  at  the  north,  it  is  descendiiig  on 
the  east  of  its  axis  of  rotation,  and  ascending  on  the  west. 

This  property,  which  can  be  shown  by  means  of  the  apparatus  repre- 
sented in  fig.  658,  is  a  consequence  of  what  has  been  said  about  horizontal 
and  vertical  currents.  For  in  the  closed 
circuit  BA,  the  current  in  the  upper 
and  lower  parts  tends  to  turn  in  opposite 
directions,  from  the  law  of  horizontal 
currents  (820);  and  hence  is  in  equi- 
librium, while  in  the  lateral  parts  the 
current  on  the  one  side  tends  towards  the 
east,  and  on  the  other  side  to  the  west, 
from  the  law  of  vertical  currents  (819). 

From  the  directive  action  of  the  earth 
on  currents,  it  is  necessary,  in  most  ex- 
periments, to  obviate  this  action.  This 
is  effected  by  arranging  the  movable 
circuit  symmetrically  about  its  axis  of 
rotation,  so  that  the  directive  action  of  the  earth  tends  to  turn  them  in 


Fig.  65c. 


742  Dynamical  Electricity.  [821- 

opposite  directions,  and  hence  destroys  them.  This  condition  is  fulfilled 
in  the  circuit  represented  in  fig,  652.  Such  circuits  are  hence  called 
astatic  circuits. 

SOLENOIDS. 

822.  structure  of  a  solenoid. — A  solenoid  is  a  system  of  equal  and 
parallel  circular  currents  formed  of  the  same  piece  of  covered  copper  wire, 
and  coiled  in  the  form  of  a  helix  or  spiral,  as  represented  in  fig.  660.     A 

^  solenoid,  however,   is   only  complete 

?Vyr?QVA7Qr?^?9^y?r^n      when  part  of  the  wire  BC  passes  in 
C—  VjyjUVJUVUUUVVU  the  direction  of  the  axis  in  the  interior 

F^s-  660.  of  thg  helix.     With  this  arrangement, 

when  the  circuit  is  traversed  by  a  current,  it  follows  from  what  has  been 
said  about  sinuous  currents  (780)  that  the  action  of  a  solenoid  in  a  longi- 
tudinal direction,  AB,  is  counterbalanced  by  that  of  the  rectilinear  current 
BC.  This  action  is  accordingly  null  in  the  direction  of  the  length,  and 
the  action  of  a  solenoid  in  a  direction  perpendicular  to  its  axis  is  exactly 
equal  to  that  of  a  series  of  equal  parallel  currents. 

823.  ilction  of  currents  on  solenoids. — What  has  been  said  of  the 
action  of  fixed  rectilinear  currents  on  finite  rectangular,  or  circular  cur- 
rents (812),  applies  evidently  to  each  of  the  circuits  of  a  solenoid,  and 
hence  a  rectiUnear  current  must  tend  to  direct  these  circuits  parallel  to 
itself.  To  demonstrate  this  fact  experimentally,  a  solenoid  is  constructed 
as  shown  in  fig.  661,  so  that  it  can  be  suspended  by  two  pivots  in  the 
cups  a  and  c  of  the  apparatus  represented  in  fig.  633.    The  solenoid  is  then 


Fig.  66 


movable  about  a  vertical  axis,  and  if  beneath  it  a  rectilinear  current  QP 
be  passed,  which  at  the  same  time  traverses  the  wires  of  the  solenoid,  the 
latter  is  seen  to  turn  and  set  at  right  angles  to  the  lower  current — that  is, 
in  such  a  position  that  its  circuits  are  parallel  to  the  fixed  current ;  and, 
further,  in  the  lower  part  of  each  of  the  circuits  the  current  is  in  the  same 
direction  as  in  the  rectifinear  wire 

If,  instead  of  passing  a  rectihnear  current  below  the  solenoid,  it  is 
passed  vertically  on  the  side,  an  attraction  or  repulsion  will  take  place, 


-826] 


Action  of  Solenoids. 


743 


according,  as  in  the  vertical  wire,  and  in  the  nearest  part  of  the  solenoid, 
the  two  currents  are  in  the  same  or  in  contrary  directions. 

824.  Directive  action  of  tlie  eartb  on  solenoids. — If  a  solenoid  be 
suspended  in  the  two  cups  (fig.  633),  not  in  the  direction  of  the  magnetic 
meridian,  and  a  current  be  passed  through  the  solenoid,  the  latter  will 
begin  to  move,  and  will  finally  set  in  such  a  position  that  its  axis  is  in 
the  direction  of  the  magnetic  meridian.  If  the  solenoid  be  removed,  it 
will,  after  a  few  oscillations,  return,  so  that  its  axis  is  in  the  magnetic 
meridian.  Further,  it  will  be  found  that  in  the  lower  half  of  the  coils  of 
which  the  solenoid  consists,  the  direction  of  the  current  is  from  east  to 
west ;  in  other  words,  the  current  is  descending  on  that  side  of  the  coil 
turned  towards  the  east,  and  ascending  on  the  west.  The  directive 
action  of  the  earth  on  solenoids  is  accordingly  a  consequence  of  that 
which  it  exerts  on  circular  currents.  In  this  experiment  the  solenoid  is 
directed  like  a  magnetic  needle,  and  the  north  pole,  as  in  magnets,  is  that 
end  which  points  towards  the  north,  and  the  soiith  pole  that  which  points 
towards  the  south.  This  experiment  may  be  well  made  by  means  of  a 
solenoid  fitted  on  a  De  la  Rive's  floating  battery. 

825.  IVEutual  action  of  magnets  and  solenoids. — Exactly  the  same 
phenomena  of  attraction  and  repulsion  exist  between  solenoids  and 
magnets  as  between  magnets  themselves.  For  if  to  a  movable  solenoid 
traversed  by  a  current  one  of  the  poles  of  a  magnet  be  presented,  at- 
traction or  repulsion  will  take  place,  according  as  the  poles  of  the  magnet 
and  of  the  solenoid  are  of  contrary  or  of  the  sam.e  name.  The  same 
phenomenon  takes  place  when  a  solenoid  traversed  by  a  current  and  held 
in  the  hand  is  presented  to  a  movable  magnetic  needle.  Hence  the  law 
of  attractions  and  repulsions  applies  exactly  to  the  case  of  the  mutual 
action  of  solenoids  and  of  magnets. 

826.  Mutual  actions  of  solenoids.  -When  two  solenoids  traversed 
by  a  powerful  current  are  allowed  to  act  on  each  other,  one  of  them  being 


^^>>^^ 


Fig.  662. 


held  in  the  hand,  and  the  other  being  movable  about  a  vertical  axis,  as 
shown  in  fig.  662,  attraction  and  repulsion  will  take  place  just  as  in  the 
case  of  two  magnets.     These  phenomena  are  readily  explained  by  refer- 


744 


Dynamical  Electricity. 


[826 


ence  to  what  has  been  said  about  the  mutual  action  of  the  currents, 
bearing  in  mind  the  direction  of  the  currents  in  the  extremities  presented 
to  each  other. 

827.  Ampere's  theory  of  magrnetism. — Ampere  propounded  a 
theory,  based  on  the  analogy  which  exists  between  solenoids  and 
magnets,  by  which  all  magnetic  phenomena  may  be  referred  to  electro- 
dynamical  principles. 

Instead  of  attributing  magnetic  phenomena  to  the  existence  of  two 
fluids,  Ampere  assumes  that  each  individual  molecule  of  a  magnetic 
substance  is  traversed  by  a  closed  electric  current.  It  is  further  assumed 
that  these  molecular  currents  are  free  to  move  about  their  centres. 
The  coercive  force,  however,  which  is  little  or  nothing  in  soft  iron, 
but  considerable  in  steel,  opposes  this  motion,  and  tends  to  keep 
them  in  any  position  in  which  they  happen  to  be.  When  the  magnetic 
substance  is  not  magnetised,  these  molecular  currents,  under  the  influ- 
ence of  their  mutual  attractions,  occupy  such  positions  that  their  total 
action  on  any  external  substance  is  null.  Magnetisation  consists  in 
giving  to  these  molecular  currents  a  parallel  direction,  and  the  stronger 
the  magnetising  force  the  more  perfect  the  parallelism.  The  limit  of 
magnetisation  is  attained  when  the  currents  are  completely  parallel. 

The  resultant  of  the  actions  of  all  the  molecular  currents  is  equivalent 
to  that  of  a  single  current  which  traverses  the  outside  of  a  magnet. 

For  by  inspection  of  fig.  663, 
in  which  the  molecular  cur- 
r'^S!^     0' — -"""^-v  rents   are   represented  by  a 

series  of  small  internal  circles 
in  the  two  ends  of  a  cylin- 
drical bar,  it  will  be  seen 
that  the  adjacent  parts  of  the 
currents  oppose  one  another, 
and  cannot  exercise  any  ex- 
ternal electrodynamic  action. 
i\  1.    W  ^>y  This  is  not  the  case  with  the 

surface :  there  the  molecular 
^^"     ^'  currents  at  ab  are  not  neutra- 

lised by  other  currents,  and  as  the  points  abc  are  infinitely  near,  they 
form  a  series  of  elements  in  the  same  direction  situated  in  planes  perpen- 
dicular to  the  axis  of  the  magnet,  and  which  constitute  a  true  solenoid. 

The  direction  of  these  currents  in  magnets  can  be  ascertained  by  con- 
sidering the  suspended  solenoid  (fig.  662).  If  we  suppose  it  traversed  by 
a  current,  and  in  equilibrium  in  the  magnetic  meridian,  it  will  set  in  such 
a  position  that  in  the  lower  half  of  each  coil  the  current  flows  from  east  to 
west.  We  may  then  establish  the  following  rule.  At  the  north  pole 
{Eftglish)  of  a  magnet  the  direction  of  the  Amperian  currents  is  opposite 
that  of  the  hands  of  a  watch,  and  at  the  south  pole  the  direction  is  the 
same  as  that  of  the  hands. 

828.  Terrestrial  current. — In  order  to  explain  on  this  supposition 
terrestrial  magnetic  effects,  the  existence  of  electrical  currents  is  assumed 


-829]  Magnetisation  by  Currents.  745 

which  continually  circulate  round  our  globe  from  east  to  west  perpen- 
dicular to  the  magnetic  meridian. 

The  resultant  of  their  action  is  a  single  current  traversing  the  magne- 
tic equator  from  east  to  west.  These  currents  are  supposed  to  be  thermo- 
electric currents  due  to  the  variations  of  temperature  caused  by  the 
successive  influence  of  the  sun  on  the  different  parts  of  the  globe  from 
east  to  west. 

These  currents  direct  magnetic  needles ;  for  a  suspended  magnetic 
needle  comes  to  rest  when  the  molecular  currents  on  its  under  surface  are 
parallel;  and  in  the  same  direction  as  the  terrestrial  currents.  As  the  mole- 
cular currents  of  a  magnet  are  at  right  angles  to  the  direction  of  its  length, 
the  needle  places  its  greatest  length  at  right  angles  to  east  and  west,  or 
north  and  south.  Natural  magnetisation  is  probably  imparted  in  the  same 
way  to  iron  minerals. 


CHAPTER   V. 


MAGNETISATION   BY  CURRENTS.      ELECTROMAGNETS.      ELECTRIC 
TELEGRAPHS. 

829,  Magrnetisation  by  currents. — From  the  influence  which  cur- 
rents exert  upon  magnets,  turning  the  north  pole  to  the  left  and  the  south 
pole  to  the  right,  it  is  natural  to  think  that  by  acting  upon  magnetic  sub- 
stances in  the  natural  state  the  currents  would  tend  to  separate  the  two 
magnetisms.  In  fact  when  a  wire  traversed  by  a  current  is  immersed 
in  iron  filings,  they  adhere  to  it  in  large  quantities,  but  become  detached 
as  soon  as  the  current  ceases,  while  there  is  no  action  on  any  other  non- 
magnetic metal. 

The  action  of  currents  on  magnetic  substances  is  well  seen  in  an  ex- 
periment due  to  Ampere,  which  consists  in  coiling  an  insulated  copper 
wire  round  a  glass  tube,  in  which  there  is  an  unmagnetised  steel  bar.  If 
a  current  be  passed  through  the  wire,  even  for  a  short  time,  the  bar 
becomes  strongly  magnetised. 

If,  as  we  have  already  seen,  the  discharge  of  a  Leyden  jar  be  trans- 
mitted through  the  wire,  by  connecting  one  end  with  the  outer  coating, 
and  the  other  with  the  inner  coating,  the  bar  is  also  magnetised.  Hence 
both  voltaic  and  frictional  electricity  can  be  used  for  magnetising. 


Fig.  664. 

If  in  this  experiment  the  wire  be  coiled  on  the  tube  in  such  a  manner 
that  when  it  is  held  vertically  the  downward  direction  of  the  coils  is  from 
right  to  left  on  the  side  next  the  observer,  this  constitutes  a  right-handed 
or  dextrorsal  spiral  or  helix  (fig.  664),  of  which  the  ordinary  screw  is  an 

K  K 


746 


Dynamical  Electricity. 


[829- 


example.     In  a  lefl-handed  or  sinistrorsal  helix  the  coiling  is  in  the 
opposite  direction,  that  is  from  left  to  right  (fig.  665). 

In  a  right-handed  spiral  the  north  pole  is  at  the  end  at  which  the 


Fig.  665. 

current  emerges,  and  the  south  pole  at  the  end  at  which  it  enters ;  the 
reverse  is  the  case  in  a  left-handed  spiral.  But  whatever  the  direction  of 
the  coiling,  the  polarity  is  easily  found  by  the  following  rule  :  If  a  person 
swimming  in  the  current  look  at  the  axis  of  the  spiral  the  Jiorth  pole  is 

always  on  his  left.  If  the  wire  be 
not  coiled  regularly,  but  its  direction 
be  reversed,  at  each  change  of 
direction  a  consequent  pole  (643)  is 
formed  in  the  magnet.  The  sim- 
plest method  of  remembering  the 
polarity  produced  is  as  follows : 
Whatever  be  the  nature  of  the  helix, 
either  right  or  left-handed,  if  the  end 
facing  the  observer  has  the  current 
flowing  in  the  direction  of  the 
hands  of  a  watch,  it  is  a  sonth 
pole  and  vice  versa.  The  same 
polarity  is  produced,  whether  or  not 
there  is  an  iron  core  within  the  helix. 
The  nature  of  the  tube  on  which 
the  helix  is  coiled  is  not  without 
influence.  Wood  and  glass  have 
o  effect,  but  a  thick  cylinder  of 
copper  may  greatly  affect  the  action 
of  the  current  unless  the  copper  be 
slit  longitudinally.  This  action  will 
be  subsequently  explained.  The 
same  is  the  case  with  iron,  silver, 
and  tin. 

In  order  to  magnetise  a  steel 
bar  by  mearts  of  electricity,  it  need  not  be  placed  in  a  tube,  as  shown  in 
figs.  664  and  665.  It  is  sufficient  to  coil  round  it  a  copper  wire  covered 
with  silk,  cotton,  or  gutta-percha  in  order  to  insulate  the  circuits  from  one 
another.  The  action  of  the  current  is  thus  multiplied,  and  a  feeble  current 
is  sufficient  to  produce  a  powerful  magnetising  effect. 

830.  Slectromagrnets. — Electromagnets  are  bars  of  soft  iron  which, 
under  the  influence  of  a  voltaic  current,  become  magnets  ;  but  this 
magnetism  is  only  temporary,  for  the  coercive  force  of  perfectly  soft  iron 
is  null,  and  the  two  magnetisms  neutralise  each  other  as  soon  as  the 
current  ceases  to  pass  through  the  wire.     If,  however,  the  iron  is  not 


-830]  Electromagnets.  747 

quite  pure,  it  retains  more  or  less  traces  of  magnetism.  The  electro- 
magnets have  the  horse-shoe  form,  as  shown  in  fig.  666,  and  a  copper 
wire,  covered  with  silk  or  cotton,  is  rolled  several  times  round  them  on 
the  two  branches,  so  as  to  form  two  bobbins,  A  and  B.  In  order  that 
the  two  ends  of  the  horse-shoe  may  be  of  opposite  polarity,  the  winding 
on  the  two  limbs  A  and  B  must  be  such  that  if  the  horse-shoe  were 
straightened  out,  it  would  be  in  the  same  direction. 

Electromagnets,  instead  of  being  made  in  one  piece,  are  frequently 
constructed  of  two  cylinders,  firmly  screwed  to  a  stout  piece  of  the  same 
metal.  Such  are  the  electromagnets  in  Morse's  telegraph  (835),  the 
electromagnetic  motor  (840).  The  helices  on  them  must  be  such  that 
the  current  shall  flow  in  the  same  direction  as  the  hands  of  a  watch  as 
seen  from  the  south  pole,  and  against  the  hands  of  a  watch  as  seen  from 
the  north  pole. 

The  results  at  which  various  experimenters  have  arrived  as  regards 
the  force  of  electromagnets  are  often  greatly  divergent,  which  is  partly  due 
to  the  different  senses  they  have  attached  to  the  notion  of  electromagnetic 
force.  For  this  may  mean  (I.)  the  induction  current  which  the  develop- 
ment and  disappearance  of  the  magnetism  of  an  iron  core  indicate  in  a 
spiral  which  surrounds  it  ;  this  is  the  excited  magjietism  :  or  (II.)  the  free 
magnetism  measured  by  the  action  on  a  magnetic  needle,  oscillating  at  a 
distance  ;  (III.)  the  attractive  force,  or  the  force  required  to  hold  an  ar- 
mature at  a  distance  from  the  electromagnet;  (IV.)  the  lifting  power 
measured  by  the  force  with  which  an  armature  is  held  in  direct  contact 
with  the  pole. 

The  most  important  results  which  have  been  arrived  at  are  the  fol- 
lowing : 

(i.)  Using  the  term  electromagnetic  force  in  the  first  two  senses,  it  is 
proportional  to  the  intensity  of  the  currejit.  This  only  applies  when  the 
currents  are  not  very  powerful,  and  to  stout  bars  ;  for  in  each  bar  there 
is,  as  Miiller  has  found,  a  maximum  of  magnetisation  which  cannot  be 
exceeded. 

(ii.)  Taking  into  account  the  resistance,  the  electromagnetic  force  is 
independent  of  the  nature  and  thickness  of  the  wire.  Thus  the  intensity 
of  the  current  and  the  number  of  coils  being  the  same,  thick  and  thin 
wires  produce  the  same  effect. 

(iii.)  With  the  same  current  the  electromagnetic  force  is  independent  oj 
the  width  of  the  coils,  provided  the  iron  projects  beyond  the  coils,  and 
the  diameter  of  the  coil  is  small  compared  with  its  length. 

(iv.)  The  temporary  magnetic  moment  of  an  iron  bar  is  within  certain 
limits  proportional  to  the  number  of  windings.  The  product  of  the  in- 
tensity into  the  number  of  turns  is  usually  spoken  of  as  the  magnetising 
poiuer  of  the  spiral.  The  greatest  magnetising  power  is  obtained  when 
the  resistance  in  the  magnetising  spiral  is  equal  to  the  sum  of  the  other 
resistances  in  the  circuit,  those  of  the  battery  included,  and  the  length 
and  diameter  of  the  wire  must  be  so  arranged  as  to  satisfy  these  con- 
ditions. 

(v.)  The  magnetism  in  solid  and  in  hollow  cylinders  of  the  same 


74^  Dynamical  Electricity.  [830- 

diameters  is  the  same,  provided  in  the  latter  case  there  is  sufficient  iron 
for  the  development  of  the  magnetism. 

(vi.)  The  attraction  of  an  armature  by  an  electromagnet  is  proportional 
to  the  square  of  the  intensity  of  the  current  so  long  as  the  magnetic 
moment  does  not  attain  its  maximum.  Two  unequally  strong  electro- 
magnets attract  each  other  with  a  force  proportional  to  the  square  of  the 
sum  of  both  currents. 

(vii.)  For  powerful  currents  the  length  of  the  branches  of  an  electro- 
magnet is  without  influence  on  the  weight  which  it  can  support. 

As  regards  the  quality  of  the  iron  used  for  the  electromagnet,  it  must 
be  pure,  and  be  made  as  soft  as  possible  by  being  reheated  and  cooled 
a  great  many  times  ;  it  is  polished  by  means  of  a  file  so  as  to  avoid  twist- 
ing. If  this  is  not  the  case  the  bar  retains,  even  after  the  passage  of  the 
current,  a  quantity  of  magnetism  which  is  called  the  rema?te?it  magnetism . 
A  bundle  of  soft  iron  wires  loses  its  magnetism  more  rapidly  than  a 
massive  bar  of  the  same  size. 

During  magnetisation  the  volume  of  a  magnet  does  not  vary.  This 
has  been  established  by  placing  the  bar  to  be  magnetised  with  its  helix 
in  a  sort  of  water  thermometer,  consisting  of  a  flask  provided  with  a 
capillary  tube.  On  magnetising  no  alteration  in  the  position  of  the  water 
is  observed.  But  the  dimensions  vary,  the  diameter  is  somewhat  lessened, 
and  the  length  increased  ;  according  to  Joule  to  the  extent  of  about  3^^, 
if  the  bar  is  magnetised  to  saturation. 

We  shall  presently  see  the  numerous  applications  which  have  been 
made  of  electromagnets  in  electric  telegraphs,  in  electromagnetic  motors, 
in  electric  clocks,  and  in  the  study  of  diamagnetic  phenomena. 

831.  Vibratory  motion  and  sounds  produced  by  currents. — When 
a  rod  of  soft  iron  is  magnetised  by  a  strong  electric  curren  t,  it  gives  a 
very  distinct  sound,  which,  however,  is  only  produced  at  the  moment  of 
closing  or  opening  the  current.  This  phenomenon,  which  was  first  observed 
by  Page  in  America,  and  by  Delezenne  in  France,  has  been  particularly 
investigated  by  De  la  Rive,  who  has  attributed  it  to  a  vibratory  motion 
of  the  molecules  of  iron  in  consequence  of  a  rapid  succession  of  magneti- 
sations and  demagnetisations. 

When  the  current  is  broken  and  closed  at  very  short  intervals,  De  la 
Rive  has  observed,  that  whatever  be  the  shape  or  magnitude  of  the  iron 
bars,  two  sounds  may  always  be  distinguished  :  one,  which  is  musical, 
corresponds  to  that  which  the  rod  would  give  by  vibrating  transversely  ; 
the  other,  which  consists  of  a  series  of  harsh  sounds,  corresponding  to  the 
interruptions  of  the  current,  is  compared  by  De  la  Rive  to  the  noise  of 
rain  falling  on  a  metal  roof  The  most  marked  sound,  says  he,  is  that 
obtained  by  stretching  on  a  sounding  board  pieces  of  soft  iron  wire,  well 
annealed,  from  i  to  2  mm.  in  diameter,  and  i  to  2  yards  long.  These 
wires  being  placed  in  the  axis  of  one  or  more  bobbins  traversed  by  power- 
ful currents,  send  forth  a  number  of  sounds,  which  produce  a  surprising 
effect,  and  much  resemble  that  of  a  number  of  church  bells  heard  at  a 
distance. 

Wertheim  has  obtained  the  same  sounds  by  passing  a  discontinuous 


-832]  Electric  Telegraph.  749 

current,  not  through  the  bobbins  surrounding  the  iron  wires,  but  through 
the  wires  themselves.  The  musical  sound  is  then  stronger  and  more^ 
sonorous  in  general  than  in  the  previous  experiment.  The  hypothesis 
of  a  molecular  movement  in  the  iron  wires  at  the  moment  of  their  mag- 
netisation, and  of  their  demagnetisation,  is  confirmed  by  the  researches 
of  Wertheim,  who  has  found  that  their  elasticity  is  then  diminished. 


ELECTRIC  TELEGRAPH. 

832.  Electric  telegraplis. — These  are  apparatus  by  which  signals  can 
be  transmitted  to  considerable  distances  by  means  of  voltaic  currents 
propagated  in  metalhc  wires.  Towards  the  end  of  the  last  century,  and 
at  the  beginning  of  the  present,  many  philosophers  proposed  to  corre- 
spond at  a  distance  by  means  of  the  effects  produced  by  electrical  machines 
when  propagated  in  insulated  conducting  wires.  In  181 1,  Scemmering 
invented  a  telegraph  in  which  he  used  the  decomposition  of  water  for 
giving  signals.  In  1820,  at  a  time  when  the  electromagnet  was  unknown, 
Ampere  proposed  to  correspond  by  means  of  magnetic  needles,  above 
which  a  current  was  sent,  as  many  wires  and  needles  being  used  as  letters 
were  required.  In  1834,  Gauss  and  Weber  constructed  an  electromagnetic 
telegraph,  in  which  a  voltaic  current  transmitted  by  a  wire  acted  on  a 
magnetised  bar;  the  oscillations  of  which  under  its  influence  were  ob- 
served by  a  telescope.  They  succeeded  in  thus  sending  signals  from  the 
Observatory  to  the  Physical  Cabinet  in  Gottingen,  a  distance  of  a  mile 
and  a  quarter,  and  to  them  belongs  the  honour  of  having  first  demon- 
strated experimentally  the  possibility  of  electrical  communication  at  a 
considerable  distance.  In  1837,  Steinheil  in  Munich,  and  Wheatstone 
in  London,  constructed  telegraphs  in  which  several  wires  each  acted  on  a 
single  needle ;  the  current  in  the  first  case  being  produced  by  an  electro- 
magnetic machine,  and  in  the  second  by  a  constant  battery. 

Every  electric  telegraph  consists  essentially  of  three  parts  :  i,  a  circiiit 
consisting  of  a  metallic  connection  between  two  places,  and  an  dec- 
tromotor  for  producing  the  current ;  2,  a  communicator  for  sending  the 
signals  from  the  one  station  ;  and,  3,  an  indicator  for  receiving  them  at 
the  other  station.  The  manner  in  which  these  objects,  more  especially 
the  last  two,  are  effected  can  be  greatly  varied,  and  we  shall  limit  our- 
selves to  a  description  of  the  three  principal  methods. 

One  form  of  electromotor  still  frequently  used  in  England  is  a  modi- 
fication of  Wollaston's  battery.  It  consists  of  a  trough  divided  into  com- 
partments, in  each  of  which  is  an  amalgamated  zinc  plate  and  a  copper 
plate ;  these  plates  are  usually  about  4^  inches  in  height  by  3^  in  breadth. 
The  compartments  are  filled  with  sand,  which  is  moistened  with  diUite 
sulphuric  acid.  This  battery  is  inexpensive  and  easily  worked,  only 
requiring  from  time  to  time  the  addition  of  a  little  acid  ;  but  it  has  very 
low  electromotive  force  and  considerable  resistance,  and  when  it  has  been 
at  work  for  some  time,  the  effects  of  polarisation  begm  to  be  perceived. 
On  the  telegraphs  of  the  South  Eastern  Railway,  the  platinised  graphite 


750 


Dynamical  Electricity. 


[832- 


(765)  battery  invented  by  Mr.   C.  V.  Walker  is  used  with  success.     In 
France,  Daniell's  battery  is  used  for  telegraphic  purposes. 

The  connection  between  two  stations  is  made  by  means  of  galvanised 

iron  wire  suspended  by  porcelain 
supports  (fig.  667),  which  insulate 
and  protect  them  against  the  rain, 
either  on  posts  or  against  the  sides 
of  buildings.  In  towns,  wires  co- 
vered with  gutta-percha  are  placed 
in  tubes  laid  in  the  ground.  Sub- 
marine cables,  where  great  strength 
is  required  combined  with  lightness 
and  high  conducting  power,  are 
formed  on  the  general  type  of  one 
of  the  Atlantic  cables,  a  longitudinal 
view  of  which  is  given  in  fig.  668, 
while  fig.  669  represents  a  cross  section.  In  the  centre  is  the  core  which 
is  the  conductor ;  it  consists  of  seven  copper  wires,  each  i  mm.  irt diameter 
twisted  in  a  spiral  strand  and  covered  with  several  layers  of  gutta  percha, 
between  each  of  which  is  a  coating  of  Chatterton^s  compound— 2i  mixture 
of  tar,  resin,  and  gutta  percha.  This  forms  the  msulator  proper,  and  it 
should  have  great  resistance  to  the  passage  of  electricity,  combined  with 
low  specific  inductive  capacity  (702).      Round  the  insulator  is  a  coat- 


Fig.  667. 


Fig.  668. 


Fig.  669. 


ing  of  hemp,  and  on  the  outside  is  wound  spirally  a  protecting  sheath  of 
steel  wire,  each  of  which  is  spun  round  with  hemp. 

At  the  station  which  sends  the  despatch,  the  line  is  connected  with  the 
positive  pole  of  a  battery,  the  current  passes  by  the  line  to  the  other  station, 
and  if  there  were  a  second  return  line,  it  would  traverse  it  in  the  opposite 
direction  to  return  to  the  negative  pole.  In  1837,  Steinheil  made  the  very 
important  discovery  that  the  earth  might  be  used  for  the  return  conductor, 
thereby  saving  the  expense  of  the  second  line.  For  this  purpose  the  end 
of  the  conductor  at  the  one  station,  and  the  negative  pole  of  the  battery 
at  the  other,  are  connected  with  large  copper  plates,  which  are  sunk  to 
some  depth  in  the  ground.  The  action  is  then  the  same  as  if  the  earth 
acted  as  a  return  wire.  The  earth  is,  indeed,  far  superior  to  a  return 
wire  ;  for  the  added  resistance  of  such  a  wire  would  be  considerable, 
whereas  the  resistance  of  the  earth  beyond  a  short  distance  is  absolutely 
nil.  The  earth  really  dissipates  the  electricity,  and  does  not  actually 
return  the  same  current  to  the  battery. 


-833] 


Single  Needle  Telegraph. 


751 


833.  ixnieatstone's  and  Cooke's  singrle  needle  telegrrapb. — "fhis 
consists  essentially  of  a  vertical  multiplier  (773)  with  an  astatic  needle,  the 
arrangement  of  which  is  seen  in  fig,  671,  while  fig.  670  gives  a  front  view~ 


Fig.  670. 


of  the  case  in  which  the  apparatus  is  placed.  A  (fig.  671)  is  the  bobbin 
consisting  of  about  400  feet  of  fine  copper  wire,  wound  in  a  frame  in  two 
connected  coils.  Instead  of  an  astatic  needle,  Mr.  Walker  has  found  it 
advantageous  to  use  a  single  needle  formed  of  several  pieces  of  very  thin 
steel  strongly  magnetised ;  it  works  within  the  bobbin,  and  a  light  index 
joined  to  it  by  a  horizontal  axis  indicates  the  motion  of  the  needle  on  the 
dial. 

The  signs  are  made  by  transmitting  the  current  in  different  directions 
through  the  multiplier,  by  which  the  needle  is  deflected  either  to  the  right 
or  left,  according  to  the  will  of  the  operator.  The  instrument  by  which 
this  is  effected  is  a  cojiiimctator  or  key,  G ;  its  construction  is  shown  in 
fig.  671,  while  fig.  672  shows  on  a  large  scale  how  two  stations  are  con- 
nected. It  consists  of  a  cylinder  of  boxwood  with  a  handle,  which 
projects  in  front  of  the  case  (fig.  670).  On  its  circumference  parallel  to 
the  axis  are  seven  brass  strips  (fig.  672),  the  spaces  between  which  are 
insulated  by  ivory  ;  these  strips  are  connected  at  the  end  by  metallic 


752 


Dynamical  Electricity. 


[833- 


wires,  also  insulated  from  each  other,  in  the  following  manner  :  a  with  b 
and  <;,y"with  d,  and  e  with^.  Four  springs  press  against  the  cylinder  ;  x 
and^y  are  connected  with  the  poles  of  the  battery,  m  with  the  earth  plate, 
and  71  with  one  end  of  the  multiplier,  N. 

When  not  at  work  the  cylinder  and  the  handle  are  in  a  vertical  posi- 
tion, as  seen  on  the  left  of  the  diagram.  The  circuit  is  thus  open,  for  the 
pole  springs,  x  and  j,  are  not  connected  with  the  metal  of  the  commutator. 
But  if,  as  in  G',  the  key  is  turned  to  the  right,  the  battery  is  brought  into 
the  circuit,  and  the  current  passes  in  the  following  direction:  +  pole 
x'a'b'71'Wq"^,  conductor  q^pyinbaciriY^p^  earth  p'E'm'e'g'y,— -pole.  The 
coils  N  and  N'  are  so  arranged  that  by  the  current  the  motion  of  the  needle 


corresponds  to  the  motion  of  the  handle.  By  turning  the  handle  to  the 
left  the  current  would  have  the  following  direction  :  +  pole  x'd'fvi'Y.'p^ 
earth  pY^jncabttlAq,  conductor  ^'M';/'<^'rty,  — pole,  and  thus  the  needle 
would  be  deflected  in  the  opposite  direction. 

The  signs  are  given  by  differently  combined  deflections  of  the  needle, 
as  represented  in  the  alphabet  on  the  dial  (fig.  670).  \  denotes  a  deflec- 
tion of  the  upper  end  of  the  needle  to  the  left,  and  /  a  deflection  to  the 
right ;  I,  for  instance,  is  indicated  by  two  deflections  to  the  left,  and  M 
by  two  to  the  right.     Some  of  the  marks  on  the  alphabet  are  only  half  as 


-834] 


Dial  Telegraphs. 


753 


long  as  the  others;  this  indicates  that  the  shortest  of  the  connected 
marks  must  first  be  signalled.  Thus,  D  is  expressed  by  right-left-left,  and 
C  by  right-left-right-left,  etc. 

These  signs  are  somewhat  complicated,  and  require  great  practice ; 


Fig   672. 


usually  not  more  than  12  to  20  words  can  be  sent  in  a  minute.  Hence 
the  single  needle  telegraph  is  in  many  cases  replaced  by  the  double  needle 
one,  which  is  constructed  on  the  same  principle,  but  there  are  two  needles 
and  two  wires  instead  of  one. 

834.  Bial  telegrraphs. — Of  these  many  kinds  exist.  Figs.  674  and  675 
represent  a  lecture-model  of  one  form,  constructed  by  M,  Froment,  and 
which  well  serves  to  illustrate  the  principle.  It  consists  of  two  parts  :  the 
manipulator  for  transmitting  signals  (fig.  674),  and  the  indicator  (fig.  675) 
for  receiving  them.  The  first  apparatus  is  connected  with  a  battery,  Q, 
and  the  two  apparatus  are  in  communication  by  means  of  metal  wires, 
one  of  which,  AOD  (fig.  674),  goes  from  the  departure  to  the  arrival 
station,  and  the  other,  HKLI  (fig.  675),  from  the  arrival  to  the  departure. 
In  practice,  the  latter  is  replaced  by  the  earth  circuit.  Each  apparatus  is 
furnished  with  a  dial  with  25  of  the  letters  of  the  alphabet,  on  which  a 
needle  moves.  The  needle  at  the  departure  station  is  moved  by  hand, 
that  of  the  arrival  by  electricity. 

The  path  of  the  current  and  its  effects  are  as  follows  :  From  the  battery 
it  passes  through  a  copper  wire,  A  (fig.  674),  into  a  brass  spring  N,  which 
presses  against  a  metal  wheel,  R,  then  by  a  second  spring,  M,  into  the 

K  K  3 


754 


Dynamical  Electricity. 


[834- 


wire,  O,  which  joins  the  other  station.  Thence  the  current  passes  into 
the  bobbin  of  an  electromagnet,  b^  not  fully  shown  in  fig.  675,  but  of 
which  fig.  673  represents  a  section,  showing  the 
anterior  part  of  the  apparatus.  This  electro- 
magnet is  fixed  horizontally  at  one  end,  and  at 
the  other  it  attracts  an  armature  of  soft  iron,  a, 
which  forms  part  of  a  bent  lever,  movable  about 
its  axis,  o,  while  a  spring,  r,  attracts  the  lever  in 
the  opposite  direction. 

When  the  current  passes,  the  electromagnet 
attracts  the  lever  aC,  which  by  a  rod,  /,  acts 
on  a  second  lever,  d,  fixed  to  a  horizontal  axis, 
itself  connected  with  a  fork,  F.  When  the  cur- 
rent is  broken  the  spring  r  draws  the  lever  aC^ 
ms^^^^^^  and  therewith  all  the  connected  pieces ;  a  back- 
^^s-  673-  ward  and  forward  motion  is  produced,  which 

is  communicated  to  the  fork  F,  which  transmits  it  to  a  toothed 
wheel,  G,  on  the  axis  of  which  is  the  needle.  From  the  arrangement 
of  its  teeth,  the  wheel  G  is  always  moved  in  the  same  direction  by  the 
fork. 

To  explain  the  intermittent  action  of  the  magnet,  we  must  refer  to 
fig.  674.  The  toothed  wheel,  R,  has  26  teeth,  of  which  25  correspond  to 
letters  of  the  alphabet,  and  the  last  to  the  interval  reserved  between  the 
letters  A  and  Z.  When  holding  the  knob  P  in  the  hand  the  wheel  R  is 
turned,  the  end  of  the  plate  N  from  its  curvature  is  always  in  contact  with 
the  teeth ;  the  plate  M,  on  the  contrary,  terminates  in  a  catch  cut  so  that 
contact  is  alternately  made  and  broken.  Hence  the  connections  with 
the  battery  having  been  made,  if  the  needle  P  is  advanced  through  four 
letters,  for  example,  the  current  passes  four  times  in  N  and  M,  and  is 
four  times  broken.  The  electromagnet  of  the  arrival  station  will  then  have 
attracted  four  times,  and  have  ceased  to  do  so  four  times.  Lastly,  the 
wheel  G  will  have  turned  by  four  teeth,  and  as  each  tooth  corresponds  to 
a  letter,  the  needle  of  the  arrival  station  will  have  passed  through  exactly 
the  same  number  of  letters  as  that  of  the  departure  station.  The  piece 
S,  represented  in  the  two  figures,  is  a  copper  plate,  moveable  on  a  hinge, 
which  serves  to  make  or  to  break  the  current  at  will. 

From  this  explanation  it  will  be  readily  intelligible  how  communica- 
tions are  made  between  different  places.  Suppose,  for  example,  that  the 
first  apparatus  being  at  London  and  the  second  at  Brighton,  there  being 
metallic  connection  between  the  two  towns,  it  is  desired  to  send  the  word 
signal  to  the  latter  town  :  as  the  needles  correspond  on  each  apparatus  to 
the  interval  retained  between  A  and  Z,  the  person  sending  the  despatch 
moves  the  needle  P  to  the  letter  S,  where  it  stops  for  a  very  short  time ; 
as  the  needle  at  Brighton  accurately  reproduces  the  motion  of  the  London 
needle,  it  stops  at  the  same  letter,  and  the  person  who  receives  the  des- 
patch notes  this  letter.  The  one  at  London  always  continuing  to  turn  in 
the  same  direction,  stops  at  the  letter  I,  the  second  needle  immediately 
stops  at  the  same  letter;  and  continuing  in  the  same  manner  with  the 


834] 


Dial  Telegraphs. 


755 


letters  G,  N,  A,  L,  all  the  word  is  soon  transmitted  to  Brighton.     The 
attention  of  the  observer  at  the  arrival  station  is  attracted  by  means  of  an 


electric  alarum.     Each  station  further  must  be  provided  with  the  two  ap- 
paratus (figs.  674  and  675),  without  which  it  would  be  impossible  to  answer. 


756 


Dynamical  Electricity. 


[836- 


835.  Morse's  telegrrapb. — The  telegraphs  hitherto  described  leave  no 
trace  of  the  despatches  sent,  and  if  any  errors  have  been  made  in  copying 
the  signals  there  is  no  means  of  remedying  them.  These  inconveniences 
are  not  met  with  in  the  case  of  the  writing  telegraphs,  in  which  the  signs 
themselves  are  printed  on  a  strip  of  paper  at  the  time  at  which  they  are 
transmitted. 

Of  the  numerous  printing  and  writing  telegraphs  which  have  been  de- 
vised, that  of  Mr.  Morse,  first  brought  into  use  in  North  America,  is  best 
known.  It  has  been  almost  universally  adopted  on  the  Continent.  In 
this  instrument  there  are  three  distinct  parts  :  the  indicator,  the  commu- 
nicator, and  the  relay,  figs.  676,  677,  and  678  represent  these  ap- 
paratus. 

Indicator.     We  will  first  describe  the  indicator  (fig.  676),  leaving  out 


Fig.  676. 


of  sight  for  the  moment  the  accessory  pieces,  G  and  T,  placed  on  the 
right  of  the  figure.  The  current  which  enters  the  indicator  by  the  wire, 
C,  passes  into  an  electromagnet,  E,  which,  when  the  current  is  closed, 
attracts  an  armature  of  soft  iron.  A,  fixed  at  the  end  of  a  horizontal  lever 
movable  about  an  axis,  x;  when  the  current  is  open  the  lever  is  raised 
by  a  spring,  r.  By  means  of  two  screws,  m  and  v,  the  amplitude  of  the 
oscillations  is  regulated.  At  the  other  end  of  the  lever  there  is  a  pencil, 
o,  which  writes  the  signals.  For  this  purpose  a  long  band  of  strong 
paper,  pp,  rolled  round  a  drum,  R,  passes  between  two  copper  rollers 
with  a  rough  surface,  m,  and  turning  in  contrary  directions.      Drawn 


-835] 


Morse's  Telegraph. 


7S7 


in  the  direction  of  the  arrows,  the  band  of  paper  becomes  rolled  on  a 
second  drum,  Q,  which  is  turned  by  hand.  A  clockwork  motion  placed 
in  the  box,  BD,  works  the  rollers,  between  which  the  band  of  paper 
passes. 

The  paper  being  thus  set  in  motion,  whenever  the  electromagnet 
works,  the  point  o  strikes  the  paper,  and,  without  perforating  it,  produces 
an  indentation,  the  shape  of  which  depends  on  the  time  during  which  the 
point  is  in  contact  with  the  paper.  If  it  only  strikes  it  instantaneously,  it 
makes  a  dot  (.)  or  short  stroke  ( — ) ;  but  if  the  contact  has  any  duration  a 
dash  of  corresponding  length  is  produced.  Hence,  by  varying  the  length 
of  contact  of  the  transmitting  key  at  one  station,  a  combination  of  dots 
and  dashes  may  be  produced  at  another  station,  and  it  is  only  necessary 
to  give  a  definite  meaning  to  these  combinations. 

The  same  telegraphic  alphabet  is  now  universally  used  wherever  tele- 
graphic communication  exists ;  and  the  signals  for  the  single  needle  in- 
strument (fig,  676),  as  well  as  those  used  for  printing  have  been  modified, 
so  that  they  now  correspond  to  each  other.  Thus  a  beat  of  the  top  of 
the  needle  to  the  left  \  is  equivalent  to  a  dot ;  and  a  beat  to  the  right  / 
to  a  dash.     The  following  figure  gives  the  alphabet : — 


SINGLE 

SINGJX 

PRINTING. 

XEEDIE. 

PBINHXG. 

UEEDIE. 

A 

v/ 

N 

A 

B      

An^ 

0^ 

I/I 

C^ 

AA 

P  X 

Jls 

D 

As 

Q> 

IIJ 

E      - 

\ 

R   ^ 

vA 

F^ 

«A 

S       — 

/ 

G 

/A 

T        -- 

H 

WW 

TJ 

vx/ 

I      -- 

\x 

V 

vw/ 

J^ 

J// 

w 

^// 

K 

IJ 

X  ^ 

Ax/ 

L^ 

sL 

Y  ^,. 

A// 

M 

// 

/Av 

Communicator  or  key.  This  consists  of  a  small  mahogany  base,  which 
acts  as  support  for  a  metallic  lever  ab  (fig.  677),  movable  in  its  middle  on 
a  horizontal  axis.  The  extremity  a  of  this  lever  is  always  pressed  up- 
wards by  a  spring  beneath,  so  that  it  is  only  by  pressing  with  the  finger 
on  the  key  B  that  the  lever  sinks  and  strikes  the  bottom  x.     Round  the 


758  Dynamical  Electricity.  [835- 

base  there  are  three  binding  screws;  one  connected  with  the  wire  P, 
which  comes  from  the  positive  pole  of  the  battery  ;  the  second  connected 
with  L,  the  wire  of  the  line;  and  the  third  with  the  wire  A,  which  passes 
to  the  indicator,  for  of  course  two  places  in  communication  are  each  pro- 
vided with  an  indicator  and  communicator. 

These  details  known,  there  are  two  cases  to  be  considered:  i.  The 
communicator  is  arranged  so  as  to  receive  a  despatch  from  a  distant 
station  ;  the  extremity  b  is  then  depressed,  as  represented  in  the  drawing, 


Fig.  677. 

so  that  the  current  which  arrives  by  the  wire  of  the  line  L,  and  ascends 
in  the  metallic  piece  m,  redescends  in  the  wire  A,  which  leads  it  to  the 
indicator  of  the  station  at  which  the  apparatus  is  placed.  2.  A  despatch  is 
to  be  transmitted  ;  in  this  case  the  key  B  is  pressed  so  that  the  lever 
comes  in  contact  with  the  button  x.  The  current  of  the  local  battery, 
which  comes  by  the  wire  P,  ascending  then  in  the  lever,  redescends  by  m 
and  joins  the  wire  L,  which  conducts  it  to  the  station  to  which  the  despatch 
is  addressed.  According  to  the  length  of  time  during  which  B  is  pressed, 
a  dot  or  a  line  is  produced  in  the  receiver  to  which  the  current  proceeds. 

Relay.  In  describing  the  receiver  we  have  assumed  that  the  current  of 
the  hne  coming  by  the  wire  C  (fig.  676)  entered  directly  into  the  electro- 
magnet, and  worked  the  armature  A,  producing  a  despatch  ;  but  when 
the  current  has  traversed  a  distance  of  a  few  miles  its  intensity  has 
diminished  so  greatly  that  it  cannot  act  upon  the  electromagnet  with 
sufficient  force  to  print  a  despatch.  Hence  it  is  necessary  to  have  re- 
course to  a  relay — that  is,  to  an  auxiliary  electromagnet  which  is  still 
traversed  by  the  current  of  the  line,  but  which  serves  to  introduce 
into  the  communicator  the  current  of  a  local  battery  of  4  or  5  elements 
placed  at  the  station,  and  which  is  only  used  to  print  the  signals  trans- 
mitted by  the  wire. 

•  For  this  purpose  the  current  entering  the  relay  by  the  binding  screw, 
L  (fig.  678),  passes  into  an  electromagnet,  E,  whence  it  passes  into  the 
earth  by  the  binding  screw  T.  Now,  each  time  that  the  current  of  the 
line  passes  into  the  relay,  the  electromagnet  attracts  an  armature.  A,  fixed 
at  the  bottom  of  a  vertical  lever  /,  which  oscillates  about  a  horizontal 
axis 

At  each  oscillation  the  top  of  the  lever/  strikes  against  a  button,  n, 
and  at  this  moment  the  current  of  the  local  battery  which  enters  by  the 


-835] 


Morse  s  Telegraph. 


759 


binding  screw,  c,  ascends  the  column  ;«,  passes  into  the  lever/,  descends 
by  the  rod  o,  which  transmits  it  to  the  screw  Z  :  thence  it  enters  the-; 
electromagnet  of  the  indicator,  whence  it  emerges  by  the  wire  Z,  to  return 
to  the  local  battery  from  which  it  started.     Then  when  the  current  of  the 
line  is  open,  the  electromagnet  of  the  relay  does  not  act,  and  the  lever  p^ 


Fig.  678. 

drawn  by  a  spring  r,  leaves  the  button  n^  as  shown  in  the  drawing,  and 
the  local  current  no  longer  passes.  Thus  the  relay  transmits  to  the 
indicator  exactly  the  same  phases  of  passage  and  intermittence  as  those 
effected  by  the  manipulator  in  the  post  which  sends  the  despatch. 

With  a  general  battery  of  25  Daniell's  elements  the  current  is  strong 
enough  at  upwards  of  90  miles  from  its  starting-point  to  work  a  relay. 
For  a  longer  distance  a  new  current  must  be  taken,  as  will  be  seen  in  the 
paragraph  on  the  change  of  current  {vide  infra). 

Woi'kitig  of  the  three  apparatus.  The  three  principal  pieces  of 
Morse's  apparatus  being  thus  known,  the  following  is  the  actual  path  of 
the  current. 

The  current  of  the  line  coming  by  the  wire  L  (fig.  678)  passes  at  first 
to  the  piece  T  intended  to  serve  as  lightning  conductor,  when,  from  the 
influence  of  atmospheric  electricity  in  time  of  storm,  the  conducting  wires 
become  charged  with  so  much  electricity  as  to  give  dangerous  sparks. 
This  apparatus  consists  of  two  copper  discs,  d  and  f  provided  with  teeth 
on  the  sides  opposite  each  other,  but  not  touching.  The  disc  d  is  con- 
nected with  the  earth  by  a  metallic  plate  at  the  back  of  the  stand  which 
supports  this  lightning  conductor,  while  the  disc /is  in  the  current.  The 
latter  coming  by  the  line  L  enters  the  lightning  conductor  by  the  binding 
screw  fixed  at  the  lower  part  of  the  stand  on  the  left ;  then  rises  to  a 
commutator,  «,  which  conducts  it  to  a  button,  <r,  whence  it  reaches  the 
disc  /  by  a  metallic  plate  at  the  back  of  the  stand  ;  in  case  a  lightning 
discharge  should  pass  along  the  wire,  it  would  now  act  inductively  on  the 
disc  d,  and  emerge  by  the  points  without  danger  to  those  about  the 
apparatus.  Moreover,  from  the  disc/,  the  current  passes  into  a  very  fine 
iron  wire  insulated  on  a  tube  e.     As  the  wire  is  melted,  when  the  dis- 


760  Dynamical  Electricity.  [835- 

charge  is  too  intense,  the  electricity  does  not  pass  into  the  apparatus, 
which  still  further  removes  any  danger. 

Lastly,  the  current  proceeds  from  the  foot  of  the  support  j  to  a  screw 
on  the  right,  which  conducts  it  to  a  small  galvanometer,  G,  serving  to 
indicate  by  the  deflection  of  the  needle  whether  the  current  passes. 
From  this  galvanometer  the  current  proceeds  to  a  communicator  (fig.  677), 
which  it  enters  at  L,  whence  it  emerges  at  A  to  go  to  the  relay  (fig.  678). 
Entering  this  at  L.  it  works  the  electromagnet,  and  establishes  the  com- 
munication necessary  for  the  passage  of  the  current  of  the  local  battery, 
as  has  been  said  in  speaking  of  the  relay. 

Chatige  of  current.  To  complete  this  description  of  Morse's  apparatus 
it  must  be  observed  that  in  general  the  current  which  arrives  at  L,  after 
having  traversed  several  miles,  has  not  sufficient  force  to  register  the 
despatch,  nor  to  proceed  to  a  new  distant  point.  Hence,  in  each  tele- 
graphic station  a  new  current  must  be  taken,  that  of  the  postal  battery^ 
which  consists  of  20  to  30  Daniell's  elements,  and  is  not  identical  with 
the  local  battery. 

This  new  current  enters  at  P  (fig.  676),  reaches  a  binding  screw  which 
conducts  it  to  the  column  H,  and  thence  only  proceeds  further  when  the 
armature  A  sinks.  A  small  contact  placed  under  the  lever  touches  then 
the  button  v  ;  the  current  proceeds  from  the  column  H  to  the  metallic 
mass  BD,  whence  by  a  binding  screw  and  a  wire,  not  represented  in  the 
figure,  it  reaches  lastly  the  wire  of  the  line,  which  sends  it  to  the  follow- 
ing post,  and  so  on  from,  one  point  to  another. 

836.  Induction  in  teleg-rapb  cables. — In  the  earliest  experiments  on 
the  use  of  insulated  subterranean  wires  for  telegraphic  communication  it 
was  found  that  difficulties  occurred  in  their  use  which  were;  not  expe- 
rienced with  overland  wires.  This  did  not  arise  from  defective  insulation, 
for  the  better  the  insulation  the  greater  the  difficulty.  It  was  suspected 
by  Siemens  and  others  that  the  retardation  was  due  to  statical  induction 
taking  place  between  the  inner  wire  through  the  insulator  and  the  ex- 
ternal moisture ;  and  that  this  was  the  case  Faraday  proved  by  the 
following  experiments  among  others.  A  length  of  about  100  miles  of 
gutta-percha  covered  copper  wire  was  immersed  in  water,  the  ends  being 
led  into  the  chamber  of  observation.  When  the  pole  of  a  battery  con- 
taining a  large  number  of  cells  was  momentarily  connected  with  one  end 
of  the  wire,  the  other  end  being  insulated,  and  a  person  simultaneously 
touched  the  wire  and  the  earth  contact,  he  obtained  a  violent  shock. 

When  the  wire,  after  being  in  momentary  contact  with  the  battery, 
was  placed  in  connection  with  a  galvanometer,  a  considerable  deflection 
was  observed  ;  there  was  a  feebler  one  3  or  4  minutes  after,  and  as  long 
as  20  or  30  minutes  afterwards. 

When  the  insulated  galvanometer  was  permanently  connected  with  one 
end  of  the  wire,  and  then  the  free  end  of  the  galvanometer  wire  joined 
to  the  pole  of  the  battery,  a  rush  of  electricity  through  the  galvanometer 
into  the  wire  was  perceived.  This  speedily  diminished  and  the  needle 
ultimately  came  to  rest.     When  the  galvanometer  was  detached  from  the 


-837]  Duplex  Telegraphy.  y6i 

battery  and  put  to  earth,  the  electricity  flowed  as  rapidly  out  of  the  wire, 
and  the  needle  was  momentarily  deflected  in  the  opposite  direction. 

These  phenomena  are  not  difficult  to  explain.  The  wire  with  its  thin 
insulating  coating  of  gutta-percha  becomes  statically  charged  with  elec- 
tricity from  the  battery.  The  coating  of  gutta-percha  through  which  the 
inductive  action  takes  place  is  only  ~  of  an  inch  in  thickness,  and  the 
extent  of  the  coatings  is  very  great.  The  surface  of  the  copper  wire 
amounts  to  8,300  square  feet,  and  that  of  the  outside  coating  is  four  times 
as  much.  The  potential  can  only  be  as  great  as  that  of  the  battery,  but 
from  the  enormous  surface  the  quantity  is  very  great.  Thus  the  wires, 
after  being  detached  from  the  battery,  showed  all  the  actions  of  a  power- 
ful electric  battery.  These  effects  cannot  take  place  with  wires  m  air,  for 
the  external  coating  is  wanting,  or  at  all  events  is  so  distant  that  induction 
and  charge  cannot  occur. 

Hence  the  difficulty  in  submarine  telegraphy.  The  electricity  which 
enters  the  insulating  wire  must  first  be  used  in  charging  the  large  Leyden 
jar  which  it  constitutes,  and  only  after  this  has  happened  can  the  current 
reach  the  distant  end  of  the  circuit.  The  current  begins  later  at  the 
distant  end,  and  ceases  sooner.  If  the  electrical  currents  follow  too  rapidly, 
an  uninterrupted  current  will  appear  at  the  other  end,  which  indicates 
small  differences  in  strength,  but  not  with  sufficient  clearness  differences 
in  duration  or  direction.  Hence  in  submarine  wires  the  signals  must  be 
slower  than  in  air  wires  to  obtain  clear  indications.  By  the  use  of 
alternating  currents — that  is,  of  currents  which  are  alternately  positive 
and  negative — their  disturbing  influences  may  be  materially  lessened,  and 
communication  be  accelerated  and  made  more  certain,  but  they  can  never 
be  entirely  obviated. 

In  the  Atlantic  Cable  instruments  on  the  principle  of  Thomson's 
reflecting  galvanometer  are  used  for  the  reception  of  signals,  the  mo- 
tions of  the  spot  of  hght  to  the  right  and  left  forming  the  basis  of  the 
alphabet. 

837.  Duplex  telegrrapby. — By  this  is  meant  a  system  of  telegraphy  by 
which  messages  may  be  simultaneously  sent  in  opposite  directions  on 
one  and  the  same  wire,  whereby  the  working  capacity  of  a  line  is  practi- 
cally doubled. 

Several  plans  have  been  devised  for  accomplishing  this  very  im- 
portant improvement ;  no  more  can  here  be  attempted  than  to  give  a 
general  account  of  the  principle  of  the  method  in  one  case. 

Let  m,  fig.  679,  represent  the  electro-magnets  of  a  Morse's  instrument 
which  is  wound  round  with  two  equal  coils  in  opposite  directions  ;  these 
coils  are  represented  by  the  thick  and  thin  lines,  and  one  of  them,  which 
may  be  called  the  h'ne  coil,  is  joined  to  the  line  LL^,  which  connects  the 
two  stations.  The  other  coil,  that  represented  by  the  thicker  line,  which 
may  be  called  the  equating  coil,  is  in  connection  with  the  earth  at  E  by 
means  of  an  adjustable  resistance,  or  artificial  line  R.  By  this  means 
the  resistance  of  the  branch  a  RE  may  be  made  equal  to  that  of  the 
branch  a  LL„  a  .     The  battery  d  has  one  pole  to  earth  at  E,  and  the  other 


']62 


Dynamical  Electricity, 


[837 


pole,  by  means  of  a  make  and  break  key  r,  can  be  connected  at  a^  where 
the  two  oppositely  wound  coils  bifurcate. 

The  station  at  B  is  arranged  in  a  similar  manner  as  is  represented  by 
correspondmg  letters  with  suffixes. 

Now  when  A  depresses  his  key  and  sends  a  current  into  the  line,  in- 
asmuch as  the  electro-magnet  of  his  instrument  is  wound  with  equal  coils 
in  opposite  directions,  the  armature  is  not  attracted  for  the  core  is  not 
magnetised,  because  the  currents  in  the  two  coils  counteract  one  another. 
Thus  although  a  current  passes  from  A,  there  is  no  indication  of  it  in  his 
own  instrument,  a  condition  essential  in  all  systems  of  duplex  telegraphy. 

But  with  regard  to  the  effect  on  B,  there  are  two  cases  according  as  he 
is  or  is  not  sending  a  message  at  the  same  time.     If  B's  key  is  not  down. 


Fig.  679. 

then,  seeing  that  there  is  a  break  at  c^^  the  current  will  circulate  continuously 
round  the  core  of  the  electro-magnet  in  one  direction  only,  it  will  in  fact 
reach  the  earth  by  the  path  a^  L^  R^  E^ ;  the  core  will  therefore  become 
magnetised,  the  armature  attracted,  and  a  signal  be  produced  in  the 
ordinary  way. 

If,  however,  at  the  moment  at  which  A  has  his  key  down,  B  also  de- 
presses his,  then  it  will  be  seen  that  as  currents  are  sent  in  opposite 
directions  from  both  A  and  B,  they  neutralise  one  another,  no  current 
passes  in  the  line  a  LL^  a^  ;  it  is,  as  it  were,  blocked.  But  though  no 
current  passes  in  the  line  coil,  a  current  does  pass  at  each  station  to 
earth,  through  the  equating  coil,  which  being  no  longer  counterbalanced 
by  any  opposite  current  in  the  line  coil,  magnetises  the  core  of  the 
electro-magnet,  which  thus  attracts  the  armature  and  produces  a 
signal. 

We  have  here  supposed  that  A  and  B  both  send  for  instance  the  same 
currents  to  line;  the  final  effect  is  not  different  if  they  send  opposite 
currents  at  the  same  time.     For  then,  as  they  neutralise  each  other  in  the 


-839]  Electrochemical  Telegraph.  763 

line  LL^,  the  effect  of  which  is  the  same  as  if  the  resistance  of  the  hne 
were  diminished.  More  electricity  flows  at  line  from  each  station 
through  the  line  coil,  being  no  longer  balanced  by  the  equating  coil, 
the  current  of  the  line  coil  preponderates  and  works  the  electro- 
magnet. 

Hence  in  both  these  cases,  each  station,  so  to  speak,  produces  the 
signal  which  the  other  one  wishes  to  send. 

838.  Bain's  electrocbemical  telegrrapb. — If  a  strip  of  paper  be 
soaked  in  an  aqueous  solution  of  ferrocyanide  of  potassium  and  con- 
nected with  the  negative  pole  of  a  battery,  and  if  the  other  face  be 
touched  with  a  steel  pointer  connected  with  the  positive  pole,  a  blue 
mark  due  to  the  formation  of  some  Prussian  blue  will  be  formed  about 
the  iron,  so  long  as  the  current  passes.  The  first  telegraph  based  on  this 
principle  was  invented  by  Mr.  Bain.  The  alphabet  is  the  same  as  Morse's, 
but  the  despatch  is  first  composed  at  the  departure  station  on  a  long 
strip  of  ordinary  paper.  It  is  perforated  successively  by  small  round  and 
elongated  holes,  which  correspond  respectively  to  the  dots  and  marks. 
This  strip  of  paper  is  interposed  between  a  small  metal  wheel  and  a 
metal  spring,  both  forming  part  of  the  circuit.  The  wheel  in  turning 
carries  with  it  the  paper  strip,  all  parts  of  which  pass  successively 
between  the  wheel  and  the  plate.  If  the  strip  were  not  perforated,  it 
would,  not  being  a  conductor,  constantly  offer  a  resistance  to  the  passage 
of  the  current ;  but,  in' consequence  of  the  holes,  every  time  one  of  them 
passes  there  is  contact  between  the  wheel  and  the  plate.  Thus  the 
current  works  the  relay  of  the  post  to  which  it  is  sent,  and  traces  in  blue, 
on  a  paper  disc,  impregnated  with  ferrocyanide  of  potassium,  the  same 
series  of  points  and  marks  as  those  on  the  perforated  paper. 

839.  The  Sounder. — The  sound  produced  when  the  armature  of  the 
electromagnet  in  a  Morse's  instrument  is  attracted  by  the  passage  of  the 
current  is  so  distinct  and  clear  that  many  telegraph  operators  have  been 
in  the  habit  of  reading  the  messages  by  the  sounds  thus  produced,  and 
at  most  of  checking  their  readmg  by  comparison  with  the  signs  produced 
on  the  paper. 

Based  on  this  fact  a  form  of  instrument  invented  in  America  has 
come  into  use  for  the  purpose  of  reading  by  sound.  The  soutider,  as  it 
is  called,  is  essentially  a  small  electromagnet  on  an  ebonite  base, 
resembling  the  relay  in  (835).  The  armature  is  attached  to  one  end 
of  a  lever,  and  is  kept  at  a  certain  distance  from  the  electromagnet  by  a 
spring.  When  the  current  passes  the  armature  is  attracted  against  the 
electromagnet,  with  a  sharp  click,  and  when  the  current  ceases  it  is 
withdrawn  by  the  spring.  Hence  the  interval  between  the  sounds  is  of 
longer  or  shorter  duration  according  to  the  will  of  the  sounder,  and  thus 
in  effect  a  series  of  short  and  long  sounds  can  be  produced  w^hich 
correspond  to  the  dots  and  dashes  of  the  Morse  alphabet. 

Such  instruments  are  simple,  easily  adjusted,  and  portable,  not 
occupying  more  space  than  an  ordinary  fieldglass.  They  are  coming 
into  extended  use  especially  for  military  telegraph  work. 


764 


Dynamical  Electricity. 


[840- 


840.  Electric  alarum. — One  form  of  these  instruments  is  represented 
in  fig.  680.     On  a  wooden  board  arranged  vertically  is  fixed  an  electro- 

magnet   E  ;  the  line   wire  is   connected 

^^^--^^^i^^^^^~'^^^.%.  «,X.«  i.^iiii.iiij>  with  the  binding  screw  m,  with  which  is 
Ji||llllil««lil11^Ai|  ,,i3„  ,„„„ected  one  end  of  the  wire  of  the 
"''"^  ^  electromagnet  ;  the  other  end  is  connected 

with  a  spring  c,  to  which  is  attached  the 
armature  a ;  this  again  is  pressed  against 
by  a  spring  C,  which  in  turn  is  connected 
with  the  binding  screw  n  from  which  the 
wire  leads  to.  earth. 

Whenever  the  current  passes,  the 
armature  is  attracted,  carrying  with  it  a 
hammer  P,  which  strikes  against  the  bell 
T  and  makes  it  sound.  The  moment  this 
takes  place  contact  is  broken  between  the 
armature  a  and  the  spring  C,  the  current 
being  stopped  the  electromagnet  does  not 
act ;  the  spring  c  however  in  virtue  of  its 
elasticity  brings  the  armature  in  contact 
with  the  spring  C,the  current  again  passes, 
and  so  on  as  long  as  the  current  passes. 
841.  Electrical'  clocks.  —  Electrical 
clocks  are  clockwork  machines,  in  which  an  electromagnet  is  both  the 
motor  and  the   regulator,   by  means   of  an  electric  current  regularly 


Fig.  680. 


Fig.  681 


Fig.  682. 


interrupted,  in  a  manner  resembling  that  described  in  the  preceding 
paragraph.  Fig.  681  represents  the  face  of  such  a  clock,  and  fig.  682  the 
mechanism  which  works  the  needles. 


-842]  Electromagnetic  Machines.,  765 

An  electromagnet,  B,  attracts  an  armature  of  soft  iron,  P,  movable 
on  a  pivot,  a.  The  armature  P  transmits  its  oscillating  motion  to  a  lever, 
^,  which,  by  means  of  a  ratchet,  n,  turns  the  wheel,  A.  This,  by  the 
pinion,  D,  turns  the  wheel  C,  which  by  a  series  of  wheels  and  pinions 
moves  the  hands.  The  small  one  marks  the  hours,  the  large  one  the 
minutes  ;  but  as  the  latter  does  not  move  regularly,  but  by  sudden  starts 
Irom  second  to  second,  it  follows  that  it  may  also  be  used  to  indicate  the 
seconds. 

It  is  obvious  that  the  regularity  of  the  motion  of  the  hands  depends 
on  the  regularity  of  the  oscillations  of  the  piece  P.  For  this  purpose,  the 
oscillations  of  the  current,  before  passing  into  the  electromagnet  B,  are 
regulated  by  a  standard  clock,  which  itself  has  been  previously  regulated 
by  a  seconds  pendulum.  At  each  oscillation  of  the  pendulum,  there  is 
nn  arrangement  by  which  it  opens  and  closes  the  current,  and  thus  the 
armature  P  beats  seconds  exactly. 

To  illustrate  the  use  of  these  electrical  clocks,  suppose  that  on  the 
railway  from  London  to  Birmingham  each  station  has  an  electric  clock, 
and  that  from  the  London  station  a  conducting  wire  passes  to  all  the 
clocks  on  the  line  as  far  as  Birmingham.  When  the  current  passes  in 
this  wire  all  the  clocks  will  simultaneously  indicate  the  same  hour,  the 
same  minute,  and  the  same  second  ;  for  electricity  travels  with  such 
enormous  velocity,  that  it  takes  an  inappreciable  time  to  go  from  London 
to  Birmingham. 

842.  Electromag-netic  maclilnes. — Numerous  attempts  have  been 
made  to  apply  electromagnetism  as  a  motive  force  in  machines.  Fig. 
683  represents  a  machine  of  this  kind  constructed  by  M.  Froment .  It 
consists  of  four  powerful  electromagnets,  ABCD,  fixed  on  an  iron  frame, 
X.  Between  these  electromagnets  is  a  system  of  two  iron  wheels  mov- 
able on  the  same  horizontal  axis,  with  eight  soft  iron  armatures,  M,  on 
their  circumference. 

The  current  arrives  at  K,  ascends  in  the  wire  E,  and  reaches  a  metallic 
arc,  O,  which  serves  to  pass  the  current  successively  into  each  electro- 
magnet, so  that  the  attractions  exerted  on  the  armatures  M  shall  always 
be  in  the  same  direction.  Now  this  can  only  be  the  case  provided  the 
current  is  broken  in  each  electromagnet  just  when  an  armature  comes  in 
front  of  the  axis  of  the  bobbin.  To  produce  this  interruption  the  arc  O 
has  three  branches,  e,  each  terminating  with  a  steel  spring,  to  which  a 
small  sheave  is  attached.  Two  of  these  establish  the  communication 
respectively  with  an  electromagnet,  and  the  third  with  two.  On  a 
central  wheel,  a,  there  are  cogs,  on  which  the  sheaves  alternately  rest. 
Whenever  one  of  them  rests  on  a  cog,  the  current  passes  into  the  corre- 
sponding electromagnet,  but  ceases  to  pass  when  there  is  no  longer  con- 
tact. On  emerging  from  the  electromagnets  the  current  passes  to  the 
negative  pole  of  the  battery  by  the  wire  H. 

In  this  manner,  the  armatures  M  being  successively  attracted  by  the 
four  electromagnets,  the  system  of  wheels  which  carries  them  assumes  a 
rapid  rotatory  motion,  which  by  the  wheel  P  and  an  endless  band  is 


^66 


Dynamical  Electricity. 


[842- 


transmitted  to  a  sheave,  O,  which  sends  it  finally  to  any  machine,  a 
grinding  mill  for  example. 

In  his  workshops  M.  Froment  has  an  electromotive  engine  of  one- 
horse  power.  But  as  yet  these  machines  have  not  been  applied  in 
manufactures,  for  the  expense  of  the  acids  and  the  zinc  which  they  use 


Fig.  683. 

very  far  exceeds  that  of  the  coal  in  steam  engines  of  the  same  force. 
Until  some  cheaper  source  of  electricity  shall  have  been  discovered  there 
is  no  expectation  that  they  can  be  applied  at  all  advantageously. 

Thus  a  machine  devised  by  Kravogl  produces  about  17  per  cent,  of 
the  useful  effect  due  to  the  zinc,  and  therefore  in  utilising  this  force  they 
are  about  equal  to  the  best  steam  engines.  But  a  pound  of  coal  yields 
7,200  thermal  units,  and  a  pound  of  zinc  only  1,200;  and  as  zinc  is  ten 
times  as  dear  as  coal,  engines  worked  by  electricity  are  sixty  times  as 
dear  as  steam  engines. 


\ 


^843] 


Voltaic  Induction. 


767 


CHAPTER  VI. 


VOLTAIC   INDUCTION. 

843.  Induction  by  currents. — We  have  already  seen  (699)  that  under 
the  name  indnctio7i  is  meant  the  action  which  electrified  bodies  exert  at 
a  distance  on  bodies  in  the  natural  state.  Hitherto  we  have  only  had  to 
deal  with  electrostatical  induction;  we  shall  now  see  that  dynamical 
electricity  produces  analogous  effects. 

Faraday  discovered  this  class  of  phenomena  in  1832,  and  he  gave  the 
name  of  currents  of  induction  or  induced  currents  to  instantaneous  currents 
developed  in  metallic  conductors  under  the  influence  of  metallic  conductors 
traversed  by  electric  currents,  or  by  the  influence  of  powerful  magnets, 
or  even  by  the  magnetic  action  of  the  earth;  and  the  currents  which  give 
rise  to  them  he  called  inducing  currents. 

The  inductive  action  of  a  current  at  the  moment  of  opening  or  closing 
may  be  shown  by  means  of  a  bobbin  with  two  wires.  This  consists  (fig. 
684)  of  a  cylinder  of  wood  or  of  cardboard,  on  which  a  quantity  of  silk- 
covered  No.  16  copper  wire  is  coiled;  on  this  is  coiled  a  considerably 


Fig.  684. 


greater  length  of  fine  copper  wire  about  No.  35,  also  insulated  by  being 
covered  with  silk.  This  latter  coil,  which  is  called  the  secondary  coil,  is 
connected  by  its  ends  with  two  binding  screws,  a,  b,  from  which  wires 
pass  to  a  galvanometer,  while  the  thicker  wire,  the  primary  coil,  is  con- 
nected by  its  extremities  with  two  binding  screws,'  c  and  d.  One  of 
these,  d,  being  connected  with  one  pole  of  a  battery,  when  a  wire  from 
the  other  pole  is  connected  with  c,  the  current  passes  in  the  primary  coil, 
and  in  this  alone.     The  following  phenomena  are  then  observed  : — 

i.  At  the  moment  at  which  the  thick  wire  is  traversed  by  the  current 
the  galvanometer  by  the  deflection  of  the  needle  indicates  the  existence 
in  the  secondary  coil  of  a  current  inverse  to  that  in  the  primary  coil,  that 
is,  in  the  contrary  direction ;  this  is  only  instantaneous,  for  the  needle 


768 


Dy7tamical  Electricity. 


[843- 


immediately  reverts  to  zero,  and  remains  so  long  as  the  inducing  current 
passes  through  cd. 

ii.  At  the  moment  at  which  the  current  is  opened,  that  is,  when  the 
wire  cd  ceases  to  be  traversed  by  a  current,  there  is  again  produced  in  the 
wire  ab  an  induced  current  instantaneous  hke  the  first,  but  direct,  that  is, 
in  the  same  direction  as  the  inducing  current. 

844.  Production  of  induced  currents  by  continuous  ones. — Induced 
currents  are  also  produced  when  a  primary  coil  traversed  by  a  current  is 
approached  to  or  removed  from  a  secondary  one :  this  may  be  shown  by 
the  following  apparatus,  fig.  685,  in  which  B  is  a  hollow  coil  consisting  of 
a  great  length  of  fine  wire,  and  A  a  coil  consisting  of  a  shorter  and  thicker 
wire,  and  of  such  dimensions  that  it  can  be  placed  in  a  secondary  coil. 


Fig.  685. 

The  coil  A  being  traversed  by  a  current,  if  it  is  suddenly  placed  in  the 
coil  B,  a  galvanometer  connected  with  the  latter  indicates  by  the  direction 
of  its  deflection  the  existence  in  it  of  an  inverse  current ;  this  is  only 
instantaneous,  the  needle  rapidly  returns  to  zero,  and  remains  so  long  as 
the  small  bobbin  is  in  the  large  one.  If  it  is  rapidly  withdrawn,  the  gal- 
vanometer shows  that  the  wire  is  traversed  by  a  direct  current.  If,  instead 
of  rapidly  introducing  or  replacing  the  primary  coil,  this  is  done  slowly, 
the  galvanometer  only  indicates  a  weak  current,  and  which  is  the  feebler 
the  slower  the  motion. 

If,  instead  of  varying  the  distance  of  the  inducing  current,  its  intensity 
be  varied,  that  is,  either  increased  by  bringing  additional  battery  power 
into  the  circuit,  or  diminished  by  increasing  the  resistance,  an  induced 
current  is  produced  in  the  secondary  wire,  which  is  inverse  if  the  intensity 
of  the  inducing  current  increases  and  direct  if  it  diminishes. 


-846]         Inductive  Action  of  the  Ley  den  Discharge.  769 

845.  Conditions  of  induction.  Kenx's  la\(r. — From  the  experiments 
which  have  been  described  in  the  previous  paragraphs  the  following  prin- 
ciples may  be  deduced  : — 

I.  The  distance  remaining  the  same,  a  continuous  a?id  constant  current 
does  not  induce  any  curre?it  iti  an  adjacent  conductor. 

II.  A  current  at  the  ino?nent  0/  being  dosed,  produces  in  an  adjacent 
.  conductor,  an  inverse  current. 

III.  A  current,  at  the  moment  it  ceases, produces  a  direct  current. 

IV.  A  current  which  is  removed,  or  whose  intensity  diminishes,  gives 
rise  to  a  direct  induced  current. 

V.  A  current  which  is  approached,  or  whose  intensity  increases,  gives 
rise  to  an  inverse  induced  current. 

VI.  On  the  induction  produced  between  a  closed  circuit  and  a  current 
in  activity,  when  their  relative  distance  varies,  Lenz  has  based  the  follow- 
ing law,  which  is  known  as  Lenzs  law: — 

If  the  relative  position  of  two  conductors  A  a7id  B  be  changed,  of  which 
A  is  traversed  by  a  ctcrrent,  a  current  is  induced  in  B  in  such  a  direction, 
that  by  its  electrodynamic  action  on  the  ctn'rent  in  A,  it  would  have  im- 
parted to  the  conductors  a  motioji  of  the  coittrary  kind  to  that  by  which  the 
,    inducing  action  was  produced. 

Thus,  for  instance,  in  V,  when  a  current  is  approached  to  a  conductor, 
an  inverse  cuiTent  is  produced ;  but  two  conductors  traversed  by  currents 
in  opposite  directions,  repel  one  another  according  to  the  received  law  of 
electrodynamics.  Inversely  when  a  current  is  moved  away  from  a  con- 
ductor, a  current  of  the  same  direction  is  produced ;  now  two  currents  in 
the  same  direction  attract  one  another. 

On  bringing  the  inducing  wire  near  the  induced  as  well  as  in  removing 
it  away,  work  is  required ;  hence  a  quantity  of  heat  proportional  to  the 
work  consumed  must  result,  as  Edlund's  investigations  have  shown.  On 
the  other- hand,  when  induction  results  from  the  opening  and  closing  of 
the  circuit  (II.  and  III.)  no  work  is  lost,  but  the  inducing  current  loses  as 
much  heat  as  is  produced  in  the  induced  circuit. 

846.  Inductive  action  of  the  Xieyden  discbargre. — Figure  686  repre- 
sents an  apparatus  devised  by  Matteucci,  which  is  very  well  adapted  for 
showing  the  development  of  induced  currents  produced  either  by  the  dis- 
charge of  a  Leyden  jar  or  by  the  passage  of  a  voltaic  current. 

It  consists  of  two  glass  plates  about  12  inches  diameter,  fixed  vertically 
on  the  two  supports  A  and  B.  These  supports  are  on  movable  feet,  and 
can  either  be  approached  or  removed  at  will.  On  the  anterior  face  of  the 
plate  A  are  coiled  about  30  yards  of  copper  wire,  C,  a  millimetre  in 
diameter.  The  two  ends  of  this  wire  pass  through  the  plate,  one  in  the 
centre,  the  other  near  the  edge,  terminating  in  two  binding  screws,  like 
those  represented  in  m  and  n,  on  the  plate  B.  To  these  binding  screws 
are  attached  two  copper  wires,  c  and  d^  through  which  the  inducing 
current  is  passed. 

On  the  face  of  the  plate  B,  which  is  towards  A,  is  enrolled  a  spiral  of 
much  finer  copper  wire  than  the  wire  C.  Its  extremities  terminate  in  the 
binding  screws  m  and  n,  on  which  are  fixed  two  wires,  h  and  /,  intended 

LL 


770  Dynamical  Electricity.  [846- 

to  transmit  the  induced  current.     The  two  wires  on  the  plates  are  not 
only  covered  with  silk,  but  each  circuit  is  insulated  from  the  next  one  by 


JL>U-JA)fUlnK    fir 

Fig.  686. 

a  thick,  layer  of  shellac  varnish,  a  condition  necessary  in  experimenting 
with  statical  electricity,  which  is  always  more  difficult  to  insulate  than 
that  of  the  voltaic  current. 

In  order  to  show  the  production  of  the  induced  current  by  the  discharge 
of  a  Leyden  jar,  one  end  of  the  wire  C  is  connected  with  the  outer  coating, 
and  the  other  end  with  the  knob  of  the  Leyden  jar,  as  shown  in  the  figure. 
When  the  spark  passes,  the  electricity  traversing  the  wire  C  acts  by  in- 
duction on  the  neutral  fluid  of  the  wire  on  the  plate  B,  and  produces  an 
instantaneous  current  in  this  wire.  A  person  holding  two  copper  handles 
connected  with  the  wires  i  and  h,  receives  a  shock,  the  intensity  of  which 
is  greater  in  propertion  as  the  plates  A  and  B  are  nearer.  This  experi- 
ment proves  that  frictional  electricity  can  give  rise  to  induced  currents  as 
well  as  voltaic  electricity. 

The  above  apparatus  can  also  be  used  to  show  the  production  of  in- 
duced currents  by  the  influence  of  voltaic  currents.  For  this  purpose  the 
current  of  a  battery  is  passed  through  the  inducing  wire  C,  while  the  ends 
of  the  other  wire,  h  and  /,  are  connected  with  a  galvanometer.  At  the 
moment  at  which  the  current  commences  or  finishes,  or  when  the  distance 
of  the  two  conductors  is  varied,  the  same  phenomena  are  observed  as  in 
the  case  of  the  apparatus  (843). 

847.  Induction  by  magrnets. — It  has  been  seen  that  the  influence  of 
a  current  magnetises  a  steel  bar ;  in  like  manner  a  magnet  can  produce 
induced  currents  in  metallic  circuits.  Faraday  has  shown  this  by  means 
of  a  coil  with  a  single  wire  of  200  to  300  yards  in  length.  The  two 
extremities  of  the  wire  being  connected  with  a  galvanometer,  as  shown  in 
fig.  687,  a  strongly  magnetised  bar  is  suddenly  inserted  in  the  bobbin,  and 
the  following  phenomena  are  observed  : — 

i.  At  the  moment  at  which  the  magnet  is  introduced,  the  galvanometer 
indicates  in  the  wire  the  existence  of  a  current,  the  direction  of  which  is 
opposed  to  that  which  circulates  round  the  magnet,  considering  the  latter 
as  a  solenoid  on  Ampere's  theory  (827). 


-848] 


Induction. 


771 


ii.  When  the  bar  is  withdrawn,  the  needle  of  the  galvanometer,  which 
has  returned  to  zero,  indicates  the  existence  of  a  direct  current. 

The  inductive  action  of  magnets  may  also  be  illustrated  by  the  follow- 


Kig.  687. 

ing  experiment :  a  bar  of  soft  iron  is  placed  in  the  above  bobbin  and  a  strong 
magnet  suddenly  brought  in  contact  with  it;  the  needle  of  the  galvano- 
meter is  deflected,  but  returns  to  zero  when  the  magnet  is  stationary,  and 
is  deflected  in  the  opposite  direction  when  it  is  removed.  The  induction 
is  here  produced  by  the  magnetisation  of  the  soft  iron  bar  in  the  interior 
of  the  bobbin  under  the  influence  of  the  magnet. 

The  same  inductive  effects  are  produced  in  the  wires  of  an  electro- 
magnet, if  a  strong  magnet  be  made  to  rotate  rapidly  in  front  of  the 
extremities  of  the  wire  in  such  a  manner  that  its  poles  act  successively  by 
influence  on  the  two  branches  of  the  electromagnet :  or  also  by  forming 
two  coils  round  a  horse-shoe  magnet,  and  passing  a  plate  of  soft  iron 
rapidly  in  front  of  the  poles  of  the  magnet;  the  soft  iron  becoming 
magnetised  reacts  by  influence  on  the  magnet,  and  induced  currents  are 
produced  in  the  wire  alternately  in  different  directions. 

The  inductive  action  of  magnets  is  a  striking  confirmation  of  Ampere's 
theory  of  magnetism.  For  as  on  this  theory  all  magnets  are  solenoids, 
ail  the  experiments  which  have  been  mentioned  may  be  explained  by  the 
inductive  action  of  currents  which  traverse  the  surface  of  magnets ;  the 
induction  of  magnets  is  in  short  an  induction  of  currents.  And  it  is  a 
useful  exercise  to  see  how,  on  this  view,  the  inductive  action  of  magnets 
falls  under  Lenz's  law  (845). 

848.  Inductive  action  of  mag^nets  on  bodies  in  motion. — Arago 
was  the  first  to  observe,  in  1824,  that  the  number  of  oscillations  which  a 
magnetised  needle  makes  in  a  given  time,  under  the  influence  of  the 
earth's  magnetism,  is  very  much  lessened  by  the  proximity  of  certain 
metallic  masses,  and  especially  of  copper,  which  may  reduce  the  number. 


772  Dynamical  Electricity.  [848- 

in  a  given  time  from  300  to  4.  This  observation  led  Arago  in  1825  to 
an  equally  unexpected  fact ;  that  of  the  rotative  action  which  a  plate  of 
copper  in  motion  exercises  on  a  magnet. 

This  phenomenon  may  be  shown  by  means  of  the  apparatus  represented 
in  fig.  688.  It  consists  of  a  copper  disc,  M,  movable  about  a  vertical 
axis.     On  this  axis  is  a  sheave,  B,  round  which  is  coiled  an  endless  cord 


Fig.  688 

passing  also  round  the  sheave  A.  By  turning  this  with  the  hand,  the  disc 
M  may  be  rotated  with  great  rapidity.  Above  the  disc  is  a  glass  plate, 
on  which  is  a  small  pivot  supporting  a  magnetic  needle,  ab.  If  the  disc 
be  now  moved  with  a  slow  but  uniform  velocity,  the  needle  is  deflected  in 
the  direction  of  the  motion,  and  stops  at  an  angle  of  from  20°  to  30°  with 
the  direction  of  the  magnetic  meridian,  according  to  the  velocity  of  the 
rotation  of  the  disc.  But  if  this  velocity  increases,  the  needle  is  ulti- 
mately deflected  more  than  90°  ;  it  is  then  carried  along,  describes  an 
entire  revolution,  and  follows  the  motion  of  the  disc  until  this  stops. 

Babbage  and  Herschel  modified  Arago's  experiment  by  causing  a  horse- 
shoe magnet  placed  vertically  to  rotate  below  a  copper  disc  suspended 
on  silk  threads  without  torsion  ;  the  disc  rotated  in  the  same  direction 
as  the  magnets. 

The  effect  decreases  with  the  distance  of  the  disc,  and  varies  with  its 
nature.  The  maximum  effect  is  produced  with  metals  ;  with  wood,  glass, 
water,  etc.  it  disappears.  Babbage  and  Herschel  have  found  that  repre- 
senting this  action  on  copper  at  100,  the  action  on  other  metals  is  as 
follows  :  zinc  95,  tin  46,  lead  25,  antimony  9,  bismuth  2.  Lastly,  the  effect 
is  enfeebled  if  the  disc  presents  breaks  in  the  continuity,  especially  in  the 
direction  of  the  radii  ;  but  the  same  physicists  have  observed  that  it 
virtually  regains  the  same  intensity  if  these  breaks  have  been  soldered 
with  any  metal. 

Faraday  made  an  experiment  the  reverse  of  Arago's  first  observation  ; 
since  the  presence  of  a  metal  at  rest  stops  the  oscillations  of  a  magnetic 
needle,  the  neighbourhood  of  a  magnet  at  rest  ought  to  stop  the  motion 


-849]  Induction  by  the  Action  of  the  Earth.  773 

of  a  rotating  mass  of  metal.  Faraday  suspended  a  cube  of  copper  to  a 
twisted  thread,  which  was  placed  between  the  poles  of  a  powerful  electro- 
magnet. When  the  thread  was  left  to  itself,  it  began  to  spin  round  with 
great  velocity,  but  stopped  the  moment  a  powerful  current  passed  through 
the  electromagnet. 

Faraday  was  the  first  to  give  an  explanation  ot  all  these  phenomena 
of  magnetism  by  rotation.  They  depend  on  the  circumstance  that  a 
magnet  or  a  solenoid  can  induce  currents  in  a  solid  mass  of  metal.  In 
the  above  case  the  magnet  induces  currents  in  the  disc,  when  the  latter 
is  rotated  ;  and  conversely  when  the  magnet  is  rotated  while  the  disc  is 
primarily  at  rest.  Now  these  induced  currents  by  their  electrodynamic 
action  tend  to  destroy  the  motion  which  gave  rise  to  them ;  they  are 
simple  illustrations  of  Lenz's  law ;  they  act  just  in  the  same  way  as  friction 
would  do. 

i.  For  instance,  let  AB  (fig.  689)  be  a  needle  oscillating  over  a  copper 
disc,  and  suppose  that  in  one  of  its  oscillations  it 
goes  in  the  direction  of  the  arrows  from  N  to  M.  In 
approaching  the  point  M,  for  instance,  it  developes 
there  a  current  in  the  opposite  direction,  and  which 
therefore  repels  it ;  in  moving  away  from  N  it  pro- 
duces currents  which  are  of  the  same  kind,  and 
which  therefore  attract,  and  both  these  actions  con- 
cur in  bringing  it  to  rest. 

ii.  Suppose   the  metallic  mass  turns  from  N  to-  '^'    ^' 

wards  M,  and  that  the  magnet  is  fixed  ;  the  magnet  will  repel  by  induc- 
tion points  such  as  N  which  are  approaching  A,  and  will  attract  M  which 
is  moving  away ;  hence  the  motion  of  the  metal  stops,  as  in  Faraday's 
experiment. 

iii.  If  in  Arago's  experiment  the  disc  is  moving  from  N  to  M  ;  N  ap- 
proaches A  and  repels  it,  while  M  moving  away  attracts  it;  hence  the 
needle  moves  in  the  same  direction  as  the  disc. 

If  this  explanation  is  true,  all  circumstances  which  favour  induction 
will  increase  with  dynamic  reaction;  and  those  which  diminish  the  former 
will  also  lessen  the  latter.  We  know  that  induction  is  greater  in  good 
conductors,  and  that  it  does  not  take  place  in  insulating  substances ;  but 
we  have  seen  that  the  needle  is  moved  with  a  force  which  is  less,  the 
less  the  conducting  powers  of  the  disc,  and  it  is  not  moved  when  the  disc 
is  of  glass.  Dove  has  found  that  there  is  no  induction  on  a  tube  split 
lengthwise  in  which  a  coil  is  introduced. 

In  order  to  bring  the  oscillations  of  the  needle  of  a  galvanometer  more 
quickly  to  rest,  the  wire  is  coiled  upon  a  copper  frame.  Such  an  arrange- 
ment is  called  a  damper^  and  in  practice  it  is  frequently  used. 

849.  Induction  by  the  action  of  the  earth. — Faraday  discovered 
that  terrestrial  magnetism  can  develope  induced  currents  in  metallic 
bodies  in  motion,  acting  like  a  powerful  magnet  placed  in  the  interior  of 
the  earth  in  the  direction  of  the  dipping  needle,  or,  according  to  the 
theory  of  Ampere,  like  a  series  of  electrical  currents  directed  from  east 
to  west  parallel  to  the  magnetic  equator.     He  first  proved  this  by  placing 


774 


Dynamical  Electricity. 


[849- 


a  long  helix  of  copper  wire  covered  with  silk  in  the  plane  of  the  magnetic 
meridian  parallel  to  the  dipping  needle  ;  by  turning  this  helix  i8o°  round 
an  axis  perpendicular  to  its  length  in  its  middle,  he  observed  that  at  each 
turn  a  galvanometer  connected  with  the  two  ends  of  the  helix  was  de- 
flected.    The  apparatus  depicted  in  fig.  690,  and  known  as  Delezenne's 


Fig.  6go. 

circle,  serves  for  showing  the  existence  of  terrestrial  induced  currents.  It 
consists  of  a  wooden  ring,  RS,  about  two  feet  in  diameter,  fixed  to  an  axis 
ao,  about  which  it  can  be  turned  by  means  of  a  handle,  M.  The  axis  oa  is 
itself  fixed  in  a  frame,  PQ,  movable  about  a  horizontal  axis.  By  needles 
fixed  to  these  two  axes  the  inclination  towards  the  horizon  of  the  frame 
PQ,  and  therefore  of  the  axis  oa,  is  indicated  on  a  dial,  b,  while  a  second 
dial,  c,  gives  the  angular  displacement  of  the  ring.  This  ring  has  a  groove 
in  which  is  coiled  a  large  quantity  of  insulated  copper  wire.  The  two  ends 
of  the  wire  terminate  in  a  comfnutator  analogous  to  that  in  Clarke's  appa- 
ratus (855),  the  object  of  which  is  to  pass  the  current  always  in  the  same 
sense,  although  its  direction,  SR,  changes  at  each  semi-revolution  of  the 
ring.  Oh  each  of  the  rings  of  the  commutator  are  two  brass  plates, 
which  successively  transmit  the  current  to  two  wires  in  contact  with  the 
galvanometer.  The  axis  oa  being  in  the  magnetic  meridian,  and  the  ring 
RS  at  right  angles  to  the  direction  XY  of  the  dipping  needle,  if  it  is 
slowly  rotated  the  needle  of  the  galvanometer  is  deflected,  and  by  its 
deflection  indicates  in  the  wire  coiled  on  the  ring,  an  induced  current 
whose  intensity  increases  until  it  has  been  turned  through  90°  ;  the  devia- 
tion then  decreases,  and  is  zero  when  the  ring  has  made  a  semi-revolu- 
tion. If  the  rotation  continues,  the  current  reappears,  but  in  a  contrary 
direction,  and  attains  a  second  maximum  at  270°  ;  becoming  null  again 
after  a  complete  turn.  When  the  axis  oa  is  parallel  to  the  dip  there  is  no 
current. 

850.  Induction  of  a  current  on  itself.     Extra  current.— If  a  closed 
circuit  traversed  by  a  voltaic  current  be  opened,  a  scarcely  perceptible 


850] 


Inductio7i  of  a  Qm'efit  on  itself. 


77S 


spark  is  obtained,  if  the  wire  joining  the  two  poles  be  short.  Further,  if 
the  observer  himself  form  part  of  the  circuit  by  holding  a  pole  in  each 
hand,  no  shock  is  perceived  unless  the  current  is  very  strong.  If,  on  the 
contrary,  the  wire  is  long,  and  especially  if  it  makes  a  great  number  of 
turns,  so  as  to  form  a  bobbin  with  very  close  folds,  the  spark,  which  is  in- 
appreciable when  the  current  is  closed,  acquires  a  great  intensity  when  it 
is  opened,  and  an  observer  in  the  circuit  receives  a  shock  which  is  the 
stronger  the  greater  number  of  turns. 

Faraday  has  referred  this  strengthening  of  the  current  when  it  is  broken 
to  an  inductive  action  which  the  current  in  each  coil  exerts  upon  the  ad- 
jacent coils  :  an  action  in  virtue  of  which  there  is  produced  in  the  bobbin 
a  direct  induced  current — that  is,  one  in  the  same  direction  as  the  principal 
one.     This  is  known  as  the  extra  current. 

To  show  the  existence  of  this  current,  at  the  moment  of  opening,  Fara- 
day has  arranged  the  experiment  as  seen  in  fig.  691.     Two  wires  from  the 


Fig.  691, 

poles  of  a  battery  are  connected  with  two  binding  screws,  D  and  F,  with 
which  are  also  connected  the  two  ends  of  a  bobbin,  B,  with  a  long  fine 
wire  which  offers  therefore  a  great  resistance.  On  the  path  of  the  wires 
at  the  points  A  and  C  are  two  other  wires,  which  are  connected  with  a 
galvanometer,  G.  Hence  the  current  from  the  pole  E  branches  at  A  into 
two  currents,  one  which  traverses  the  galvanometer,  the  other  the  bobbin, 
and  both  joining  the  negative  pole  E'. 

The  needle  of  the  galvanometer  being  then  deflected  by  the  current 
which  goes  from  A  to  C,  it  is  brought  back  to  zero,  and  kept  there  by  an 
obstacle  which  prevents  it  from  turning  in  the  direction  Qa,  but  leaves 
it  free  in  the  opposite  direction.  On  breaking  contact  at  E,  it  is  seen 
that  the  moment  the  circuit  is  open  the  needle  is  deflected  in  the  direction 
Qa' ;  showing  a  current  contrary  to  that  which  passed  during  the  exist- 
ence of  the  current — that  is,  showing  a  current  from  C  to  A.  But  the 
battery  current  having  ceased,  the  only  remaining  one  is  the  current 
AFBDCA  ;  and  since  in  the  part  CA  the  current  goes  from  C  to  A,  it 


'jj6  Dyftamical  Electricity.  [850- 

must  traverse  the  entire  circuit  in  the  direction  AFBDC — that  is,  the  same 
as  the  principal  current.  This  current,  which  thus  appears  when  the 
circuit  is  opened,  is  the  extra  current. 

851.  Extra  current  on  opening:  and  on  closing-. — The  coils  of  the 
spiral  act  inductively  on  each  other,  not  merely  on  opening,  but  also  on 
closing  the  current.  Hence,  in  accordance  with  the  general  law  of  induc- 
tion, each  spire  acting  on  each  succeeding  one  induces  a  current  in  the 
opposite  direction  to  its  own — that  is,  an  inverse  current ;  this,  which  is 
the  extra  current  on  closing,  or  the  inverse  extra  current,  being  of  con- 
trary direction  to  the  principal  one,  diminishes  its  intensity,  and  lessens 
or  suppresses  the  spark  on  closing. 

When,  however,  the  current  is  opened,  each  spire  then  acts  inductively 
on  each  succeeding  one,  producing  a  current  in  the  same  direction  as  its 
own,  and  which  therefore  greatly  heightens  the  intensity  of  the  principal 
current.     This  is  the  extra  current  on  opening,  or  direct  extra  current. 

To  observe  the  direct  extra  current,  the  conductor  on  which  its  effect 
is  to  be  traced  may  be  introduced  into  the  circuit,  by  being  connected  in 
any  suitable  manner  with  the  binding  screws  A  and  C  in  the  place  of  the 
galvanometer. 

It  can  thus  be  shown  that  the  direct  extra  current  gives  violent  shocks, 
bright  sparks,  decomposes  water,  melts  platinum  wires,  and  magnetises 
steel  needles.  Abria  has  found  that  the  intensity  of  the  extra  current 
is  about  072  of  the  principal  current.  The  shock  produced  by  the 
current  may  be  tried  by  attaching  the  ends  of  the  wire  to  two  files,  which 
are  held  in  the  hands.  On  moving  the  point  of  one  file  over  the  teeth  of 
the  other  a  series  of  shocks  is  obtained,  due  to  the  alternate  opening  and 
closing  of  the  current. 

The  above  effects  acquire  greater  intensity  when  a  bar  of  soft  iron  is 
introduced  into  the  bobbin,  or,  what  is  the  same  thing,  when  the  current 
is  passed  through  the  bobbin  of  an  electromagnet ;  and  still  more  is  this 
the  case  if  the  core,  instead  of  being  massive,  consists  of  a  bundle  of 
straight  wires.  Faraday  explains  this  strengthening  action  of  soft  iron 
as  follows :  If  inside  the  spiral  there  is  an  iron  bar,  when  on  opening  the 
circuit  the  principal  current  disappears,  the  magnetism  which  it  evokes 
in  the  bar  disappears  too ;  but  the  disappearance  of  this  magnetism  acts 
like  the  disappearance  of  the  electrical  current,  and  the  disappearing 
magnetism  induces  a  current  in  the  same  direction  as  the  disappearing 
principal  current,  the  effect  of  which  is  thus  heightened. 

In  the  experiments  just  described  the  effects  of  the  two  extra  currents 
accompany  those  of  the  principal  current.  Edlund  has  devised  an  in- 
genious arrangement  of  apparatus  by  which  the  action  of  the  principal 
current  on  the  measuring  instruments  can  be  completely  avoided,  so  that 
only  that  of  the  extra  current  remains.  In  this  way  he  has  arrived  at  the 
following  laws : 

i.  The  intensity  of  the  currents  used  being  the  same,  the  extra  currents 
obtained  on  opening  and  closing  have  the  same  electromotive  Jar ce. 

ii.  The  electromotive  force  of  the  extra  current  is  proportional  to  the 
intensity  of  the  primary  current. 


-854]  Laws  of  hidiiced  Currents.  yjy 

852.  Induced  currents  of  different  orders. — Spite  of  their  instan- 
taneous character,  induced  currents  can  themselves,  by  their  action  on 
closed  circuits,  give  rise  to  new  induced  currents,  these  again  to  others, 
and  so  on,  producing  induced  currents  of  different  orders. 

These  currents,  discovered  by  Henry,  may  be  obtained  by  causing  to 
act  on  each  other  a  series  of  bobbins,  each  formed  of  a  copper  wire  covered 
with  silk,  and  coiled  spirally  in  one  plane,  like  that  represented  in  the 
plate  A,  in  fig.  673.  The  currents  thus  produced  are  alternately  in  oppo- 
site directions,  and  their  intensity  decreases  in  proportion  as  they  are  of 
a  higher  order. 

853.  Properties  of  induced  currents. — Notwithstanding  their  instan- 
taneous character,  it  appears  from  the  preceding  experiments  that  in- 
duced currents  have  all  the  properties  of  ordinary  currents.  They  produce 
violent  physiological,  luminous,  calorific,  and  chemical  effects,  and  finally 
give  rise  to  new  induced  currents.  They  also  deflect  the  magnetic  needle, 
and  magnetise  steel  bars  when  they  are  passed  through  a  copper  wire 
coiled  in  a  helix  round  the  bars. 

The  strength  of  the  shock  produced  by  induced  currents  renders  their 
effects  comparable  to  those  of  electricity  of  high  potential. 

The  direct  induced  current  and  the  inverse  induced  current  have  been 
compared  as  to  three  of  their  actions :  the  violence  of  the  shock,  the  de- 
flection of  the  galvanometer,  and  the  magnetising  action  on  steel  bars. 
In  these  respects  they  differ  greatly :  they  are  about  equal  in  their  action 
on  the  galvanometer;  but  while  the  shock  of  the  direct  current  is  very 
powerful,  that  of  the  inverse  current  is  scarcely  perceptible.  The  same 
difference  prevails  with  reference  to  the  magnetising  force.  The  direct 
current  magnetises  to  saturation,  while  the  inverse  current  does  not  mag- 
netise. 

854.  3baws  of  induced  currents. — In  his  special  treatise  on  induction, 
Matteucci  has  deduced  from  his  own  researches,  and  from  those  of  Fara- 
day, Lenz,  Dove,  Abria,  Weber,  Marianini,  and  Felici,  the  following  laws 
in  reference  to  induced  currents  : 

i.  The  strength  of  induced  currents  is  proportional  to  that  of  the  in- 
ducing  currents. 

ii.  This  strength  is  proportional  to  the  product  of  the  length  0/  the 
inducing  and  induced  currents. 

iii.  The  electromotive  force  developed  by  a  given  quantity  of  electricity 
is  the  same  whatever  be  the  nature ^  section,  or  shape  of  the  inducing  cir- 
cuit. 

iv.  The  electromotive  force  developed  by  the  induction  of  a  current  on 
any  given  conducting  circuit  is  independent  of  the  nature  of  the  con- 
ductor. 

V.  The  development  ofitiduction  is  independent  of  the  nature  of  the  in 
sulating  body  ijiterposed  between  the  induced  and  tJtducing  circuit. 

This  latter  law  is  in  disaccord  with  the  experiments  of  Faraday,  on 
the  induction  of  statical  electricity  (702). 


L  L3 


7/8 


Dynamical  Electricity. 


[855 


APPARATUS   FOUNDED   ON    INDUCTION. 

855.  Magneto-electrical  apparatus. — After  the  discovery  of  magneto- 
electrical  induction,  several  attempts  were  made  to  produce  an  uninter- 
rupted series  of  sparks  by  means  of  a  magnet.  Apparatus  for  this  purpose 
were  devised  by  Pixii  and  Ritchie,  and  subsequently  by  Saxton,  Ettings- 
hausen,  and  Clarke.  Fig.  692  represents  that  invented  by  Clarke.  It  con- 
sists of  a  powerful  horse-shoe  magnetic  battery,  A,  fixed  against  a  vertical 


Fig.  692. 


wooden  support.  In  front  of  this  there  are  two  bobbins,  BB^,  movable 
round  a  horizontal  axis.  These  bobbins  are  coiled  on  two  cylinders  of 
soft  iron  joined  at  one  end  by  a  plate  of  soft  iron,  V,  and  at  the  other  by 
a  similar  plate  of  brass.  These  two  plates  are  fixed  on  a  copper  axis, 
terminated  at  one  end  by  a  commutator,  qi,  and  at  the  other  by  a  pulley, 
which  is  moved  by  an  endless  band  passing  round  a  large  wheel,  which 
is  turned  by  a  handle. 

Each  bobbin  consists  of  about  1,500  turns  of  very  fine  copper  wire 
covered  with  silk.  One  end  of  the  wire  of  the  bobbin  B  is  connected  on 
the  axis  of  rotation  with  one  end  of  the  wire  of  the  bobbin  B",  and  the 
two  other  ends  of  these  wires  terminate  in  a  copper  ferrule  or  washer,  q^ 
which  is  fixed  to  the  axis,  but  is  insulated  by  a  cylindrical  envelope  of 


855] 


Apparatus  founded  on  Induction. 


779 


ivory.  In  order  that  in  each  wire  the  induced  current  may  be  in  the  same 
direction,  it  is  coiled  on  the  two  bobbins  in  difterent  directions— that  is, 
one  is  right-handed,  the  other  left-handed.  '  ^^ 

When  now  the  electromagnet  turns,  its  two  branches  become  alter- 
nately magnetised  in  contrary  directions  under  the  influence  of  the 
magnet  A,  and  in  each  wire  an  induced  current  is  produced,  the  direction 
of  which  changes  at  each  half  turn. 

Let  us  follow  one  of  the  bobbins — B,  for  instance — while  it  makes  a 
complete  revolution  in  front  of  the  poles  a  and  b  of  the  magnet ;  calling  the 
poles  of  the  electromagnet  successively  a'  and  b'.  Let  us  further  consider 
the  latter  when  it  passes  in  front  of  the  north  pole  of  the  magnetic  battery 
(fig.  694).     The  iron  has  then  a  south  pole  in  which,  as  we  know,  the  Am- 


Fig.  694. 


Fig.  695. 


Fig.  696. 


Fig.  697. 


perian  currents  move  like  the  hands  of  a  watch.  The  contrary  seems  to 
be  represented  in  fig.  694,  but  it  must  be  remembered  that  the  bobbins 
are  seen  here  as  they  are  in  fig.  692;  and  hence,  when  viewed  at  the 
end  which  grazes  the  magnet,  the  Amperian  currents  seem  to  turn 
like  the  hands  of  a  watch.  These  currents  act  inductively  on  the  wire  of 
the  bobbin,  producing  a  current  in  the  same  direction  (854,  iii.),  for  the 
bobbin  moves  away  from  the  pole  a,  its  soft  iron  is  demagnetised,  and 
the  Amperian  currents  cease  (845).  The  intensity  of  the  induced  current 
in    the  bobbin  decreases,  until  the  right  line  joining  the  axes   of  the 


780 


Dynamical  Electricity. 


[855- 


twq  bobbins  is  perpendicular  to  that  which  joins  the  poles  a  and  b  of  the 
bar.  There  is  now  no  magnetism  in  the  bar,  but  quickly  approaching  the 
pole  b,  its  soft  iron  is  then  magnetised  in  the  opposite  direction — that  is,  it 
iDecomes  a  north  pole  (fig.  695).  The  Amp^rian  currents  are  then  in  the 
direction  of  the  arrow  a' :  and  as  they  are  commencing,  they  develope  in 
the  wire  of  the  bobbin  an  inverse  current  (845),  which  is  in  the  same 
direction  as  that  developed  in  the  first  quarter  of  the  revolution.  More- 
over, this  second  current  adds  itself  to  the  first,  for  while  the  bobbin 
moves  away  from  a,  it  approaches  b.  Hence,  during  the  lower  half 
revolution  from  a  to  b,  the  wire  was  successively  traversed  by  two  induced 
currents  in  the  same  direction,  and  if  the  rotatory  motion  is  sufficiently 
rapid,  we  might  admit  during  this  half  revolution  the  existence  of  a  single 
current  of  the  wire. 

The  same  reasoning  applied  to  the  figures  696  and  697  will  show  that 
during  the  upper  half  revolution  the  wire  of  the  bobbin  B  is  still  traversed 
by  a  single  current,  but  in  the  opposite  direction  to  that  of  the  lower  half 
revolution.  What  has  been  said  about  the  bobbin  B  applies  obviously  to 
the  bobbin  B' ;  yet  as  one  of  these  is  right-handed  and  the  other  left- 
handed,  during  each  upper  or  lower  half  revolution  the  currents  are 
constantly  in  the  same  direction  in  the  two  bobbins.  At  each  successive 
half  revolution  they  both  change,  but  are  in  the  same  direction  as  regards 
each  other ;  the  term  direction  having  here  reference  to  figs.  694-697. 

856.  Commutator. — The  object  of  this  apparatus  (fig.  698),  of  which 
fig.  699  is  a  section,  is  to  bring  the  two  alternating  currents  always  in  the 


Fig. 


same  direction.     It  consists  of  an  insulating  cylinder  of  ivory  or  ebony,  J, 
in  the  axis  of  which  is  a  copper  cylinder,  K,  of  smaller  diameter,  fixed  to 


-856] 


Commutator. 


781 


the  armature  V,  and  turning  with  the  bobbins.  On  the  ivory  cyHnder  is 
first  a  brass  ferrule,  q,  and  in  front  of  it  two  half  ferrules,  o  and  o\  also  of 
brass  and  completely  insulated  from  one  another.  The  half  ferrule  o  is 
connected  with  the  ferrule  ^  by  a  tongue,  x.  On  the  sides  of  a  block  of 
wood,  M,  there  are  two  brass  plates,  ;«,  «,  on  which  are  screwed  two 
elastic  springs,  b  and  c^  which  press  successively  on  the  half  ferrules  0 
and  o',  when  rotation  takes  place. 

We  have  already  seen  that  the  two  ends  of  the  wire  of  the  bobbin, 
those  in  the  same  direction  with  respect  to  the  currents  passing  through 
them  at  any  time,  which  will  be  found  to  be  those  farthest  away  from  the 
armature  V,  terminate  in  the  metalhc  axis  k,  and  therefore  on  the  half 
ferrule  0' ;  while  the  other  two  ends,  both  in  the  same  direction  with 
respect  to  the  current,  are 
joined  to  the  ferrule  q,  and 
therefore  to  the  half  fer- 
rule 0.  It  follows  that  the 
pieces  o  0'  are  constantly 
poles  of  alternating  cur- 
rents which  are  developed 
in  the  bobbins  ;  and  as 
these  are  alternately  in 
contrary  directions,  the 
pieces  o  and  o'  are  al- 
ternately positive  and  ne- 
gative. Now,  taking  the 
case  in  which  the  half  ferrule  o'  is  positive, 
spring  b^  follows  the  plate  ;«,  arrives  at  n  by  the  joining  wire  /,  ascends 
in  Cj  and  is  closed  by  contact  with  the  piece  0  ;  then,  when  in  consequence 
of  rotation  o  takes  the  place  of  o\  the  current  retains  the  same  direction ; 
for,  as  it  is  then  reversed  in  the  bobbins,  0  has  become  positive  and 
0'  negative,  and  so  forth  as  long  as  the  bobbin  is  turned. 

With  the  two  springs  b  and  c  alone,  the  opposite  currents  from  the 
two  pieces  0  and  0'  could  not  unite  when  m  and  «  are  not  joined ;  this 
is  effected  by  means  of  a  third  spring,  a  (fig.  692),  and  of  two  appendices, 
/,  only  one  of  which  is  visible  in  the  figure.  These  two  pieces  are  insu- 
lated from  one  another  on  an  ivory  cylinder,  but  communicate  respectively 
with  the  pieces  0  and  0'.  As  often  as  the  spring  a  touches  one  of  these 
pieces  it  is  connected  with  the  spring  b^  and  the  current  is  closed,  for  it 
passes  from  b  to  ^,  and  then  reaches  the  spring  c  by  the  plate  n.  On  the 
contrary,  as  long  as  the  spring  a  does  not  touch  one  of  these  appendices 
the  current  is  broken. 

For  physiological  effects  the  use  of  the  spring  a  greatly  increases  the 
intensity  of  the  shocks.  For  this  purpose  two  long  spirals  of  copper  wire 
with  handles,  /  and  ^',  are  fixed  at  n  and  in.  Holding  the  handles  in 
the  hands  so  long  as  the  spring  a  does  not  touch  the  appendices  /,  the 
current  passes  through  the  body  of  the  experimenter,  but  without  appre- 
ciable effect ;  while  each  time  that  the  plate  a  touches  one  of  the  appen- 
dices /,  the  current,  as  we  have  seen  above,  is  closed  by  the  pieces  b,  a. 


Fig.  699. 

the  current  descends  by  the 


782  Dynamical  Electricity.  [856- 

and  c  and  ceasing  then  to  pass  through  the  wires  7ip,  inp\  there  is  pro- 
duced in  this  and  through  the  body  a  direct  extra-current  which  produces 
a  violent  shock. 

This  is  renewed  at  each  semi-revolution  of  the  electromagnet,  and  its 
intensity  increases  with  the  velocity  of  the  rotation.  The  muscles  con- 
tract with  such  force  that  they  do  not  obey  the  will,  and  the  two  hands 
cannot  be  detached.  With  a  well-constructed  apparatus  of  large  dimen- 
sions a  continuance  of  the  shock  is  unendurable  ;  the  person  receiving  it 
is  prostrated,  rolls  on  the  ground,  and  is  soon  completely  at  the  mercy  of 
the  operator. 

All  the  effects  of  voltaic  currents  may  be  produced  by  the  induced 
current  of  Clarke's  machine.  Fig.  693  shows  how  the  apparatus  is  to 
be  arranged  for  the  decomposition  of  water.  The  spring  a  is  suppressed, 
the  current  being  closed  by  the  two  wires  which  represent  the  electrodes. 

For  physiological  and  chemical  effects  the  wire  rolled  on  the  bobbins 
is  fine,  and  each  about  500  to  600  yards  in  length.  For  physical  effects, 
on  the  contrary,  the  wire  is  thick,  and  there  are  about  25  to  35  yards  on 
each  bobbin.  Figs.  700  and  701  represent  the  arrangement  of  the 
bobbins  and  the  commutator  in  each  case.  The  first  represents  the  in- 
flammation of  ether,  and  the  second  the  incandescence  of  a  metal  wire. 


Fig.  700.  Fig.  701. 

0.  in  which  the  current  from  the  plate  a  to  the  plate  c  always  passes  in 
the  same  direction. 

Pixii's  and  Saxton's  electromagnetic  machine  differs  from  Clarke's  in 
having  the  electromagnet  fixed  while  the  magnet  rotates. 

Wheatstone  has  recently  devised  a  compendious  form  of  the  magneto- 
electrical  machine,  for  the  purpose  of  using  the  induced  spark  in  firing 
mines  (746). 

857.  WCagrneto-electrical  machine. — The  principle  of  Clarke's  ap- 
paratus has  received  in  the  last  few  years  a  remarkable  extension  in  large 
magneto-electrical  machines,  by  means  of  which  mechanical  work  is 
transformed  into  powerful  electric  currents  by  the  inductive  action  of 
magnets  on  bobbins  in  motion. 

The  first  machine  of  this  kind  was  invented  by  Nollet,  in  Brussels,  in 
1850  ;  this  has  been  greatly  improved  by  Van  Malderen,  who  has  also 
applied  it  to  electrical  illumination. 

This  machine  is  represented  in  fig,  702,  as  it  stands  in  a  workshop  at 
the  Hotel  des  Invalides,  in  Paris,  where  it  was  constructed.     One    of 


857] 


Magneto- Electrical  Machine. 


783 


these  machines  was  exhibited  in  the  International  Exhibition  of  1862.  It 
consists  of  a  cast-iron  frame,  5^  feet  in  height,  on  the  circumference  of 
which  eight  series  of  five  powerful  horse-shoe-magnetic  batteries,  A,  A,  A, 
are  arranged  in  a  parallel  order  on  wooden  cross-pieces.  These  batteries, 
each  of  which  can  support  from  120  to  130  pounds,  are  so  arranged  that, 


W      W  II    1 1  illl 


Fig  702, 

if  they  are  considered  either  parallel  to  the  axis  of  the  frame,  or  in  a  plane 
perpendicular  to  this  axis,  opposite  poles  always  face  one  another.  In 
each  series  the  outside  batteries  consist  of  three  magnetised  plates, 
while  the  three  middle  ones  have  six  plates,  because  they  act  by  both 
faces,  while  the  first  only  acts  by  one. 

On  a  horizontal  iron  axis  going  from  one  end  to  the  other  of  the  frame 


784  Dynamical  Electricity.  [857- 

four  bronze  wheels  are  fixed,  each  corresponding  to  the  intervals  between 
the  magrtetic  batteries  of  two  vertical  series.  There  are  16  bobbins  on 
the  circumference  of  each  of  these — that  is,  as  many  as  there  are  magnetic 
poles  in  each  vertical  series  of  magnets.  These  bobbins,  represented  in 
fig.  704,  differ  from  those  of  Clarke's  apparatus  in  having,  instead  of  a 
single  wire,  12  wires  each,  11^  yards  in  length,  by  which  the  resistance  is 
diminished.  The  coils  of  these  bobbins  are  insulated  by  means  of 
bitumen  dissolved  in  oil  of  turpentine.  These  are  not  rolled  upon  solid 
cylinders  of  iron,  but  on  two  iron  tubes,  slit  longitudinally  ;  this  device 
renders  the  magnetisation  and  demagnetisation  more  rapid  when  the 
bobbins  pass  in  front  of  the  poles  of  the  magnet.  Further,  the  discs  of 
copper  which  terminate  the  bobbins  are  divided  in  the  direction  of  the 
radius,  in  order  to  prevent  the  formation  of  induced  currents  in  these 
discs.  The  four  wheels  being  respectively  provided  with  16  bobbins  each, 
there  are  altogether  64  bobbins  arranged  in  16  horizontal  series  of  four, 
as  seen  at  D,  on  the  left  of  the  frame.  The  length  of  the  wire  on  each 
bobbin  being  12  times  11^  yards,  or  138  yards,  the  total  length  in 
the  whole  apparatus  is  64  times  138  yards,  or  8,832  yards. 

The  wires  are  coiled  on  all  the  bobbins  in  the  same  direction,  and  not 
only  on  the  same  wheel,  but  on  all  four,  all  wires  are  connected  with  one 
another.  For  this  purpose  the  bobbins  are  joined,  as  shown  in  fig. 
703  ;  on  the  first  wheel  the  twelve  wires  of  the  first  bobbin,  x,  are  con- 
nected on  a  piece  of  mahogany  fixed  on  the  front  face  of  the  wheel  with 
a  plate  of  copper,  w,  connected  by  a  wire,  O,  with  the  centre  of  the  axis 


Fig.  703.  Fig.  704. 

which  supports  the  wheels.  At  the  other  end,  on  the  other  face  of  the 
wheel,  the  same  wires  are  soldered  to  a  plate  indicated  by  a  dotted  line 
which  connects  them  with  the  bobbin  y  ;  from  this  they  are  connected 
with  the  bobbin  s'  by  a  plate,  /,  and  so  on,  for  the  bobbins  /,  ?^  .  .  .  up  to 
the  last,  V.  The  wires  of  this  bobbin  terminate  in  a  plate  «,  which 
traverses  the  first  wheel,  and  is  soldered  to  the  wires  of  the  first  bobbin 
of  the  next  wheel,  on  which  the  same  series  of  connections  is  repeated  ; 
these  wires  pass  to  the  third  wheel,  thence  to  the  fourth,  and  so  on,  to  the 
end  of  the  axis. 

The  bobbins  being  thus  arranged,  one  after  another,  like  the  elements 
of  a  battery  connected  in  a  series  {T]']),  the  electricity  has  high  potential. 
But  the  bobbins  may  also  be  arranged  by  connecting  the  plates  alternately, 


-857] 


Magneto-Electrical  Machine. 


785 


not  with  each  other,  but  with  two  metal  rings  in  such  a  manner  that  all 
the  ends  of  the  same  name  are  connected  with  the  same  ring.  Each  of 
these  rings  is  then  a  pole,  and  this  arrangement  may  be  used  where  a 
high  degree  of  potential  is  not  required. 

From  these  explanations  it  will  be  easy  to  understand  the  manner  in 
which  electricity  is  produced  and  propagated  in  this  apparatus.  An 
endless  band  receiving  its  motion  from  a  steam  engine  passes  round  a 
pulley  fixed  at  the  end  of  the  axis  which  supports  the  wheels  and  the 
bobbins,  and  moves  the  whole  system  with  any  desired  rapidity.  Expe- 
rience has  shown  that  to  obtain  the  greatest  degree  of  light,  the  most 
suitable  velocity  is  235  revolutions  in  a  minute.  During  this  rotation,  if 
we  at  first  consider  a  single  bobbin,  the  tube  of  soft  iron  on  which  it  is 
coiled,  in  passing  in  front  of  the  poles  of  the  magnet,  undergoes  at  its  two 
ejids  an  opposite  induction,  the  effects  of  which  are  added,  but  change 
from  one  pole  to  another.  As  these  tubes,  during  one  rotation,  pass 
successively  in  front  of  sixteen  poles  alternately  of  different  names,  they 
are  magnetised  eight  times  in  one  direction,  and  eight  times  in  the 
opposite  direction.  In  the  same  time  there  are  thus  produced  in  the 
bobbin  eight  direct  induced  currents  and  eight  inverse  induced  currents  ; 
in  all,  sixteen  currents  in  each  revolution.  With  a  velocity  of  235  turns 
in  a  minute,  the  numbers  of  currents  in  the  same  tin)e  is  235  x  16  =  3,760 
alternately  in  opposite  directions.  The  same  phenomenon  is  produced 
with  each  of  the  64  bobbins ;  but  as  they  are  all  coiled  in  the  same  direc- 
tion, and  are  connected  with  each  other,  their  effects  accumulate,  and 
there  is  the  same  number  of  currents,  but  they  are  more  intense. 

To  utilise  these  currents  in  producing  an  intense  electric  light,  the 
communications  are  made  as  shown  in  fig.  705.     On  the  posterior  side 


Fig.  705. 


the  last  bobbin,  x' ,  of  the  fourth  wheel  terminates  by  a  wire,  G,  on 
the  axis  MN,  which  supports  the  wheels  :  the  current  is  thus  conducted 
to  the  axis,  and  thence  over  all  the  machine,  so  that  it  can  be  taken  from 
any  desired  point.  In  the  front  the  first  bobbin,  x,  of  the  first  wheel 
communicates  by  the  wire  0,  not  with  the  axis  itself,  but  with  a  steel 
cylinder,  c,  fitted  in  the  axis,  from  which,  however,  it  is  insulated  by  an 
ivory  collar.     The  screw  c,  to  which  the  wire  O  is  attached,  is  hkewise 


y86  Dynamical  Electricity.  [857- 

insulated  by  a  piece  of  ivory.  From  the  cylinder  c  the  current  passes  to 
a  fixed  metaUic  piece,  K,  from  which  it  passes  to  the  wire  H,  which 
transmits  it  to  the  binding  screw  a  of  fig.  702.  The  binding  screw  b 
communicates  with  the  framework,  and  therefore  with  the  wire  of  the  last 
bobbin,  x'  (fig.  705).  From  the  two  binding  screws  a  and  b  the  current 
is  conducted  by  means  of  two  copper  wires  to  two  charcoals,  the  distance 
of  which  is  regulated  by  means  of  an  apparatus  analogous  in  principle  to 
that  already  described  (786). 

In  this  machine  the  currents  are  not  rectified  so  as  to  be  in  the  same 
direction ;  hence  each  carbon  is  alternately  positive  and  negative,  and  in 
fact  they  are  consumed  with  equal  rapidity.  Experiment  has  shown  that, 
when  these  currents  are  applied  to  produce  the  electric  light,  it  is  not 
necessary  they  should  be  in  the  same  direction ;  but  when  they  are  to  be 
used  for  electrometallurgy,  or  for  magnetising,  they  must  be  rectified, 
which  is  effected  by  means  of  a  suitable  commutator. 

The  light  produced  by  the  magneto-electrical  machine  is  very  intense ; 
with  a  machine  of  four  wheels  the  hght  obtained  is  equal  to  that  of  150 
Carcel  lamps.  A  machine  of  six  wheels  gives  a  hght  equal  to  200  Carcel 
lamps. 

Serrin  has  constructed  a  new  regulator  for  this  light,  which,  like  the 
older  ones,  brings  the  charcoals  together  in  proportion  as  they  become 
used ;  and  further  removes  them  when  they  are  in  contact.  It  contains 
no  clockwork  motion,  and  is  worked  by  the  weight  of  one  of  its  pieces. 

This  light,  which  requires  no  other  expenditure  than  that  of  a  single 
horse-power  to  turn  the  coils  when  there  are  not  more  than  four  of  them, 
is  advantageously  used  for  signalling  by  night  on  large  vessels,  and  for 
lighthouses.  One  of  these,  constructed  by  Holmes,  is  now  in  use  at  the 
South  Foreland  lighthouse. 

858.  Siemens'  armature. — Siemens  has  devised  an  armature  or 
bobbin  for  magneto- electrical  machines,  in  which  the  insulated  wire  is 
wound  longitudinally  on  the  core,  instead  of  transversely,  as  is  usually  the 
case. 

It  consists  of  a  soft  iron  cylinder,  AB  (fig.  706),  from  one  foot  to  three 
feet  in  length,  according  to  circumstances. 

A  deep  groove  is  cut  on  the  outer  length  of  this  core  and  on  the  ends, 

//i 


in  which  is  coiled  the  insulated  wire  as  in  a  multiplier.  To  the  two  ends 
of  the  cylinder  brass  discs,  E  and  D,  are  secured.  With  E  is  connected 
a  commutator,  C,  consisting  of  two  pieces  of  steel  insulated  from  each 
other  and  connected  respectively  with  the  two  ends  of  the  wire.  On  the 
other  disc  is  a  pulley,  round  which  passes  a  cord,  so  that  the  bobbin  moves 
very  rapidly  on  the  two  pivots. 


-859]  Wild's  Magneto-Electrical  Machine.  y^y 

When  a  voltaic  current  circulates  in  the  wire,  the  two  cylindrical  seg- 
ments, A  and  B,  are  immediately  magnetised,  one  with  one  polarity  and 
the  other  with  the  opposite.  On  the  other  hand,  if,  instead  of  passing 
a  voltaic  current  through  the  wire  of  the  bobbin,  the  bobbin  itself  be 
made  to  rotate  rapidly  between  the  opposite  poles  of  magnetised  masses, 
as  the  segments  A  and  B  become  alternately  magnetised  and  demagnet- 
ised, their  induction  produces  in  the  wire  a  series  of  currents  alternately 
positive  and  negative,  as  in  Clarke's  apparatus  (855).  When  these 
cuirents  are  collected  in  a  commutator  which  adjusts  them — that  is,  sends 
all  the  positive  currents  on  one  spring  and  all  the  negative  on  another — 
these  springs  become  electrodes,  from  one  of  which  positive  electricity 
starts  and  from  the  other  negative.  If  these  springs  are  connected  by  a 
conductor,  the  same  effects  are  obtained  as  when  the  two  poles  of  a 
battery  are  united. 

Siemens  has  constructed  magneto-electrical  machines  in  which  this 
armature  is  utilised.  It  has  the  great  advantage  that  a  large  number  of 
small  magnets  may  be  used  instead  of  one  large  one.  As,  weight  for 
weight,  the  former  possesses  greater  magnetic  force  than  the  latter,  they 
can  be  made  more  economically.  And  as  the  armature  is  always  very 
near  the  magnets,  it  receives  greater  momentum,  and  is  more  rapidly 
changed. 

859.  IVild's  magrneto-electrical  machine. —  Mr.  Wild  has  recently 
constructed  a  magneto-electrical  machine,  in  which  Siemens'  armature  is 
used  along  with  a  new  principle — that  of  the  multiplication  of  the  current. 
Instead  of  utilising  directly  the  current  produced  by  the  induction  of  a 
magnet,  Mr.  Wild  passes  it  into  a  strong  electromagnet,  and  by  the  in- 
duction of  this  latter  a  more  energetic  current  is  obtained. 

This  machine  consists  first  of  a  battery  of  12  to  16  magnets  P,  each  of 
which  weighs  about  3  pounds,  and  can  support  about  20  pounds.  Between 
the  poles  of  the  magnets  two  soft  iron  keepers,  CC,  are  arranged,  separated 
by  a  brass  plate,  O.  These  three  pieces  are  joined  by  bolts,  and  the  whole 
compound  keeper  is  perforated  longitudinally  by  a  cylindrical  cavity,  in 
which  works  a  Siemens'  armature,  71,  about  2  inches  in  diameter.  The 
wire  of  this  armature  terminates  in  a  commutator,  which  leads  the  positive 
and  negative  currents  to  two  binding  screws,  a  and  b.  This  commutator 
is  represented  on  a  larger  scale  in  ifig.  709.  At  the  other  end  is  a  pulley 
by  which  the  armature  can  be  turned  at  the  rate  of  25  turns  in  a  second. 
The  wire  on  the  armature  is  20  yards  long. 

Below  the  support  for  the  magnets  and  their  armatures  are  two  large 
electromagnets,  BB.  Each  consists  of  a  rectangular  soft  iron  plate,  36 
inches  in  length  by  26  in  breadth  and  i\  inch  thick,  on  which  are  coiled 
about  1,600  feet  of  insulated  copper  wire.  The  wires  of  these  electro- 
magnets are  joined  at  one  end,  so  as  to  form  a  single  circuit  of  3,200  feet. 
One  of  the  other  ends  is  connected  with  the  binding  screw  a  and  the 
other  with  b.  At  the  top  the  two  plates  are  joined  by  a  transverse  plate 
of  iron  so  as  to  form  a  single  electromagnet. 

At  the  bottom  of  the  electromagnets  BB  are  two  iron  armatures  sepa- 
rated by  a  brass  plate,  O,  and  in  the  entire  length  is  a  cylindrical  channel 


7SS 


Dynamical  Electricity. 


[859- 


in  which  works  a  Siemens'  armature  711  as  above  :  this  armature,  however, 
is  above  a  yard  in  length,  nearly  6  inches  in  diameter,  and  its  wire  is  100 
feet  long.     The  ends  are  connected  with  a  commutator,  from  which  the 


Fig.  707. 


adjusted  currents  pass  to  two  wires,  r  and  s.     The  armature  m  is  rotated 
at  the  rate  of  1,700  turns  in  a  minute. 

Fig.  708  shows  on  a  larger  scale  a  cross  section  of  the  bobbin  m  of 
the  armatures  CC  and  of  the  plates  AA,  on  which  is  coiled  the  wire  of 
the  electromagnets  BB. 


860] 


Ladd's  Dynamomagnetic  Machine. 


789 


These  details  being  premised,  the  following  is  the  working  of  the 
machine.  When  the  armatures  ;/  and  vi  are  rotated  by  means  of  a  steam 
engine  with  the  velocity  mentioned,  the  magnets  produce  in  the  first 
armature  induced  currents,  which,  adjusted  by  the  commutator,  pass  into 
the  electromagnet  BB,  and  magnetise  it.  But  as  these  impart  to  the 
lower  armatures  CC  opposite  polarities,  the  induction  of  these  latter  pro- 
duces in  the  armature  ni  a  series  of  positive  and  negative  currents  far 


Fig.  708. 


Fig.  709 


more  powerful  than  those  of  the  upper  armature  ;  so  that  when  these  are 
adjusted  by  a  commutator  and  directed  by  the  wires  r  and  j,  very  power- 
ful effects  are  obtained. 

These  effects  are  still  further  intensified  if,  as  Mr.  Wild  has  done,  the 
adjusted  current  of  the  armature  m  is  passed  into  a  second  electric 
magnet,  whose  armatures  surround  a  third  and  larger  Siemens'  armature 
turning  with  the  two  others.  A  current  is  thus  obtained  which  melts  an 
iron  wire  a  foot  long  and  more  than  2  inches  in  diameter. 

860.  Ziadd's  dynamoznag-netic  machine. — Mr.  Ladd,  philosophical 
instrument  maker,  in  Beak  Street,  Regent  Street,  has  invented  a  very 
remarkable  dynamomagnetic  machine.  It  consists  of  two  Siemens'  arma- 
tures, rotating  with  great  velocity,  and  of  two  iron  plates,  AA  (fig.  710), 
surrounded  by  an  insulated  copper  wire.  Ladd's  machine  differs  from 
that  of  Wild  in  the  following  respects  : 

i.  There  are  no  permanent  magnets :  ii.  the  electromagnets  BB  are 
not  joined  so  as  to  form  a  single  electromagnet,  but  are  two  distinct 
electromagnets,  each  having  at  the  end  two  hollow  cylinders,  CC,  m 
which  are  fitted  two  Siemens'  armatures,  m  and  n\  the  current  of  the 
armature  n  passing  round  the  electromagnets  reverts  to  itself.  This 
reaction  of  the  current  upon  itself  is  an  essential  feature  of  the  machine ; 
it  is  an  application  of  a  principle  announced  simultaneously  by  Mr. 
Wheatstone  and  by  Mr.  Siemens.  The  wire  of  the  armature  in  is  inde- 
pendent, and  passes  into  the  apparatus  which  is  to  utilise  the  current — for 
instance,  two  carbon  points,  D. 

The  machine  being  thus  arranged,  if  a  voltaic  current  be  passed  once 
for  all  through  the  electromagnets  BB,  it  magnetises  the  plates  AA  and 


790 


Dynamical  Electricity. 


[860- 


their  keepers,  which  by  their  reciprocal  action  retain  a  quantity  of  rema- 
nent magnetism  sufficient  to  work  the  machine.  If,  then,  the  armatures 
in  and  7i  be  rotated  by  means  of  two  bands  passing  round  a  common 
drum,  the  magnetism  of  the  hollow  cylinders  CC  acting  upon  the  arma- 
ture «,  excites  induction  currents,  which,  adjusted  by  a  commutator,  pass 
round  the  electromagnets  BB,  and  more  strongly  magnetise  the  cylinders 
or  shoes  CC.  These  in  their  turn  reacting  more  powerfully  on  the 
armature  «,  strengthen  the  current;  we  thus  see  that  n  and  B  continu- 
ally and  mutually  strengthen  each  other  as  the  velocity  of  the  rotation 
increases.  Hence  as  the  iron  of  the  armature  m  becomes  more  and 
more  strongly  magnetised  under  the  influence  of  the  electromagnets  BB, 
a  gradually  more  intense  induced  current  is  developed  in  this  armature, 


Fig.  710. 

which  is  directed,  commutated  or  not,  according  to  the  use  for  which  it  is 
designed. 

In  a  machine  which  Mr.  Ladd  exhibited  at  the  Paris  exhibition  of  1867 
the  plates  AA  were  only  24  inches  in  length  by  1 2  inches  in  width.  With 
these  small  dimensions  the  current  is  equal  to  25  to  30  Bunsen's  cells.  It 
can  work  the  electric  light  and  keep  incandescent  a  platinum  wire  a  metre 
in  length  and  0-5  mm.  in  diameter. 

The  above  form  of  the  machine  is  worked  by  steam  power.  Mr.  Ladd 
has  devised  a  more  compact  form,  which  may  be  worked  by  hand.  This 
is  represented  in  fig,  711.  The  two  armatures  are  fixed  end  to  end,  and 
the  coils  are  wound  on  it  at  right  angles  to  each  other,  as  shown  m  the 
figure.     The  current  from  this  can  raise   to   white   heat    18   inches  of 


-861]  Gramme's  Magnetic-Electrical  Machine. 


791 


platinum  wire  o-oi  in.  thickness,  and  with  an  inductorium  containing  3 
miles  of  secondary  wire  2  in.  sparks  can  be  obtained. 

Both  Ladd's  and  Wild's  machines  are  liable  to  the  objection  of  re- 
quiring to  be  rotated  at  a  rapid  rate.     The  armatures  become  heated  by 


Fig.  7 


the  repeated  development  of  induction  currents.  This  has  been  remedied 
by  Mr.  Ladd,  who  has  introduced  into  the  shoes  or  hollow  cylinders 
several  apertures  through  which  a  stream  of  cold  water  is  made  to  flow. 
Before  they  can  be  applied  industrially,  their  velocity  must  be  reduced, 
either  by  multiplying  the  number  of  Siemens'  armatures  or  modifying 
their  arrangement. 

These  machines  furnish  a  remarkable  instance  of  the  transformation 
of  mechanical  force  into  electricity,  light,  and  heat  (273,  467). 

861.  Gramme's  magrneto-electrical  machine. — The  magneto-elec- 
trical machines  which  have  hitherto  been  described  are  all  open  to  the 
objection  that  they  only  give  momentary  currents,  alternately  positive 
and  negative.  These  currents  may  indeed  be  used  for  lighting  and  for 
physiological  purposes,  but  for  other  applications,  such  as  for  electro- 
plating, they  must  be  rectified-,  that  is,  by  means  of  a  commutator,  they 
must  be  sent  always  in  the  same  direction.  This,  however,  is  in  all  cases 
accompanied  by  a  certain  loss  of  electricity,  and  sparks  are  produced 
which  rapidly  wear  away  the  armatures  of  the  commutators. 

These  inconveniences  are  not  met  with  in  an  apparatus  invented  by 
M.  Gramme,  of  which  fig.  712  is  a  representation  in  about  ^th  of  the 
natural  size.  On  a  base  is  a  powerful  magnetic  battery,  between  the 
limbs  of  which  an  axle  is  rotated  by  means  of  a  pulley  and  an .  endless 
band.  On  this  axle,  and  in  the  same  plane  as  the  branches  of  the  magnet, 
is  a  soft  iron  ring,  on  which  are  wound  35  coils  of  insulated  copper  wire, 
each  having  nearly  300  turns.  In  each  one  the  wire  is  bent  inside  the 
ring,  and  is  soldered  to  an  insulated  piece  of  brass.     It  is  then  again 


792 


Dynamical  Electricity. 


[861- 


folded  on  the  ring  so  as  to  form  a  second  coil.  From  this  it  passes  to  a 
piece  of  brass  similar  to  the  first,  and  so  on,  forming  a  continuous  con- 
ductor divided  into  35  identical  bobbins. 


Fig.  712. 

All  the  pieces  of  brass  to  which  the  copper  wire  is  soldered  are  in- 
sulated from  the  apparatus,  and  form  a  bundle  at  c  around  the  axis. 
There,  on  the  same  horizontal  diameter  of  the  ring,  one  part  of  these 
pieces  is  in  contact  with  two  brass  discs,  m  and  ;z,  represented  in  tig. 
701,  which  shows  below  them  the  bobbins  and  their  accessories.  These 
two  discs  sHde  on  their  supports  in  the  direction  of  the  axis,  and  two 
springs  press  them  against  the  pieces  c. 

Suppose  now  that  the  ring  with  its  coils  turn  from  right  to  left  in  pass- 
ing under  the  pole  B  of  the  magnet,  the  upper  part  of  the  ring  acquires 

a  polarity  the  reverse  of  that  of  the  ring, 
and  its  magnetisation  devejopes  a  current 
the  inverse  of  the  Amperian  currents 
(845)  in  the  coils  which  approach  the 
pole,  and  direct  in  those  which  recede 
from  it.  Hence,  if  the  current  formed  on 
the  right  near  the  middle  part,  R,  of  the 
system  is  positive,  that  developed  in  the 
opposite  region  is  negative. 

In  front  of  the  pole  A  a  similar  effect 
is  produced,  but  here  the  polarity  of  A 
being  the  opposite  of  that  of  B,  the  inverse 
current  from  below  towards  R  is  positive, 
and  the  current  on  the  left  which  is 
negative. 

Thus  there  are  continually  two  positive 
currents  proceeding  from  the  upper  and 
lower  coils  towards  the  medial  region  R, 
and  two  negative  currents  directed  towards  the  opposite  sides.     These 


Fig-  713- 


-862]  hiductorium.    Rtihmkorff's  Coil,  793 

currents  pass  thence  to  the  corresponding  pieces  c,  whence  they  are 
collected  by  the  discs  m  and  «,  which  transmit  them  to  the  two  binding 
screws  a  and  b.  A  continuous  current  is  thus  produced  which  is  always 
in  the  same  direction,  m  being  the  positive  pole  and  7t  the  negative  pole. 
If  the  rotation  is  in  the  opposite  direction,  the  poles  are  reversed. 

This  apparatus,  though  small  in  size— 9  inches  in  height— is  very  power- 
ful ;  it  can  decompose  water  and  heat  to  redness  an  iron  wire  20  centi- 
metres in  length  and  a  millimetre  in  diameter.  Its  power  increases  with 
the  velocity  of  its  rotation  up  to  a  limit  of  700  to  800  turns  in  a  minute, 
and  its  effects  vary  according  as  the  wire  of  the  bobbins  is  thick  and 
short  or  fine  and  long. 

862.  znductoriuxn.  RulnukorfTs  coil. — These  are  arrangements  for 
producing  induced  currents,  in  which  a  current  is  induced  by  the  action 
of  an  electric  current,  whose  circuit  is  alternately  opened  and  closed  in 
rapid  succession.  These  instruments,  known  as  inductoriMms  or  induction 
coils,  present  considerable  variety  in  their  construction,  but  all  consist 
essentially  of  a  hollow  cylinder  in  which  is  a  bar  of  soft  iron,  or  bundle 
of  iron  wires,  with  two  helices  coiled  round  it,  one  connected  with  the 
poles  of  a  battery,  the  current  of  which  is  alternately  opened  and  closed 
by  a  self-acting  arrangement,  and  the  other  serving  for  the  development 
of  the  induced  current.  By  means  of  these  apparatus,  with  a  current  of 
three  or  four  Grove's  cells,  physical,  chemical,  and  physiological  effects 
are  produced  equal  to  and  superior  to  those  obtainable  with  electrical 
machines  and  even  the  most  powerful  Leyden  batteries. 

Of  all  the  forms  those  constructed  by  Ruhmkorff  are  the  most  powerful. 
Fig.  714  is  a  representation  of  one,  the  coil  of  which  is  about  14  inches 


Fig.  714. 

in  length.  T\i^ primary  or  inducing  wire  is  of  copper,  and  is  about  2  mm. 
in  diameter  and  40  or  50  yards  in  length.  It  is  coiled  directly  on  a 
cylinder  of  cardboard,  which  forms  the  nucleus  of  the  apparatus,  and  is 
enclosed  in  an  insulating  cylinder  of  glass,  or  of  caoutchouc.  On  these 
is  coiled  the  secondary  or  induced  wire,  which  is  also  of  copper,  and  is 
about  ^mm.  in  diameter.  A  great  point  in  these  apparatus  is  the  insula- 
tion.    The  wires  are  not  merely  insulated  by  being  in  the  first  case 

M  M 


794 


Dynamical  Electricity. 


[862- 


iFig.  715. 


covered  with  silk,  but  each  individual  coil  is  separated  from  the  rest  by  a 
layer  of  melted  shellac.  The  length  of  the  secondary  wire  varies  greatly ; 
in  some  of  Ruhmkorff's  largest  sizes  it  is  as  much  a^  60  miles.  With 
these  great  lengths  the  wire  is  thinner,  about  |mm.  The  thinner  and 
longer  the  wire  the  higher  the  potential  of  the  induced  electricity. 

The  following  is  the  working  of  the  apparatus.  The  current  arriving 
by  the  wire  P  at  a  binding  screw,  a,  passes  thence  into  the  commutator 
C,  to  be  afterwards  described  (fig.  716),  thenpe  by  the  binding  screw  b 
it  enters  the  primary  wire,  where  it  acts  inductively  on  the  secondary  wire  ; 
having  traversed  the  primary  wire,  it  emerges  by  the  wire  s  (fig.  715). 

Following  the  direction  of  the 
arrows,  it  will  be  seen  that  the 
current  ascends  in  the  binding 
screw  /,  reaches  an  oscillating 
piece  of  iron,  0,  called  the  ham- 
mer, descends  by  the  anvil  h^ 
and  passes  into  a  copper  plate, 
K,  which  takes  it  to  the  commu- 
tator C.  It  goes  from  there  to 
the  binding  screw  c,  and  finally 
to  the  negative  pole  of  the  bat- 
tery by  the  wire  N. 

The  current  in  the  primary 
wire  only  acts  inductively  on 
the  secondary  wire  (843),  when  it  opens  or  closes  and  hence  must  be 
constantly  interru,pted.  This  is  effected  by  means  of  the  oscillating 
hammer  o  (fig.  715).  In  the  centre  of  the  bolDbin  is  a  bundle  of  soft  iron 
wires,  forming  together  a  cylinder  a  little  longer  than  the  bobbin,  and 
thus  projecting  at  the  end  as  seen  at  A.  When  the  current  passes  in  the 
primary  wire,  this  hammer  o  is  attracted  ;  but  immediately,  there  being 
no  contact  between  o  and  h,  the  current  is  broken,  the  magnetisation 
ceases,  and  the  hammer  falls  ;  the  current  again  passing,  the  same  series 
of  phenomena  recommences,  so  that  the  hammer  oscillates  with  great 
rapidity. 

863.  Condenser. — In  proportion  as  the  current  passes  thus  intermit- 
tently in  the  primary  wire  of  the  bobbin,  at  each  interruption  an  induced 
current,  alternately  direct  and  inverse,  is  produced  in  the  secondary  wire. 
But  as  this  is  perfectly  insulated,  the  induced  current  acquires  such  a 
strength  as  to  produce  very  powerful  effects.  Fizeau  has  increased  this 
strength  still  more  by  interposing  a  condenser  in  the  primary  circuit. 
As  constructed  by  Ruhmkorfffor  his  largest  apparatus,  this  consists  of  150 
sheets  of  tinfoil  about  18  inches  square,  so  that  the  total  surface  is  about 
75  square  yards.  These  sheets  being  joined,  are  fastened  on  two  sides  of 
a  band  of  oiled  silk,  which  insulates  them,  forming  thus  two  coatings  ; 
they  are  then  coiled  several  times  round  each  other,  another  band  of  silk 
being  interposed,  so  that  the  whole  can  be  placed  below  the  helix  in  the 
base  of  the  apparatus.  One  of  these  coatings,  the  positive,  is  connected 
with  the  binding  screw  2,  which  receives  the  current  on  emerging  from 


-864]  Effects  of Kuhinkorff's' Coil,  795 

the  bobbin  ;  and  the  other,  the  negative,  is  connected  with  the  binding 
screw  7n,  which  communicates  by  the  plate  K  with  the  commutator  C, 
and  with  the  battery. 

To  understand  the  effect  of  the  condenser,  it  must  be  observed  that  at 
each  break  of  the  inducing  current  an  extra  current  is  produced  in  the 
same  direction,  which,  continuing  in  a  certain  manner,  prolongs  its  dura- 
tion. It  is  this  extra  current  which  produces  the  spark  that  passes  at 
.each  break  between  the  hammer  and  the  anvil  ;  when  the  current  is 
strong  this  spark  rapidly  alters  the  surface  of  the  hammer  and  anvil, 
though  they  are  of  platinum.  By  interposing  the  condenser  in  the  in- 
ducing circuit,  the  extra  current,  mstead  of  producing  so  strong  a  spark, 
passes  into  the  condenser  ;  the  positive  electricity  in  the  coating  connec- 
ted with  /,  and  the  negative  in  that  connected  with  in.  But  the  opposite 
electricities  combining  quickly  by  the  thick 
wire  of  the  primary  coil,  by  the  battery  and 
the  circuit  CK;;z,  give  rise  to  a  current  con- 
trary to  that  of  the  battery,  which  instanta- 
neously demagnetises  the  bundle  of  soft  iron  ; 
the  induced  current  is  thus  shorter  and  more 
intense.  The  binding  screws  in  and  n  on 
the  base  of  the  apparatus  are  for  receiving 

this  extra  current.  ,„„ , . 

The  commutator  or  key  serves  to  break       ^  l^^^m^WW^ 
contact  or  send  the  current  in  either  direc-  Fig.  ^^g. 

tion.     The  section  in  fig.  716  is  entirely  of 

brass,  excepting  the  core  A,  which  is  ebonite  ;  on  the  two  sides  are  two 
brass  plates  CC.  Against  these  press  two  elastic  brass  springs,  joined  to 
two  binding  screws,  a  and  r,  with  which  are  also  connected  the  elec- 
trodes 01  the  battery.  The  current  arriving  at  a  ascends  in  C,  thence 
by  a  screw  y  it  attains  the  binding  screw  b  and  the  bobbin  ;  then  re- 
turning by  the  plate  K,  which  is  connected  with  the  hammer,  the  current 
goes  to  Q'  by  the  screw  x^  descends  to  ^,  and  rejoins  the  battery  by  the 
wire  N.  If  by  means  of  the  milled  head  the  key  is  turned  180  degrees, 
it  is  easy  to  see  that  exactly  the  opposite  takes  place  ;  the  current 
reaches  the  hammer  by  the  plate  K  and  emerges  at  b.  Finally,  if  it 
is  only  turned  through  90  degrees,  the  elastic  plates  rest  on  the  ebonite 
A  instead  of  on  the  plates  CC,  and  the  current  is  broken. 

The  two  wires  from  the  bobbin  at  0  and  o'  (fig.  714)  are  the  two  ends  of 
the  secondary  wire.  They  are  connected  with  the  thicker  wires  PP^,  so 
that  the  current  can  be  sent  in  any  desired  direction.  With  large  coils 
the  hammer  cannot  be  used,  for  the  surfaces  become  so  much  heated  as 
to  melt.  But  M.  Foucault  has  recently  invented  a  mertury  interrupter 
which  is  free  from  this  inconvenience,  and  which  is  an  important  im- 
provement. 

-  864.  Sffects  produced  by  RubrnkorfTs  coil. — The  high  degree  of 
tension  which  the  electricity  of  induction  coil  machines  possesses  has 
Tong  been  known,  and  many  luminous  and  calorific  effects  have  been 
obtained  by  their  means.     But  it  is  orJy  since  the.  improvements  which" 


^* 


796  Dynamical  Electricity.  [864- 

Ruhmkorff  has  introduced  into  his  coil,  that  it  has  been  possible  to 
utilise  all  the  potential  of  induced  currents,  and  to  show  that  these  currents 
possess  the  properties  of  statical  as  well  as  dynamical  electricity. 

Induced  currents  are  produced  in  the  coil  at  each  opening  and  break- 
ing of  contact.  But  these  currents  are  not  equal  either  in  duration  or  in 
potential.  The  direct  current,  or  that  on  openings  is  of  shorter  duration, 
but  higher  potential ;  that  of  closing  of  longer  duration  but  lower  potential. 
Hence  if  the  two  ends  P  and  P'  of  the  fine  wire  (figs.  714  and  715)  are 
connected,  as  there  are  two  equal  and  contrary  quantities  of  electricity  in 
the  wire  the  two  currents  neutralise  each  other.  If  a  galvanometer  is 
placed  in  the  circuit,  only  a  very  feeble  deflection  is  produced  in  the 
direction  of  the  direct  current.  This  is  not  the  case  if  the  two  extremities 
P  and  P'  of  the  wire  are  separated.  As  the  resistance  of  the  air  is  then 
opposed  to  the  passage  of  the  currents,  that  which  has  highest  potential,  that 
is,  the  direct  one,  passes  in  excess,  and  the  more  so  the  greater  the 
distance  of  P  and  P'  up  to  a  certain  limit  at  which  neither  pass.  There 
are  then  at  P  and  P'  nothing  but  potentials  which  are  alternately  con- 
trary. 

The  effects  of  the  coil,  like  those  of  the  battery,  may  be  classed  under 
the  heads  physiological,  chemical,  calorific,  luminous,  mechanical ;  with 
this  difference,  that  they  are  enormously  more  intense. 

T\i^ physiological  effects  of  Ruhmkorff's  coil  are  very  powerful:  in  fact, 
the  shocks  are  so  violent  that  many  experimenters  have  been  suddenly 
prostrated  by  them.  A  rabbit  may  be  killed  with  two  of  Bunsen's  elements, 
and  a  somewhat  larger  number  of  couples  would  kill  a  man. 

The  calorific  effects  are  also  easily  observed  ;  it  is  simply  necessary  to 
interpose  a  very  fine  iron  wire  between  the  two  ends  P  and  P'  of  the 
induced  wire  ;  this  iron  wire  is  immediately  melted,  and  burns  with  a 
bright  light.  A  curious  phenomenon  may  here  ^  be  observed,  namely, 
that  when  each  of  the  wires  P  and  P'  terminates  in  a  very  fine  iron  wire, 
and  these  two  are  brought  near  each  other,  the  wire  corresponding  to 
the  negative  pole  alone  melts,  indicating  that  the  tension  is  greater  at  the 
negative  than  at  the  positive  pole. 

The  chemical  effects  are  very  varied,  inasmuch  as  the  apparatus 
produces  electricity  both  in  quantity  and  of  high  potential.  Thus, 
according  to  the  shape  and  distance  of  the  platinum  electrodes  im- 
mersed in  water,  and  to  the  degree  of  acidulation  of  the  water,  either 
luminous  effects  may  be  produced  in  water  without  decomposition,  or  the 
water  may  be  decomposed  and  the  mixed  gases  disengaged  at  the  two 
poles,  or  the  decomposition  may  take  place,  and  the  mixed  gases  separate 
either  at  a  single  pole  or  at  both  poles. 

Gases  may  also  be  decomposed  or  combined  by  the  continued  action 
of  the  spark  from  the  coil.  Becquerel  and  Fr^my  have  found  that  if  the 
current  of  a  Ruhmkorff's  coil  be  passed  through  a  hermetically  sealed 
tube  containing  air,  as  shown  in  fig.  717,  nitrogen  and  oxygen  combine 
to  form  nitrous  acid. 

The  himinous  effects  of  Ruhmkorff's  coil  are  also  very  remarkable,  and 
vary  according  as  they  take  place  in  air,  in  vapour,  or  in  very  rarefied 


>864] 


Eff£cts  of  Rhumkorff's  Coit. 


797. 


vapours.  In  air  the  coil  produces  a  very  bright  loud  spark,  which,  with 
the  largest-sized  coils,  has  a  length  of  i8  inches.  In  vacuo  the  effects 
are  also  remarkable.  The  experiment  is  made  by 
connecting  the  two  wires  of  the  coil  P  and  P'  with  the 
two  rods  of  the  electrical  ^gg  (fig.  580)  used  for  pro- 
ducing in  vacuo  the  luminous  effects  of  the  electrical 
machine.  A  vacuum  having  been  produced  up  to  I 
or  2  millimetres,  a  beautiful  luminous  trail  is  produced 
from  one  knob  to  the  other,  which  is  virtually  con- 
stant, and  has  the  same  intensity  as  that  obtained 
with  a  powerful  electrical  machine  when  the  plate  is 
rapidly  turned.  This  experiment  is  shown  in  figs.  722 
and  723.  Fig.  721  represents  a  remarkable  deviation 
which  light  undergoes  when  the  hand  is  presented  to 
the  tgg. 

The  positive  pole  of  the  current  shows  the  greatest 
brilliancy ;  its  light  is  of  a  fiery  red,  while  that  of  the  negative  pole  is  of 
a  feeble  violet  colour ;  moreover,  the  latter  extends  along  all  the  length 
of  the  negative  rod,  which  is  not  the  case  with  the  positive  pole. 

The  coil  also  produces  mechanical  effects  so  powerful  that  with  the 
largest  apparatus  glass  plates  two  inches  thick  have  been  perforated. 
This  result,  however,  is  not  obtained  by  a  single  charge,  but  by  several 
successive  charges. 

The  experiment  is  arranged  as  shown  in  fig.  718.     The  two  poles  of 


Fig.  718. 

the  induced  current  correspond  to  the  binding  screws  a  and  b ;  by  means 
of  a  copper  wire,  the  pole  a  is  connected  with  the  lower  part  of  an 
apparatus  for  piercing  glass  like  that  already  described  (fig.  585),  the 
other  pole  is  attached  to  the  other  conductor  by  a  wire  d.  The  latter  is 
insulated  in  a  large  glass  tube  r,  filled  with  shellac,  which  is  run  in  while 
in  a  state  of  fusion.  Between  the  two  conductors  is  the  glass  to  be  per- 
forated, V,     When  this  presents  too  great  a  resistance,  there  is  danger 


^/ 


798". 


'Dyjihimcal  Electricity, 


[864 


lest  the  spark  pass  in  the  coil  itself,  perforating  the  insulating  layer 
which. separates  the  wire,  and  then  the  coil  is  destroyed.  To  avoid  this, 
two  wires,  e  and  c,  connect  the  poles  of  the  coil  with  two  metallic  rods 
whose  distance  from  each  other  can  be  regulated.  If  then  the  spark 
cannot  penetrate  through  the  glass,  it  bursts  across,  and  the  coil  is  not 
injured. 

The  coil  can  also  be  used  to  charge  Leyden  jars.  With  a  large  coil: 
giving  sparks  of  6  to  8  inches,  and  using  6  Bunsen's  elements  with  a  large 
surface,  Ruhmkorff -charged  large  batteries  of  6  jars  each,  having  about  3l 
square  yards  of  coated  surface.  : 

The  experiment  with  a  single  Leyden  jar  (fig.  719)  is  made  as  follows. 


The  coatings  of  the  latter  are  in  connectibn  with  the  poles  of  the  coil  by 
the  wires  ^and  /,  and  these  same  poles  are  also  connected,  by  means  of 


Fig.  720. 

the  wires  e  and  ^:,'With  the  two  horizontal  rods  of  a  universal  discharger 
(%•  574)-   :Th^  jar  is  then  b^ing  constantly  charged  by  the  wires  2  and  dy 


865] 


Stratification  of  the  Electric  Light. 


799 


sometimes  in  one  direction  and  sometimes  in  another,  and  as  constantly 
discharged  by  the  wires  e  and  c ;  the  discharge  from  m  to  n  taking  place 
as  a  spark  two  or  three  inches  in  length,  very  luminous,  and  producing  a 
deafening  sound  5  they  can  scarcely  be  compared  with  the  sparks  of  the 
electrical  machine,  but  are  rather  true  lightning  discharges. 

To  charge  a  battery  the  form  of  the  experiment  is  somewhat  varied  ; 
the  external  coating  being  connected  with  one  pole  of  the  coil  by 
the  wire  d,  and  the  internal  coating  with  the  other  by  the  rods  m,  7i, 
and  the  wire  c  (fig.  720).  The  rods  w  and  n  are  not,  however,  in  contact. 
If  they  were,  as  the  two  currents,  the  inverse  and  direct,  pass  equally, 
the  battery  would  not  be  constantly  charged  and  discharged  ;  while 
from  the  distance  between  ?n  and  n  the  direct  current,  that  of  opening,~ 
which  has  higher  potential,  passes  alone,  and  it  is  this  which  charges  the 
battery. 

865.  Stratification  of  the  electric  ligrht. — M.  Quet  has  observed,  in 
studying  the  electric  light  which  Ruhmkorff 's  coil  gives  in  a  vacuum,  that 
if  some  of  the  vapour  of  turpentine,  wood  spirit,  alcohol,  or  bisulphide  of 
carbon,  etc.,  be  introduced  into  the  vessel  before  exhaustion,  the  aspect  of 


Fig.  721 


Fig.  722. 


Fig.  723, 


the  ight  is  totally  modified.  It  appears  then  like  a  series  of  alternately 
bright  and  dark  zones,  forming  a  pile  of  electric  light  between  the  two 
poles  (fig.  722). 


8oo 


Dynamical  Electricity. 


[865- 


In  this  experiment  it  follows  from  the  discontinuity  of  the  current  of 
induction,  that  the  light  is  not  continuous,  but  consists  of  a  series  of  dis- 
charges which  are  nearer  each  other  in  proportion  as  the  hammer  a  (fig. 
7 1 5)  oscillates  more  rapidly.  The  zones  appear  to  possess  a  rapid  gyratory 
and  undulatory  motion.  M.  Quet  considers  this  as  an  optical  illusion  ; 
for  if  the  hammer  is  slowly  moved  by  the  hand,  the  zones  appear  very 
distinct  and  fixed. 

The  light  of  the  positive  pole  is  most  frequently  red,  and  that  of  the 
negative  pole  violet.  The  tint  varies,  however,  with  the  vapour  or  gas  in 
the  globe. 

M.  Despretz  has  observed  that  the  phenomena  obtained  by  Ruhmkorff 
and  by  Quet,  with  a  discontinuous  current,  are  also  reproduced  with  an 
ordinary  continuous  current,  with  this  important  difference,  that  the  con- 
tinuous current  requires  a  considerablenumberof  couples,  while  the  discon- 
tinuous current  of  the  coil  only  requires  a  single  element.  It  is  remarkable 
that  the  luminous  effects  of  this  coil  are  very  little  increased  by  an  increase 
in  the  number  of  elements. 

866.  Geissler's  tubes. — The  brilliancy  and  beauty  of  the  stratification 
of  the  electric  light  are  most  remarkable  when  the  discharge  of  the  Ruhm- 
korff s  coil  takes  place  in  glass  tubes  containing  a  highly  rarefied  vapour 
or  gas.  These  phenomena,  which  have  been  investigated  by  Masson, 
Grove,  Gassiot,  Pliicker,  etc.,  are  produced  by  means  of  sealed  glass  tubes 
first  constructed  by  Geissler,  of  Bonn.  These  tubes  are  filled  with  different 
gases  or  vapours,  and  are  then  exhausted,  so  that  the  pressure  does  not 
exceed  half  a  millimetre.  At  the  ends  of  the  tubes  two  platinum  wires 
are  soldered  into  the  glass. 

When  the  two  platinum  wires  are  connected  with  the  ends  of  a  Ruhm- 
korff's  coil,  magnificent  lustrous  striag,  separated  by  dark  bands,  are  pro- 
duced all  through  the  tube.  These  striae  vary  in  shape,  colour,  and  lustre 
with  the  degree  of  the  vacuum,  the  nature  of  the  gas  or  vapour,  and  the 
dimensions  of  the  tube.  The  phenomenon  has  occasionally  a  still  more 
brilliant  aspect  from  the  fluorescence  which  the  electric  discharge  excites 
in  the  glass. 

Fig.  724  represents  the  striae  given  by  hydrogen  under  half  a  milli- 


tjuum^ 


Fig.  724. 

metre  of  pressure ;  in  the  bulbs  the  light  is  white,  in  the  capillary  parts 
it  is  red. 

Fig.  725  shows  the  striae  in  carbonic  acid  under  a  quarter  of  a  millimetre 


-867]- 


Rotation  of  Induced  Currents. 


80 1 


pressure  ;  the  colour  is  greenish,  and  the  striae  have  not  the  same  form  as 
hydrogen.     In  nitrogen  the  light  is  orange  yellow. 

Pliicker  has  found  that  the  light  in  Geissler's  tube  does  not  depend 


Fig.  725. 


on  the  substance  of  the  electrodes,  but  simply  on  the  nature  of  the  gas 
or  vapour  in  the  tube.  He  has  found  that  the  lights  furnished  by  hydro- 
gen, nitrogen,  carbonic  oxide,  etc.,  give  different  spectra  when  they  are 
decomposed  by  a  prism.  The  discharge  of  the  coil  which  passes  through 
a  highly  rarefied  gas  would  not  pass  through  a  perfect  vacuum,  from 
which  it  follows  that  the  presence  of  a  ponderable  substance  is  absolutely 
necessary  for  the  passage  of  electricity. 

By  the  aid  of  a  powerful  magnet  Pliicker  tried  the  action  of  mag- 
netism on  the  electric  discharge  in  a  Geissler's  tube,  as  Davy  had  done 
with  the  ordinary  voltaic  arc,  and  obtained  many  curious  results,  one  of 
which  may  be  mentioned.  He  found  that 
where  the  discharge  is  perpendicular  to  the 
line  of  the  poles,  it  is  separated  into  two 
distinct  parts,  which  can  be  referred  to  the 
different  action  exerted  by  the  electromagnet 
on  the  two  extra  currents  produced  in  the 
discharge. 

The  light  of  Geissler's  tubes  has  been  ap- 
plied to  medical  purposes.  A  long  capillary 
tube  is  soldered  to  two  bulbs  provided  with 
platinum  wires  ;  this  tube  is  bent  in  the  middle, 
so  that  the  two  branches  touch,  and  their  ex- 
tremities are  twisted,  as  shown  at  a  in  fig.  726 
This  tube  contains  a  highly  rarefied  gas,  like 

those  previously  described,  and,  when  the  discharge  passes,  a  light  is  pro- 
duced at  rt,  bright  enough  to  illuminate  any  cavity  of  the  body  into  which 
the  tube  is  introduced. 

867.  Rotation  of  Induced  currents  Xxj  magrnets. — De  la  Rive  has 
recently  devised  an  experiment  which  shows  in  a  most  ingenious  manner 
that  magnets  act  on  the  light  in  Geisslei-'s  tubes  in  accordance  with  the 
laws  with  which  they  act  on  any  other  movable  conductor. 

M  M  3 


Fie.    726. 


802 


Dynamical  Electricity. 


[867- 


This  apparatus  consists  of  a  glass  globe  or  electrical  ^<gg  (fig.  727),  pro- 
vided at  one  end  with  two  stopcocks,  one  of  which  can  be  screwed  on  the 
air  pump,  and  the  other,  which  is  a  stopcock  Hke  that  of  Gay  Lussac  (358), 
serves  to  introduce  a  few  drops  of  the  Hquid  into  the  globe.  At  the  other 
end  a  tubulure  is  cemented,  through  which  passes  a  rod  of  soft  iron 
about  I  of  an  inch  in  diameter,  the  top  of  which  is  at  about  the  centre  of 
the  globe.  Except  at  the  two  ends,  this  bar  is  entirely  covered  with 
a  very  thick  insulating  layer  of  shellac,  then  with  a  glass  tube  also 
coated  with  shellac,  and  finally  with  another  glass  tube  uniformly  coated 


Fig.  727- 


with  a  layer  of  wax.  This  insulating  layer  must  be  at  least  |  of  an 
inch  thick.  Inside  the  globe  the  insulating  layer  is  surrounded  at  x 
with  a  copper  ring  connected  by  means  of  a  copper  wire  with  a  binding 
screw,  c. 

The  vessel  having  been  exhausted  as  completely  as  possible,  a  few 
drops  of  ether  or  of  turpentine  are  introduced  by  means  of  the  stop- 
cock ^  ;  it  is  again  exhausted,  so  that  the  vapour  remaining  is  highly 
rarefied. 

A  thick  disQ  of  soft  iron,  0,  provided  with  a  binding  screw,  is  then 


-868]  Heat  developed  by  Induction,  803" 

placed  on  one  of  the  branches  of  a  powerful  electromagnet,  and  the 
end  in  of  the  rod  mn  is  placed  on  this  disc,  while  at  the  same  time  one 
of  the  ends  of  the  secondary  wire  of  Ruhmkorff  s  coil  is  connected  with 
the  binding  screw  r,  and  the  other  with  the  knob  0.  If  then  the  coil  is 
worked  without  setting  in  action  the  electromagnet,  the  electricity  of 
the  wire  s  passes  to  the  top  n  of  the  soft  iron  rod,  and  that  of  the  second 
wire  to  the  ring  x,  and  a  more  or  less  irregular  luminous  sheaf  appears 
on  the  inside  of  the  globe  round  the  rod  as  in  the  experiment  of  the 
electric  ^%g. 

But  if  a  voltaic  current  passes  into  the  electromagnet,  the  phenomenon 
is  different  ;  instead  of  starting  from  different  points  of  the  upper  surface 
w,  and  the  ring  ;r,  the  light  is  condensed  and  emits  a  single  luminous 
arc  from  n  to  x.  Further,  and  this  is  the  most  remarkable  part  of  the 
experiment,  this  arc  turns  slowly  round  the  magnetised  cylinder  mn, 
sometimes  in  one  direction,  and  sometimes  in  another,  according  to  the 
direction  of  the  induced  current,  or  the  direction  of  the  magnetism.  As 
soon  as  the  magnetism  ceases  the  luminous  phenomenon  reverts  to  its 
original  appearance. 

This  experiment  is  remarkable  as  having  been  devised  dprtorihy  De  la 
Rive  to  explain,  by  the  influence  of  terrestrial  magnetism,  a  kind  of  rotatory 
motion  from  east  to  west,  observed  in  the  aurora  boreaUs.  The  rotation 
of  the  lummous  arc  in  the  above  experiment  can  evidently  be  referred  to 
the  rotation  of  currents  by  magnets. 

Geissler  has  constructed  a  very  useful  form  of  the  above  experiment,  in 
which  the  globe  is  exhausted  once  for  all.  Apart  from  the  purpose  for  which 
it  was  originally  devised  it  is  a  very  convenient  arrangement  for  demon- 
strating the  action  of  magnets  on  movable  currents. 

868.  Heat  developed  by  tbe  induction  of  powerftil  magrnets  on 
bodies  in  motion. — We  have  already  seen  in  Arago's  experiments  (848) 
that  a  rotating  copper  disc  acts  at  a  distance  on  a  magnetic  needle  com- 
municating to  it  a  rotatory  motion.  We  shall  presently  see  that  a  cube 
of  copper,  rotating  with  great  velocity,  is  suddenly  stopped  by  the  influence 
of  the  poles  of  two  strong  magnets  (870).  It  is  clear  that  in  order  to  pre- 
vent the  rotation  of  the  needle  or  of  the  copper,  a  certain  mechanical  iforce 
must  be  consumed  in  overcoming  the  resistance  which  arises  from  the 
inductive  action  of  the  magnet.  Reasoning  upon  the  theory  of  the  trans- 
formation of  mechanical  work  into  heat,  which  has  occupied  physicists  in 
the  last  few  years  (467),  it  has  been  attempted  to  ascertain  what  quantity 
of  heat  is  developed  by  the  action  of  induced  currents  under  the  influence 
of  powerful  magnets.  Joule,  with  a  view  of  determining  the  mechanical 
equivalent  of  heat,  coiled  a  quantity  of  copper  wire  round  a  cyhnder  of 
soft  iron,  and  having  enclosed  the  whole  in  a  glass  tube  full  of  water,  he 
imparted  to  the  system  a  rapid  rotation  between  the  branches  of  an  electro- 
magnet. A  thermometer  placed  in  the  liquid  served  to  measure  the  quan- 
tity of  heat  produced  by  the  induced  currents  in  the  soft  iron  and  the  wire 
round  it.  It  was  thus  found  that  the  heat  developed  was  proportional  to 
the  square  of  the  magnetism  evoked,  and  was  equivalent  to  the  work  used 
in  the  rotation. 


8o4 


Dynamical  Electricity. 


[868- 


Foucault  has  made  a  remarkable  experiment  by  means  of  the  appa- 
ratus represented  in  fig.  728.  It  consists  of  a  powerful  electromagnet 
fixed  horizontally  on  a  table.  Two  pieces  of  soft  iron,  A  and  B,  are  in 
contact  with  the  poles  of  the  magnet,  and  becoming  magnetised  by  induc- 
tion, they  concentrate  their  magnetic  inductive  action  on  the  two  faces  of 
a  metallic  disc,  D ;  this  disc,  which  is  of  copper,  is  3  inches  in  diameter, 
and  a  quarter  of  an  inch  thick,  partly  projects  between  the  pieces  A  and 
B,  and  can  be  moved  by  means  of  a  handle  and  a  series  of  toothed  wheels 
with  a  velocity  of  1 50  to  200  turns  in  a  second. 

So  long  as  the  current  does  not  pass  through  the  wire  of  the  electro- 
magnet, very  little  resistance  is  experienced  in  turning  the  handle,  and 
when  once  it  has  begun  to  rotate  rapidly,  and  is  left  to  itself,  the  rotation 


Fig.  728. 

continues  in  virtue  of  the  acquired  velocity.  But  if  the  current  passes, 
the  disc  and  other  pieces  stop  almost  instantaneously ;  and  if  the  handle 
is  turned  considerable  resistance  is  felt.  If,  in  spite  of  this,  the  rotation  be 
continued,  the  force  used  is  transformed  into  heat,  and  the  disc  becomes 
heated  to  a  remarkable  extent.  In  an  experiment  made  by  M.  Foucault 
the  temperature  of  the  disc  rose  from  10°  to  61°,  the  current  being  formed 
by  three  of  Bunsen's  elements  ;  with  six  the  resistance  was  such  that  the 
rotation  could  not  long  be  continued. 


-869] 


Optical  Effects  of  Powerful  Magnets. 


805 


CHAPTER  VII. 

OPTICAL   EFFECTS   OF   POWERFUL  MAGNETS.      DIAMAGNETISM. 

869.  Optical  effects  of  powerful  mag-nets. — Faraday  observed  in 
1845,  that  a  powerful  electromagnet  exercises  an  action  on  many  sub- 
stances, such  that  if  a  polarised  ray  traverses  them  in  the  direction  of 
the  line  of  the  magnetic  poles,  the  plane  of  polarisation  is  deviated  either 
to  the  right  or  to  the  left,  according  to  the  direction  of  the  magnetisation. 

Figure  729  represents  Faraday^s  apparatus,  as  constructed  by  Ruhm- 
korff.     It  consists  of  two  very  powerful  electromagnets,  M  and  N,  fixed 


Fig.  729. 


on  two  iron  supports,  OO',  which  can  be  moved  on  a  support,  K.  The 
current  from  a  battery  of  10  or  11  Bunsen's  elements  passes  by  the  wire 
A  to  the  commutator  H,  the  bobbin  M,  and  then  to  the  bobbin  N,  by 
the  wire  g,  descends  in  the  wire  /,  passes  again  to  the  commutator,  and 
emerges  at  B.  The  two  cyhnders  of  soft  iron,  which  are  in  the  axis  of 
the  bobbins,  are  perforated  by  cylindrical  holes,  to  allow  the  luminous 
rays  to  pass.  At  b  and  a  there  are  two  Nicol's  prisms,  the  first  serving 
as  polariser,  and  the  second  as  analyser.  By  means  of  a  limb  this  latter 
is  turned  round  the  centre  of  a  graduated  circle,  P. 

The  two  prisms  being  then  placed  so  that  their  principal  sections  are 
perpendicular  to  each  other,  the  prism  a  completely  extinguishes  the 
light  transmitted  through  the  prism  b.  If  at  c,  on  the  axis  of  the  two 
coils,  a  plate  be  placed  with  parallel  faces,  either  of  ordinary  or  flint 
glass,  light  is  still  extinguished  so  long  as  the  current  does  not  pass  ;  but 
when  the  communications  are  established,  the  hght  reappears.      It  is 


8o6 


Dynamical  Electricity. 


[869- 


now  coloured,  and  if  the  analyser  be  turned  from  left  or  right,  according 
to  the  direction  of  the  current,  the  light  passes  through  the  different 
tints  of  the  spectrum,  as  is  the  case  with  plates  of  quartz  cut  perpendicu- 
larly to  the  axis  (637).  Bequerel  has  shown  that  a  large  number  of 
substances  can  also  rotate  the  plane  of  polarisation  under  the  influence 
of  powerful  magnets.  Faraday  assumes  that  in  these  experiments  the 
rotation  of  the  plane  of  polarisation  is  due  to  an  action  of  the  magnets 
on  the  luminous  rays,  while  Biot  and  Becquerel  ascribe  the  phenomena 
to  a  molecular  action  of  the  magnet  on  the  transparent  bodies  submitted 
to  its  influence. 

870.  Dlamagrnetism — Coulomb  observed,  in  1802,  that  magnets  act 
upon  all  bodies  in  a  more  or  less  marked  degree ;  this  action  was  at  first 
attributed  to  the  presence  of  ferruginous  particles.  Brugmann  also  found 
that  certain  bodies,  for  instance,  bars  of  bismuth,  when  suspended  be- 
tween the  poles  of  a  powerful  magnet,  do  not  set  axially  between  the 
poles,  that  is,  in  the  line  joining  the  poles,  but  equatorially,  or  at  right 
angles  to  that  line.  This  phenomenon  was  explained  by  the  assumption 
that  the  bodies  were  transversely  magnetic.  Faraday  made  the  impor- 
tant discovery  in  1845  that  all  solids  and  liquids  are  either  attracted  or 
repelled  by  a  powerful  electromagnet.  The  bodies  which  are  attracted 
are  called  magnetic  or'  paramagnetic  substances,  and  those  which  are 
repelled  are  dia7nagnetic  bodies.     Among  the  metals,  iron,  nickel,  cobalt, 


Fig.  730. 


Fig.  731- 


Fig.  732 


manganese,  platirvilim,  cerium,  osmium,  and  palladium  are  magnetic; 
while  bismuth,  antimony,  zinc,  tin,  mercury,  lead,  silver,  copper,  gold 
and  arsenic  are  diamagnetic,  bismuth  being  the  most  so  and  arsenic  the 
least.  The  diamagnetic  effects  can  only  be  produced  by  means  of  very 
powerful  magnets,  and  it  is  by  means  of  Faraday's  apparatus  that  they 
have  been  discovered  and  studied.  In  experimenting  on  the  diamagnetic 
effects — solids,  liquids,  and  gases— armatures  of  soft  iron,  S  and  Q, 
(figs.  730-732)  of  different  shapes  are  screwed  on  the  magnets. 

i.  DiamagnetisfH  of  solids.  If  a  small  cube  of  copper  suspended  by 
a  fine  silk  thread  between  the  poles  of  the  magnet  (fig.  731),  be  in  rapid 
rotation  between  the  poles  of  an  electromagnet,  it  stops  the  moment  the 
current  passes  through  the  bobbins.  If  the  movable  piece  have  the 
form  of  a  small  rectangular  bar  it  sets  equatorially ^  or  at  right  angles  to 


-870]  Diarnagnetism.  Soy 

the  axis  of  the  bobbins,  if  it  is  a  diamagnetic  substance,  such  as  bismuth, 
antimony,  or  copper ;  but  axially,  or  in  the  direction  of  the  axis,  if  it  is  a 
magnetic  substance,  such  as  iron,  nickel,  or  cobalt. 

Besides  the  substances  enumerated  above,  the  following  are  diamag- 
netic :  rock  crystal,  alum,  glass,  phosphorus,  sulphur,  sugar,  bread ;  and 
the  following  are  magnetic :  many  kinds  of  paper  and  sealing-wax, 
fluorspar,  graphite,  charcoal,  etc. 

ii.  Dia7nagnetis7}i  of  liquids.  Liquids  also  present  the  phenomena  of 
magnetism  and  of  diamagnetism.  In  making  the  experiment,  very  thin 
glass  tubes  filled  with  the  substance  are  suspended  between  the  poles 
instead  of  the  cube  7n  in  the  figure  731.  If  the  liquids  are  magnetic,  such 
as  solutions  of  iron  or  cobalt,  the  tubes  set  axially ;  if  diamagnetic,  like 
water,  alcohol,  ether,  essence  of  turpentine,  and  most  sahne  solutions, 
the  tubes  set  equatorially. 

Very  remarkable  changes  take  place  in  the  direction  of  magnetic  and 
diamagnetic  substances  when  they  are  suspended  in  Hquids.  A  magnetic 
substance  is  indifferent  in  an  equally  strong  magnetic  liquid ;  it  sets 
equatorially  in  a  stronger  magnetic  substance,  and  axially  in  a  substance 
which  is  less  strongly  magnetic ;  it  sets  axially  in  all  diamagnetic  liquids. 

A  diamagnetic  substance  surrounded  by  a  magnetic  or  diamagnetic 
Substance  sets  equatorially.  According  to  its  composition,  glass  is  some- 
times magnetic  and  sometimes  diamagnetic,  and  as  in  these  investigations- 
glass  tubes  are  used  for  containing  the  liquids,  its  deportment  must  first 
be  determined,  and  then  taken  into  account  in  the  experiment. 

The  action  of  powerful  magnets  on  liquids  may  also  be  observed  in  the 
following  experiment  devised  by  Pliicker.  A  solution  of  a  magnetic  liquid 
is  placed  on  a  watch  glass  between  the  two  poles,  S  and  Q,  of  a  powerful 
electromagnet.  When  the  current  passes,  the  solution  forms  the  enlarge- 
ment represented  in  fig.  732;  this  continues  as  long  as  the  current  passes, 
and  is  produced  to  different  extents  with  all  magnetic  liquids.  The 
changes  in  the  aspects  of  the  liquids  are,  however,  so  small  as  to  require 
careful  scrutiny  to  detect  their  existence.  A  method  of  magnifying  these 
changes  so  as  to  render  them  visible  to  large  audiences,  has  been  devised 
by  Prof.  Barrett.  A  source  of  light  is  placed  above  the  watch  glass 
containing  a  drop  of  the  solution  to  be  tried.  Below  the  watch  glass,  and 
between  the  legs  of  the  magnet,  is  placed  a  mirror  at  the  angle  of  45°.  By 
this  means  the  beam  of  light  passing  through  the  watch  glass  is  reflected 
at  right  angles  on  to  a  screen,  where  an  image  of  the  drop  is  focussed  by 
a  lens.  If  now  a  drop  of  diamagnetic  liquid,  such  as  water,  or  better, 
sulphuric  acid,  be  placed  on  the  watch  glass,  as  soon  as  the  current  passes, 
the  flattened  drop  retreats  from  the  two  poles,  and  gathers  itself  up  into 
a  little  heap,  as  at  A  (fig.  732).  So  doing  it  forms  a  double  convex  lens, 
by  which  the  light  is  brought  to  a  short  focus  below  the  drop,  an  effect, 
instantly  seen  on  the  screen.  When  the  current  is  interrupted  the  drop 
falls,  and  the  light  returns  to  its  former  appearance.  A  magnetic  liquid, 
such  as  a  solution  of  perchloride  of  iron,  has  exactly  the  opposite  effect. 
The  drop  attracted  to  the  two  poles  becomes  flattened,  and  instead  of  a 
plano-convex  shape,  at  which  it  rests,  it  becomes  nearly  concavo-convex^ 


8o8  Dynamical  Electricity,  [870- 

as  at  B.  The  light  is  dispersed,  and  the  effect  manifest  on  the  screen. 
Instead  of  a  mirror  and  lens,  a  sheet  of  white  paper  may  be  placed  in  an 
inclined  position  under  the  watch  glass,  and  the  effects  are  somewhat 
varied,  but  equally  well  pronounced. 

iii.  Diamagnetism  of  gases.  Bancalari  observed  that  the  flame  of  a 
candle  placed  between  the  two  poles  in  Faraday's  apparatus  was  strongly 
repelled  (fig.  730).  All  flames  present  the  same  phenomenon  to  different 
extents,  resinous  flames  or  smoke  being  most  powerfully  affected 

The  magnetic  deportment  of  gases  may  be  exhibited  for  lecture  pur- 
poses by  inflating  soap  bubbles  with  them  between  the  poles  of  the 
electromagnet,  and  projecting  on  them  either  the  lime  or  the  electric 
light. 

Faraday  experimented  on  the  magnetic  or  diamagnetic  nature  of 
gases.  He  allowed  gas  mixed  with  a  small  quantity  of  a  visible  gas  or 
vapour,  so  as  to  render  it  perceptible,  to  ascend  between  the  two  poles 
of  a  magnet,  and  observed  their  deflections  from  the  vertical  line  in  the 
axial  or  equatorial  direction ;  in  this  way  he  found  that  oxygen  was  least, 
nitrogen  more,  and  hydrogen  most  diamagnetic.  With  iodine  vapour, 
produced  by  placing  a  little  iodine  on  a  hot  plate  between  the  two  poles, 
the  repulsion  is  strongly  marked.  Becquerel,  who  has  made  important 
researches  on  magnetism,  has  found  that  oxygen  is  the  most  strongly  mag- 
netic of  all  gases,  and  that  a  cubic  yard  of  this  gas  condensed  would  act 
on  a  magnetic  needle  like  5-5  grains  of  iron.  Faraday  has  found  that 
oxygen,  although  magnetic  under  ordinary  circumstances,  becomes  dia- 
magnetic when  the  temperature  is  much  raised,  and  that  the  magnetism 
or  diamagnetism  of  a  substance  depends  on  the  medium  in  which  it  is 
placed.  A  substance,  for  instance,  which  is  magnetic  in  vacuo,  may 
become  diamagnetic  in  air. 

In  the  crystallised  bodies  which  do  not  belong  to  the  regular  system, 
the  directions  in  which  the  magnetism  or  diamagnetism  of  a  body  is  most 
easily  excited,  are  generally  related  to  the  crystallographic  axis  of  the 
substance.  The  optic  axis  of  the  uniaxial  crystals  sets  either  axially  or 
equatorially  when  a  crystal  is  suspended  between  the  poles  of  an  electro- 
magnet. Faraday  has  assumed  from  this  the  existence  of  a  magneto- 
crystalline  force,  but  it  appears  probable  from  Knoblauch's  researches, 
that  the  action  arises  from  an  unequal  density  in  different  directions,  in- 
asmuch as  unequal  pressure  in  different  directions  produces  the  same 
result. 

According  to  Pliicker^  for  a  given  unit  of  magnetising  force,  the  specific 
magnetisms  developed  in  equal  weights  of  the  undermentioned  substances 
are  represented  by  the  following  numbers,  those  bodies  with  the  minus 
sign  prefixed  being  diamagnetic  : — 

Iron  ....  1,000,000  Nickel  oxide     .        .        .  287 

Cobalt       .        .         .  1,009,000  Water       ,         .         .        •  —25 

Nickel       .         .         .  465,800  Bismuth   ....  —23*6 

Iron  oxide         .        .  759  Phosphorus      .        .        .  —\yi 


^871]  Thermo-electricity.  809 

iv.  Detonation  produced  by  the  rupture  of  a  current  under  the  influence 
of  a  powerful  electromagnet.  The  following  experiment  devised  by- 
Ruhmkorff  is  a  remarkable  effect  of  Faraday's  apparatus.  When  the  two 
ends  of  a  stout  wire  in  which  the  current  of  the  electromagnet  passes  are 
placed  between  the  two  poles,  S  and  Q,  of  figure  730,  that  is  to  say,  when 
the  current  is  closed  between  S  and  Q,  this  closing  takes  place  without  a 
spark  and  without  noise,  or  merely  a  feeble  noise  and  a  spark.  But  when 
the  two  ends  are  separated,  and  the  current  is  hence  broken,  a  violent 
noise  is  heard  almost  as  strong  as  the  report  of  a  pistol.  It  would  appear 
to  be  the  extra  current,  the  intensity  of  which  is  greatly  increased  by  the 
influence  of  two  poles. 


CHAPTER  VIII, 

THERMO-ELECTRIC  CURRENT. 


871.  Thermo-electricity. — In  182 1,  Professor  Seebeck,  in  Berlin, 
found  that  by  heating  one  of  the  junctions  of  a  metallic  circuit,  consisting 
of  two  metals  soldered  together,  an  electric  current  was  produced.  This 
phenomenon  may  be  shown  by  means  of  the  apparatus  represented  in  fig. 
733,  which  consists  of  a  plate  of  copper,  nin,  the  ends  of  which  are  bent 


Fig.  733. 

and  soldered  to  a  plate  of  bismuth,  op.  In  the  interior  of  the  circuit  is  a 
magnetic  needle  moving  on  a  pivot.  When  the  apparatus  is  placed  in 
the  magnetic  meridian,  and  one  of  the  solderings  gently  heated,  as  shown 
in  the  figure,  the  needle  is  deflected  in  a  manner  which  indicates  the 
passage  of  a  current  from  n  to  w,  that  is,  from  the  heated  to  the  cool 
junction  in  the  copper.  If,  instead  of  heating  the  junction  ;/,  it  is  cooled 
by  ice,  or  by  placing  upon  it  cotton  wool  moistened  with  ether,  the  other 
junction  remaining  at  the  ordinary  temperature,  a  current  is  produced, 
but  in  the  opposite  direction ;  that  is  to  say,  from  tn  to  n.  In  both  cases 
the  current  is  more  energetic  in  proportion  as  the  difference  in  tempera- 
ture of  the  solderings  is  greater.   . 


8 10  Dynamical  Electricity.  [871- 

Seebeck  gave  the  n2im.^thertno-electric  to  this  current,  and  to  the  couple 
which  produces  it,  to  distinguish  it  from  the  hydro-electric  or  ordinary 
voltaic  current  and  couple. 

•  872.  Thermo-electric  series. — If  small  bars  of  two  different  metals 
are  soldered  together  at  one  end  while  the  free  ends  are  connected  with 
the  wires  of  a  galvanometer,  and  if  naw  the  point  of  junction  of  the  two 
metals  be  heated,  a  current  is  produced,  the  direction  of  which  is  indi-- 
cated  by  the  deflection  of  the  needle  of  the  galvanometer.  Moreover,^' 
the  strength  of  the  current  calculated  from  the  deflection  of  the  galva- 
nometer is  proportional  to  the  electromotive  force  of  the  thermo-elefnent.' 
By  experimenting  in  this  way  with  different  metals,  they  may  be  formed- 
in  a  list  such  that  each  metal  gives  rise  to  positive  electricity  when  asso- 
ciated with  one  of  the  following,  and  negative  electricity  with  one  of  those 
that  precede: — that  is,  that  in  heating  the  soldering,  the  positive  current 
goes  from  the  positive  to  the  negative  metal  across  the  soldering,  just  as 
if  the  soldering  represented  the  liquid  in  a  hydro-electrical  element ;  hence 
out  of  the  element,  in  the  connecting  wire  in  the  galvanometer  for  instance, 
the  current  goes  from  the  negative  to  the  positive  metal. 

Thus  a  couple,  bismuth-antimony,  heated  at  the  junction  would  corre- 
spond to  a  couple,  zinc-copper,  immersed  in  sulphuric  acid.  The  following' 
is  a  hst  drawn  up  from  Dr.  Matthiessen's  researches,  which  also  gives, 
comparative  numerical  values  for  the  electromotive  force  : — 


Bismuth 

-J- 25 

Gas  coke    . 

.     -o-i 

Cobalt  . 

.      9 

Zinc     . 

0-2 

Potassium     . 

--i'5 

Cadmium    . 

o'3 

Nickel  . 

''-■^■'i 

Strontium    . 

2-0 

Sodium 

Arsenic 

.        3-8 

Lead     . 

.      1-03 

Iron     . 

5-2 

Tin        . 

Red  phosphorus . 

.        9-6 

Copper . 

Antimony    . 

.        9-8 

Platinum 

.      07 

Tellurium    . 

.     179-9 

Silver    . 

i-o 

Selenium    . 

.  -  290-0 

The  meaning  of  the  numbers  in  this  list  is  that,  taking  the  electromo- 
tive force  of  the  copper-silver  couple  as  unity,  the  electromotive  force  of 
any  pair  of  metals  is  expressed  by  the  difference  of  the  numbers  where 
the  signs  are  the  same  and  by  the  sum  where  the  signs  are  different. 
Thus  the  electromotive  force  of  a  bismuth-nickel  couple  would  be  25-  5' 
=  20;  of  a  cobalt-iron  9  — (  —  5-2)  =  14*2,  and  of  an  iron-antimony  — 5*2 
_9'8=a  —4-6.  Where  the  positive  sign  is  fixed,  the  current  is  from  the 
other  metal  to  silver  across  the  soldering ;  and  where  the '  negative  from 
silver  to  that  metal. 

Hence  of  these  bodies,  bismuth  and  selenium  produce  the  greatest 
electromotive  force  ;  but  from  the  expense  of  this  latter  element,  and  on 
account  of  its  low  conducting  power,  antimony  is  generally  substituted. 
The  antimony  is  the  negative  metal  but  the  positive  pole,  and  the  bis- 
muth the  positive  metal  but  the  negative  pole  and  the  current  goes  from 
bismuth  to  antimony  across  the  junction. 


■^873]  Causes  of  Thermo-electricity.  8 1 1 

-'  If  copper  wires  connected  with  the  ends  of  a  galvanometer  are  sol- 
dered together  to  the  ends  of  an  antimony  rod,  and  if  one  of  the  junctions 
is  heated  to  50°,  the  other  being  maintained  at  0°,  a  certain  deflection  is 
observed  in  the  galvanometer.  If  similarly  a  compound  bar,  consisting  of 
antimony  and  tin  soldered  together,  be  connected  with  the  ends  of  the 
galvanometer,  and  if  the  junction  copper-tin,  and  the  junction  tin-anti- 
mony, be  heated  to  50°,  while  the  junction  antimony-copper  is  kept  at  0°, 
the  deflection  is  the  same  as  in  the  previous  case.  Hence  the  electromo- 
tive force  produced  by  heating  the  two  junctions,  copper-tin  and  tin-anti- 
mony, is  equal  to  the  electromotive  force  produced  by  heating  the  copper- 
antimony.  ' 

'-  Becquerel  found  with  a  number  of  cOiiples  where  one  end  of  the  junc- 
tion was  heated  to  a  given  temperature  and  the  other  kept  at  0°,  that  the 
intensity  of  the  current  was  proportional  to  the  temperature  at  the  junc- 
tion. If  the  two  junctions  are  at  any  given \temperature,  the  intensity  of 
the  current  is  proportional  to  the  difference  of  the  temperature  of  the  two 
places,  provided  that  this  does  not  exceed  50^. 

The  direction  of  the  current  frequently  changes  when  the  temperature 
of  the  couple  is  raised  beyond  a  certain  limit.  Thus,  in  a  copper  and 
iron  circuit,  the  current  goes  from  copper  to  iron  through  the  heated  part, 
provided  the  temperature  does  not  exceed  300°;  at  a  higher  temperature 
the  current  changes  its  direction,  and  goes  from  iron  to  copper. 
^  "^As  compared  with  ordinary  hydro-electric  currents  the  electromotive 
force  of  thermocurrents  is  very  small ;  thus  the  electromotive  force  of  a 
bismuth-copper  etement  with  a  difference  of  100°  C.  in  the  temperatures 
of  their  junctions  is  according  to  Wheatstone  —,  and  according  to  Neu- 
i^ann  gl^  that  of  DanielFs  element  :  the  electromotive  force  of  an  iron- 
argentan  couple  with  10  to  15°  difference  of  temperatures  in  their  junctions 
is  g^  that  of  a  Daniell's,  according  to  Kohlrausch. 

•  %']'>).  Causes  of  tbermo-electrlc  currents. — The  thenno-electric 
Currents  cannot  be  attributed  to  contact,  for  they  can  be  produced  in-' 
circuits  formed  of  a  single  metal.  Nor  do  they  arise  from  chemical 
actions,  for  Becquerel  has  found  that  they  are  formed  in  hydrogen,  and 
even  in  vacuo.  The  same  physicist  ascribes  them  to  the  unequal  pro- 
pagation of  heat  in  the  different  parts  of  the  circuit.  He  found  that  when 
all  the  parts  of  a  circuit  are  homogeneous,  no  current  is  produced  on 
heating,  because  the  heat  is  equally  propagated  in  all  directions.  This  is 
the  case  if  the  wires  of  the  galvanometer  are  connected  by  a  second' 
copper  wire.  But  if  the  uniformity  of  this  is  destroyed  by  coiling  it  in  a 
spiral,  or  by  knotting  it,  the  needle  indicates  by  its  deflection  a  current 
going  from  the  heated  part  to  that  in  which  the  homogeneity  has  been 
destroyed.  If  the  ends  of  the  galvanometer  wires  be  coiled  in  spiral,  and 
one  end  is  heated  and  touched  with  the  other,  the  current  goes  from  the 
heated  to  the  cooled  end. 

When  two  plates  of  the  same  metal,  but  at  different  temperatures,  are 
placed  in  a  fused  salt  such  as  borax,  which  conducts  electricity  but  exerts 
no  chemical  action,  a  current  passes  from  the  hotter  metal  through  the 


8l2 


Dynamical  Electricity, 


[873 


fused  salt  to  the  colder  one.     Hot  and  cold  water  in  contact  produce  a 
current  which  goes  from  the  warm  water  to  the  cold. 

Svanberg  has  found  that  the  thermo-electromotive  force  is  influenced 
by  the  crystallisation  ;  for  instance,  if  the  cleavage  of  bismuth  is  parallel 
to  the  face  of  contact,  it  is  greater  than  if  both  are  at  right  angles,  and 
that  the  reverse  is  the  case  with  antimony.  Thermo-electric  elements  may 
be  constructed  of  either  two  pieces  of  bismuth  or  two  pieces  of  antimony, 
if  in  the  one  the  principal  cleavage  is  parallel  to  the  place  of  contact, 
and  in  the  other  is  at  right  angles.  Hence  the  position  of  metals  in  the 
thermo-electric  series  is  influenced  by  their  crystaUine  structure. 

874.  Tberino*  electric  couples. — From  what  has  been  said  it  will  be 
understood  that  a  thermo-electric  couple 
consists  of  two  metals  soldered  together, 
the  two  ends  of  which  can  be  joined  by 
a  conductor.  Fig.  734  represents  a  bis- 
muth-copper couple  ;  fig.  735  represents 
a  series  of  couples  used  by  M.  Pouillet. 
It  consists  of  a  bar  of  bismuth  bent  twice 
at  right  angles,  at  the  ends  of  which  are 
soldered  two  copper  strips,  c^  d,  which 
terminate  in  two  binding  screws  fixed  on 
some  insulating  material. 

When  several  of  these  couples  are 
joined  so  that  the  second  copper  of  the 
first  is  soldered  to  the  bismuth  of  the 
second,  then  the  second  copper  of  this 
to  the  bismuth  of  the  third,  and  so  on,  this  arrangement  constitutes  a 
thermo-electric  battery,  which  is  worked  by  keeping  the  odd  solderings, 
for  instance,  in  ice,  and  the  even  ones  in  water,  which  is  kept  at  100°. 

875.  iroblli'8  thermo-electric  pile. — Nobili  devised  a  form  of  thermo- 
electric battery,  or  pile  as  it  is  usually  termed,  in  which  there  are  a  large 


Fig.  734- 


_j|||^^ 


MO^m^m^^ 


Fig-  735. 


number  of  elements  in  a  very  small  space.     For  this  purpose  he  joined 
the  couples  of  bismuth  and  antimony  in  such  a  manner,  that  after  having 


-876] 


BecquereVs  Thermo-electric  Battery, 


813 


formed  a  series  of  five  couples,  as  represented  in  fig.  737,  the  bismuth 
from  b  was  soldered  to  the  antimony  of  a  second  series  arranged  similarly; 
the  last  bismuth  of  this  to  the  antimony  of  a  third,  and  so  on  for  four 
vertical  series,  containing  together  20  couples,  commencing  by  antimony, 
finishing  by  bismuth.  Thus  arranged,  the  couples  are  insulated  from  one 
another  by  means  of  small  paper  bands  covered  with  varnish,  and 
then  enclosed  in  a  copper  frame,  P 
(fig.  736),  so  that  only  the  solderings 
appear  at  the  two  ends  of  the  pile. 
Two  small  copper  binding-screws, 
7n  and  n,  insulated  in  an  ivory  ring, 
communicate  in  the  interior,  one 
with  the  first  antimony,  representing 
the  positive  pole,  and  the  other  with 
the  last  bismuth,  representing  the 
negative  pole.  These  binding 
screws  communicate  with  the  ex- 
tremities of  a  galvanometer  wire 
when  the  thermo-electric  current  is  to  be  observed. 

876.  Becquerel's  tbermo-electric  battery. — Becquerel  has  found 
that  artificial  sulphuret  of  copper  heated  from  200°  to  300°  is  powerfully 
positive,  and  that  a  couple  of  this  substance  and  copper  has  an  electro- 
motive force  nearly  ten  times  as  great  as  that  of  the  bismuth  and  copper 
couple  in  fig.  734.  Native  sulphuret,  on  the  contrary,  is  powerfully  nega- 
tive. As  the  artificial  sulphuret  only  melts  at  about  1035°,  it  may  be  used 
at  very  high  temperatures.  The  metal  joined  with  it  is  German  silver 
(90  of  copper  and  10  of  nickel).     Fig.  738  represents  the  arrangement  of 


Fig.  736, 


Fig-  737. 


Fig.  738. 


a  battery  of  50  couples  arranged  in  two  series  of  25.  Fig.  740  gives  on  a 
larger  scale  the  view  of  a  single  couple,  and  fig.  739  that  of  6  couples  in 
two  series  of  3.  The  sulphuret  is  cut  in  the  form  of  rectangular  prisms, 
10  centimetres  in  length,  by  i8mm.  in  breadth,  and  12mm.  thick.  In 
front  is  a  plate  of  German  silver  w,  intended  to  protect  the  sulphure 


8i4 


DynamicaC  Electricity, 


[876= 


from  roasting  when  it  is  placed  in  a  gas  flame.  Below  there  is  a  plate  of 
German  silver  MM,  which  is  bent  several  times  so  as  to  be  joined  to  the 
sulphuret  of  the  next,  and  so  on.  The  couples,  thus  arranged  in  two 
series  of  25,  are  fixed  to  a  wooden  frame  supported  by  two  brass  columns 
A  B,  on  which  it  can  be  more  or  less  raised.  Below  the  couples  there  is 
a  brass  trough,  through  w^iigh  water  is  constantly  flowing;  arriving  by 


Fig.  739. 


Fig.  740. 


the  tube  b  and  emerging  by  the  stopcock  r.  The  plates  of  German  silver 
are  thus  kept  at  a  constant  temperature.  On  each  side  of  the  trough  are 
two  long  burners,  on  the  Argand  principle,  fed  by  gas  from  a  caoutchouc 
tube,  a.  The  frame  being  sufficiently  lowered,  the  ends  are  kept  at  a 
temperature  of  200°  to  300°.  For  collecting  the  current,  two  binding 
screws  are  placed  on  the  left  of  the  frame,  one  communicating  with  the 
first  sulphuret,  that  is,  the  positive  pole,  and  the  other  with  the  last 
German  silver,  or  the  negative  pole.  At  the  other  end  of  the  frame  are 
two  binding  screws,  which  facihtate  the  arrangement  of  the  couples  in 
different  ways. 

The  current  of  this  battery  may  be  used  for  telegraphing  even  through 
a  great  distance,  and  passed  into  an  electromagnet  can  lift  a  weight 
of  200  pounds.  It  can  raise  a  short  piece  of  fine  iron  wire  to  redness,  and 
can  freely  decompose  water.  The  electromotive  force  of  a  Daniell's  cell 
is  equal  to  about  8  or  9  of  these  couples. 

877.  Melloni's  tbermomultipller. — We  have  already  noticed  the  use 
which  Melloni  has  made  of  Nobili's  pile,  in  conjunction  with  the  galva- 
nometer, for  measuring  the  most  feeble  alterations  of  temperature.  The 
arrangement  he  used  for  his  experiment  is  represented  in  fig.  741. 

On  a  wooden  base,  provided  with  levelling  screws,  a  graduated  copper 
rule,  about  a  yard  long,  is  fixed  edgeways.  On  this  rule  the  various  parts 
composing  the  apparatus  are  placed,  and  their  distances  can  be  fixed  by 
means  of  binding  screws.  ^  is  a  support  for  a  Locatelli's  lamp,  or  other 
source  of  heat ;  F  and  E  are  screens  ;  C  is  a  support  for  the  bodies 
experimented,  and  in  is  a  thermo-electrical  battery.  Near  the  apparatus 
is  a  galvanometer,  D  ;  this  has  only  a  comparatively  few  turns  of  a 
tolerably  thick  (i  mm.)  copper  wire  ;  for  the  electromotive  force  of  the 
thermocurrents  is  small,  and  as  the  internal  resistance  is  small  too,  for  it. 


-878] 


Uses^  of'Theymo-electric  Currents. 


tn 


only  consists  of  metal,  it  is  clear  that  no  great  resistance  can  be  intro- 
duced into  the  circuit  if  the  current  is  not  to  be  completely  stopped. 
JSuch  galvanometers  are  called  thermomultipliers.     The  delicacy  of  this 


Fig.  741 


apparatus  is  so  great  that  the  heat  of  the  hand  is  enough  at  a  distance  of 
a  yard  from  the  pile  to  deflect  the  needle  of  the  galvanometer. 

In  using  it  for  measuring  temperature,  the  relation  of  the  deflection  of 
the  needle,  and  therefore  of  the  intensity  of  the  current,  to  the  difference 
of  the  temperatures  of  the  two  ends,  must  be  determined.  That  known, 
the  temperatures  of  the  ends  not  exposed  to  the  source  of  heat  being 
known,  the  observed  deflection  gives  the  temperature  of  the  other,  and 
therewith  the  intensity  of  the  source  of  heat. 

878.  Properties  and  uses  of  thermo-electric  currents. — Thermo- 
electric currents  are  of  extremely  low  tension,  but  of  great  constancy ;  for 
their  opposite  junctions,  by  means  of  melting  ice  and  boiling  water,  can 
easily  be  kept  at  0°  and  100°  C.  On  this  account.  Ohm  used  them  in  the 
experimental  establishment  of  his  law.  They  can  produce  all  the  actions 
of  the  ordinary  battery  in  kind,  though  in  less  degree.  By  means  of  a 
thermo-electrical  pile  consisting  of  769  elements  of  iron  and  German 
silver,  the  ends  of  which  differed  in  temperature  by  about  10°  to  15", 
Kohlrausch  proved  the  presence  of  free  positive  and  negative  electricity 
at  the  two  ends  of  the  open  pile  respectively.  He  found  that  the  density 
of  the  free  electricity  was  nearly  proportional  to  the  number  of  elements, 
and  also  that  the  electromotive  force  of  a  single  element  under  the 
above  circumstances  was  about  -^^^-^  that  of  a  single  Daniell's  element. 
On  account  of  their  feeble  tension,  thermo-electric  piles  produce  only 
feeble  chemical  actions.  Botto,  however,  with  120  platinum  and  iron 
wires,  has  decomposed  water. 

Besides  these,  sparks  can  be  obtained  on  breaking  circuit,  and  mag- 
netic and  physiological  effects  produced  as  with  other  sources  of  elec- 
tricity. 


8i6 


Dynamical  Electricity. 


[879- 


879.  Becqnerel's  electrical  thermometer.— This  consists  of  a  copper 
and  iron  wire  of  many  yards  in  length  soldered  at  their  ends,  but  other- 
wise insulated  from  each  other  by  being  covered  with  gutta-percha.  The 
copper  wire  is  cut  twice  and  connected  with  the  binding  screws  of  a 
galvanometer  (fig.  742).     One  of  the  solderings  is  arranged  in  the  place 


Fig.  742. 

whose  temperature  is  to  be  measured.  In  the  figure  it  is  at  B  at  the 
top  of  a  pole  A,  and  is  underneath  a  hood,  which  protects  it  from  rain 
and  the  sun,  but  allows  air  to  circulate  round  it. 

The  other  soldering  is  immersed  in  mercury  contained  in  a  glass  tube, 
and  which  in  turn  is  placed  in  a  larger  cylinder  C  containing  ether.  On 
one  side  is  a  very  delicate  thermometer  /,  which  indicates  the  temperature 
of  the  ether.  By  means  of  a  small  bellows  S,  a  caoutchouc  tube  and  a 
glass  tube,  a  current  of  air  can  be  sent  through  the  ether,  which  being  thus 
vaporised  is  cooled.  If,  on  the  contrary,  the  temperature  of  the  ether  is 
to  be  raised  a  tinplate  vessel  containing  hot  water  is  brought  near  the 
cylinder  C. 

These  details  being  known,  when  the  solderings  are  at  the  same 
temperature  no  current  is  produced  in  the  circuit,  and  the  galvanometer 
remains  at  zero  ;  but  when  there  is  the  least  difference  in  temperature, 
the  deflection  of  the  galvanometer  tells  which  of  these  solderings  is  the 
hottest.  If  it  is  the  one  which  is  immersed  in  the  mercury,  the  bellows  is 
worked  until  the  ether  being  cooled  the  galvanometer  reverts  to  zero* 


-880] 


BecquereVs  Elect  fie  Pyrometer. 


817 


The  two  solderings  being  then  at  the  same  temperature,  the  thermometer 
/  at  once  indicates  the  temperature  in  B. 

Becquerel  has  applied  this  instrument  to  investigations  on  the  tem- 
perature of  the  ground  at  various  depths,  that  of  the  air  at  different 
heights,  and  also  on  the  temperature  of  plants  and  animals. 

880.  Becquerel's  electric  pyrometer. — This  apparatus  is  an  improved 
form  of  one  originally  devised  by  Pouillet.     It  consists  (fig.  743)  of  two 


Fig.  743. 


wires,  one  of  platinum  and  the  other  of  palladium,  both  two  metres  in 
length  and  a  square  millimetre  in  section.  They  are  not  soldered  at  the 
ends,  but  firmly  tied  for  a  distance  of  a  centimetre  with  fine  platinum 
wire.  The  palladium  wire  is  enclosed  in  a  thin  porcelain  tube :  the 
platinum  wire  is  on  the  outside,  and  the  whole  is  enclosed  in  a  larger 
porcelain  tube  P.  At  the  end  of  this  is  the  junction,  which  is  adjusted  in 
the  place  the  temperature  of  which  is  to  be  investigated.  At  the  other 
end  project  the  platinum  and  palladium  wires  ;«  and  n,  which  are 
soldered  to  two  copper  wires  that  lead  the  current  to  a  magnetometer 
G.     These  wires   at  the  junction  are  placed  in  a  glass  tube  immersed 

N  N 


8r8  Dynamical  Electricity.  [880- 

in  ice,  so  that,  being  both  at  the  same  temperature,  they  give  rise  to  no 
current. 

The  magnetometer,  which  was  devised  by  Weber,  is  nothing  more  than 
a  large  galvanometer.  It  consists  of  a  magnetised  bar  ab  placed  in  the 
centre  of  a  copper  frame  which  deadens  the  oscillations  (848)  and  rests 
on  a  stirrup  H,  which  in  turn  is  suspended  to  a  long  and  very  fine  platinum 
wire.  On  the  stirrup  is  fixed  a  mirror  M,  which  moves  with  the  magnet, 
and  gives  by  reflection  the  image  of  divisions  traced  on  a  horizontal  scale 
E  at  a  distance.  These  divisions  are  observed  by  a  telescope.  With  this 
view,  before  the  current  passes,  the  image  of  the  zero  of  the  scale  is 
made  to  coincide  with  the  micrometer  wire  of  the  telescope ;  then  the 
slightest  deflection  of  the  mirror  gives  the  image  of  another  division,  and 
therefore  the  angular  deflection  of  the  bar  (491).  This  angle  is  always 
small  and  should  not  exceed  3  or  4  degrees  :  this  is  effected  by  placing,  if 
necessary,  a  rheostat  or  any  resistance  coil,  in  the  circuit.  The  angular 
deflection  being  known,  the  intensity  of  the  current  and  the  temperature  of 
the  junction  are  deduced  from  pyrometric  tables.  These  are  constructed 
by  interpolation  when  the  strengths  are  known,  which  correspond  to  two 
temperatures  near  those  to  be  observed. 

The  indications  of  the  pyrometer  extend  to  the  fusing  point  of  the 
palladium. 

881.  Peltier's  cross. — Peltier  found  that  an  electric  current,  in  passing 
through  a  conductor,  in  some  cases  produces  heat,  in  others  cold.  He 
obtained  the  greatest  increase  of  temperature  when  the  negative  current 
passed  from  a  good  conductor  of  electricity  to  a  bad  one — for  example, 
from  copper  to  zinc;  and  the  least  increase  when  the  positive  current 
passed  in  this  direction.  But  when  a  bar  of  bismuth  and  a  bar  of 
antimony  were  soldered  together,  the  temperature  of  the  air  sank  at  the 
soldering  when  the  positive  current  passed  from  the  first  to  the  second 
metal,  and  rose  in  the  opposite  case.  This  experiment  may  be  made 
by  hermetically  fixing  in  two  tubulures  in  an  air  thermometer,  a  com- 
pound bar  consisting  of  bismuth  and  antimony  soldered  together,  in 
such  a  manner  that  the  ends  project  on  each  side.  The  projecting  parts 
are  provided  with  binding  screws,  so  as  to  allow  a  current  to  be  passed 
through.  When  the  positive  current  passes  from  the  antimony  to  the 
bismuth,  the  air  in  the  bulb  is  heated,  it  expands,  and  the  liquid  in  the 
stem  sinks ;  but  if  it  passes  in  the  opposite  direction  the  air  is  cooled,  it 
contracts,  and  the  liquid  rises  in  the  stem.  For  this  experiment  the 
current  must  have  a  certain  definite  strength,  which  is  found  by  experi- 
ment ;  it  is  best  regulated  by  a  rheostat  (882). 

These  experiments  form  an  interesting  illustration  of  the  principle,  that 
whenever  the  effects  of  heat  are  reversed,  heat  is  produced ;  and  whenever 
the  effects  ordinarily  produced  by  heat  are  otherwise  produced,  cold  is  the 
result. 


883] 


Determinatio7i  of  Electrical  Conductivity. 


819 


CHAPTER  IX. 

DETERMINATION  OF  ELECTRICAL  CONDUCTIVITY. 

882.  Rbeostat. — The  rheostat  is  an  instrument  by  which  the  resistance 
of  any  given  circuit  can  be  increased  or  diminished  without  opening  the 
circuit.  As  invented  by  Mr.  Wheatstone,  it  consists  of  two  parallel  cylin- 
ders, one,  A,  of  brass,  the  other,  B,  of  wood  (fig.  744).  In  the  latter  there 
is  a  spiral  groove,  which  terminates  at  ^  in  a  copper  ring,  to  which  is 
fixed  the  end  of  a  fine  brass  wire.  This  wire,  which  is  about  40  yards 
long,  is  partially  coiled  on  the  groove ;  it  passe?  to  the  cylinder  A,  and, 
after  a  great  number  of  turns  on  this  cylinder,  is  fixed  at  the  extremity  e. 
Two  binding  screws,  n  and  0,  con- 
nected with  the  battery,  communi- 
cate by  two  steel  plates  ;  one  with 
the  cylinder  A,  the  other  with  the 
ring  a. 

When  a  current  enters  at  0^  it 
simply  traverses  that  portion  of  the 
wire  rolled  on  the  cylinder  B,  where 
the  windings  are  insulated  by  the 
grooves ;  passing  thence  to  the 
cylinder  A,  which  is  of  metal,  and 
in  contact  with  the  wire,  the  current 
passes  directly  to  ;//,  and  thence  to 
n.  Hence,  if  the  length  of  the  cur- 
rent is  to  be  increased,  the  handle, 
d,  must  be  turned  from  right  to  left. 
If,  on  the  contrary,  it  is  to  be  dimin- 


Fig.  744. 


ished,  the  handle  is  to  be  fixed  on  the  axis,  c,  and  turning  then  from  left 
to  right,  the  wire  is  coiled  on  the  cylinder  A.  The  length  of  the  circuit  is 
indicated  in  feet  and  inches,  by  two  needles,  at  the  end  of  the  apparatus 
not  seen  in  the  figure,  which  are  moved  by  the  cylinders  A  and  B. 

883.  Betermination  of  the  resistance  of  a  conductor.  Reduced 
lengrtli. — If  in  the  circuit  of  a  constant  element  a  tangent  compass  be 
interposed,  a  certain  deflection  of  the  needle  will  be  produced.  If,  then, 
different  lengths  of  copper  wire  of  the  same  diameter  be  successively 
interposed,  corresponding  deflections  will  in  each  case  be  produced.  Let 
us  suppose,  that  in  a  particular  case  the  tangent  of  the  angle  of  deflection 
(775)  observed  with  the  element  and  tangent  compass  alone  was  i -88,  and 
that  when  5,40,  70,  and  100  yards  of  copper  wire  were  successively  placed 
in  the  circuit,  the  tangents  of  the  corresponding  deflections  were  0-849, 
0*172,  0*105,  and  0*074.  Now,  in  this  experiment,  the  total  resistance 
consists  of  two  components ;  the  resistance  offered  by  the  element  and 
the  tangent  compass,  and  the  resistance  offered  by  the  wire  in  each  case. 
The  former  resistance  may  be  supposed  to  be  equal  to  the  resistance  of 


820  Dynamical  Electricity.  -.         [883- 

X  yards  of  copper  wire  of  the  same  diameter  as  that  used,  and  then  we 
have  the  following  relations  : 

Length  of  wire.                                     Tangent  of  angle  of  deflection. 
X  yards i-88 

^+5  » 0'849 

;r  +  40  „  .         . 0-172 

;ir  +  7o  „ 0-105 

x-v  100  „ 0-074 

If  the  intensities  of  the  currents  are  inversely  as  the  resistances — that 
is,  as  the  lengths  of  the  circuits — the  proportion  must  prevail, 

X  :  ;ir+5=o-849  :  1-886  ; 

from  which  ;r  =  4-i  i.  Combining,  in  like  manner,  the  other  observations, 
we  get  a  series  of  numbers,  the  mean  of  which  is  4-08.  That  is,  the 
resistance  offered  by  the  element  and  galvanometer  is  equal  to  the  resist- 
ance of  4-08  yards  of  such  copper  wire,  and  this  is  said  to  be  the  reduced 
length  of  the  element  and  galvanometer  in  terms  of  the  copper  wire. 

It  is  of  great  scientific  and  practical  importance  to  have  a  U7iit  or 
standard  of  comparison  of  resistance,  and  numerous  such  have  been  pro- 
posed. Jacobi  proposed  the  resistance  of  a  metre  of  a  special  copper  wire 
a  millimetre  in  diameter.  Copper  is  however  ill  adapted  for  the  purpose, 
as  it  is  difficult  to  obtain  pure.  Matthiessen  has  proposed  an  alloy  of 
gold  and  silver,  containing  two  parts  of  gold  and  one  of  silver ;  its  con- 
ducting power  is  very  little  affected  by  impurities  in  the  metals,  by  an- 
nealing, or  by  moderate  changes  of  temperature. 

Siemens'  unit  is  a  metre  of  pure  mercury,  having  a  section  of  a  square 
millimetre.     It  is  0-9536  of  an  Ohmad  or  BA  unit  (884). 

The  Varley  U7iit,  which  is  used  in  telegraphic  work,  is  a  standard  mile 
of  a  special  copper  wire  i  of  an  inch  in  diameter.  Matthiessen  has 
proposed  instead  of  this  a  mile  of  pure  annealed  copper  wire  j\  in.  in 
diameter. 

884.  British  Association  unit  of  electrical  resistance. — The  great 
importance,  both  theoretically  and  practically,  of  having  some  uniform 
standard  for  the  comparison  of  electrical  resistance  has  for  years  past 
engaged  the  attention  of  a  committee  of  the  British  Association,  which 
includes  the  principal  electricians  in  this  country.  Their  labours  have 
resulted  in  the  adoption  of  a  standard  which  has  received  the  approval  of 
men  of  science  both  in  this  and  other  countries.  The  following  account 
of  this  unit,  which  it  is  proposed  to  call  the  Ohmad  or  BA  unit,  has 
been  kindly  furnished  by  the  secretary  to  the  Committee,  Mr.  Fleeming 
Jenkin. 

It  represents  a  convenient  multiple  of  the  so-called  absolute  unit  of 
electrical  resistance.  The  word  '  absolute,'  as  here  used,  does  not  imply 
accuracy  of  construction,  but  is  intended  to  express  that  the  measurement 
of  electrical  resistance  is  made  by  a  unit  which  bears  a  definite  relation 
to  the  fundamental  units  of  time,  mass,  and  space  only  ;  instead  of  being 
a  mere  comparison  with*  the  resistance  of  some  particular  piece  of  metal 


-884]     British  Association  Unit  of  Electrical  Resistance.    821 

arbitrarily  chosen  as  the  unit.  In  a  similar  sense  a  square  foot  and  a 
cubic  foot  may  be  called  absolute  units  of  surface  and  capacity,  an  acre 
and  a  gallon  arbitrary  units. 

It  seems  strange  at  first  that  the  unit  of  electrical  resistance  can  be 
measured  by  reference  to  time,  mass,  and  space  only,  without  reference  to 
the  specific  qualities  of  any  material  ;  but  our  chief  knowledge  of  electric 
phenomena  is  derived  from  an  observation  of  mechanical  effects,  and  we 
need,  therefore,  feel  no  surprise  at  learning  that  those  phenomena  can  be 
measured  in  purely  mechanical  units.  The  voltaic  current,  electromotive 
force,  and  resistance,  quantity,  and  capacity  can  all  be  so  measured  in 
more  than  one  way.  The  electromagnetic  measurement  of  current  is 
determined  by  the  following  considerations.  If /be  the  force  exerted 
by  a  current  of  strength  C,  and  length  L,  on  a  pole  of  a  magnet,  7n 
being  the  magnetic  strength  of  that  pole,  and  K  its  distance  from  the 

current,  it  is  found  by  experiment  that  /  varies  as       .^^,  so  that  C  = 

K  •; ,   where  k  is  some  constant.     Now  if  the  unit  current  be  that  which 

L,7n 

in  unit  length  of  circuit  exerts  unit  force  on  a  unit  pole  at  unit  distance, 

we  get  K  =  I,  and  the  equation  for  C  becomes 

-4§-    ■    -y   ■   •   ■    ^'^ 

and  C  may  be  measured  by  the  expression  J- — 
Again,  for  the  resistance  we  get 
W 

where  W  is  the  work  done  in  the  time  /  by  a  current  C  flowing  in  a 
circuit  of  the  resistance  r.  Now,  the  first  equation  allows  us  to  measure 
a  current  in  terms  of  a  force  /  two  lengths  K  and  L,  and  a  magnitude  ni, 
which  again  depends  on  measurements  of  force  and  length  only,  so  that 
we  here  have  a  current  measured  in  mechanical  units  in  virtue  of  a  ma- 
thematical relation  between  the  phenomena  produced  by  the  current  and 
the  mechanical  units.  It  follows  from  the  equation  that  the  unit  current 
will  be  that  of  which  each  unit  length  exerts  a  unit  force  on  a  unit  pole  at 
unit  distance.  The  second  equation,  like  the  first,  is  deduced  from  obser- 
vation. The  resistance  of  a  circuit  is  found  to  be  proportional  to  the  work 
done  by  a  current  in  that  circuit,  and  inversely  proportional  to  the  square 
of  the  current  and  to  the  time  during  which  it  acts  ;  any  two  circuits  for 

which  — 2>  ^s  equal  have  equal  resistances  ;  if  this  quantity  for  circuit  A 

is  double  what  it  is  for  circuit  B,  then  the  resistance  of  circuit  A  is  double 
that  of  circuit  B.     Therefore,  we  have  exactly  the  same  ground  for  saying 

that  —  measures  the  resistance  of  the  circuit  that  we  have  for  saying  c^ 
measures  the  contents  of  a  square  with  sides  equal  to  ^.     In  equation  2, 


822  Dynamical  Electricity.  [884- 

W,  the  work,  is  essentially  a  mechanical  measurement,  for,  though  gene- 
rally observed  in  the  form  of  heat,  it  is  by  Joule's  equivalent  referred  to 
the  mechanical  unit  of  energy  or  work. 

Moreover  from   Ohm's   law   C=  - (3) 

further  measures  electromotive  force  in  terms  of  C  and  r,  and  Faraday's 
discovery  expressed  by  equation 

where  Q  is  the  quantity  of  electricity  conveyed  by  the  current  C  in  the 
time  /,  shows  how  quantity  is  measured  in  the  same  mathematical 
series. 

Although  nothing  can  be  simpler  than  the  mathematical  conceptions 
here  involved,  the  practical  measurement  of  resistance,  or  any  other  ot 
the  above  magnitudes,  by  direct  reference  to  force,  work,  time,  etc.,  in- 
volves much  labour,  so  that  for  each  kind  of  measurement  it  is  necessary 
for  practical  use  to  construct  a  standard  which  affords  the  desired  mea- 
sure by  direct  and  simple  comparison  with  the  thing  measured.  Thus,  a 
Frenchman  to  measure  wine  does  not  work  out  the  cubic  contents  of  a 
bottle,  but  measures  the  number  of  litres  by  reference  to  a  standard  Htre, 
which  is  a  simple  decimal  submultiple  of  the  cubic  metre.  In  like 
manner  practical  measurements  of  resistance  are  made  by  comparison 
with  the  Ohm  or  BA  unit  prepared  to  represent  a  simple  decimal  multiple 
(ten  million  times)  the  absolute  electromagnetic  unit ;  the  metre,  the 
gramme,  and  the  second  of  time  were  taken  as  fundamental  units  by  the 
committee,  and  on  which  is  approximately  equal  to  10^  metre  seconds. 
Great  care  has  been  taken  in  the  determination  and  construction  of  the 
standard,  which  is  represented  by  several  coils  of  wires  of  various  metals 
and  alloys,  and  by  tubes  of  mercury  which  have  all  been  adjusted  to 
represent  one  and  the  same  standard  unit,  the  variety  of  materials  being 
intended  as  a  safeguard  against  possible  alteration  in  resistance  of  one  or 
more  of  the  coils  or  tubes.  Certified  copies  of  the  unit,  consisting  of  coils 
of  platinum-silver  wire,  are  issued  by  the  Committee.  It  is  intended  that 
similar  standards  for  the  measurement  of  currents,  electromotive  force, 
quantity,  and  capacity  will  also  be  issued. 

The  Ohmad  or  Ohm  is  1-0486  of  a  Siemens'  unit  (883)  ;  that  is,  it  is 
equal  to  the  resistance  of  a  prism  of  pure  mercury  i  square  millimetre 
in  section  and  i  -0486  metre  in  length  at  the  temperature  0°. 

885.  Equivalent  conductors. — The  resistance  of  a  conductor  depends, 
as  we  have  seen  ijT])^  on  its  length,  section,  and  conductivity.  Two 
conductors,  C  and  C,  whose  length,  conductivity,  and  section  are  re- 
spectively \  \',  K  k',  w  w',  would  offer  the  same  resistance,  and  might  be 
substituted  for  each  other  in  any  voltaic   circuit,   without  altering  its 

intensity,  provided  that  —  =  — -  ;   and  such  conductors  are  said  to  be 

equivalent  to  each  other.  An  example  will  best  illustrate  the  application 
of  this  principle. 

It  is  required  to  know  what  length  of  a  cylindrical  copper  wire  4  mm. 


-886]  Wheatstone's  Bridge,  '         823 

in  diameter  would  be  equivalent  to  12  yards  of  copper  wire  i  mm.  in 
diameter. 

Let  A  =  1 2  the  length  of  the  copper  wire  i  mm.  in  diameter,  and  A'  the 
length  of  the  other  wire ;  then  since  in  this  case  the  material  is  the  same, 

\       X' 

the  conductivity  is  the  same,  and  the  equation  becomes  -  =  — .       Now 

it)  to 

the  sections  of  the  wires  are  directly  as  the  squares  of  the  diameters,  and 

12      X' 
hence  we  have   -  =  — ^ ,  or  X'  =  12  x  16  =  192.    That  is  192  yards  of  copper 

wire  4  mm.  in  thickness  would  only  offer  the  same  resistance  as  12  yards 
of  copper  wire  i  mm.  in  thickness. 

How  thick  must  an  iron  wire  be  which  for  the  same  length  shall  offer 
the  same  resistance  as  a  copper  wire  2*5  mm.  in  diameter  ? 

Here  the  length  being  the  same,  the  expression  becomes  »fa;  =  KV. 
or  since  the  sections  are  as  the  squares  of  the  diameters,  K(P'  =  K'd'. 
The  conductivity  of  copper  is  unity,  and  that  of  iron  0*138.  Hence 
we  have  2-5^  =  ^/''^  x  0-138,  or  ^'^  =  6-25 -^-0-138  =  45-3  mm.,  or  d' =  6'y  mm. 
That  is,  any  length  of  a  copper  wire  2*5  mm.  in  diameter  might  be 
replaced  by  iron  wire  of  the  same  length,  provided  its  diameter  were 
67  mm. 

886.  Wheatstone's  bridge. — The  various  methods  of  determining 
the  electrical  conductivity  of  a  body  consist  essentially  in  ascertaining 
the  ratio  between  the  resistance  of  a  certain  length  of  the  conductor  in 
question,  having  a  given  section,  to  that  of  a  known  length  of  a  known 
section  of  some  substance  taken  as  standard.  The  most  convenient- 
method  of  ascertaining  experimentally  the  ratio  between  the  resistance 
of  two  conductors,  is  by  a  method  known  as  that  of  Wheatstone^s  bridge^ 
the  general  principle  of  which  may  be  thus  stated : — 

The  conductors,  which  may  be  denoted  by  AB  and  BC,  are  connected 
end  to  end  as  shown  in  fig.  745,  and  one  end  of  each  is  also  connected 


Fig.  745- 

with  a  battery,  say  the  end  A  of  AB  with  the  positive  pole,  and  the  end 
C  of  BC  with  the  negative  pole ;  the  ends  that  are  in  connection  with  the 
battery  are  likewise  connected  together  by  another  conductor  AB'C.  A 
current  will  thus  pass  from  A  to  C  by  each  of  the  two  paths  ABC  and 
AB'C,  and  there  will  be  a  gradual  fall  of  potential  in  passing  from  A  to  C 
along  either  path,  so  that  for  every  point  in  the  conductor  AB  and  BC, 
there  is  a  point  in  the  wire  AB'C  which  has  the  same  potential.  If  one 
end  of  a  galvanometer  wire  BGB'  be  connected  with  the*point  of  junction 
B,  the  point  of  AB'C  which  has  the  same  potential  as  the  point  B,  can  be 
found  by  applying  the  other  end  of  the  galvanometer  wire  to  it,  and  shifting 


824 


Dynamical  Electricity. 


[886- 


the  point  of  contact  towards  A  or  C  until  the  galvanometer  shews  no  de- 
flection. Let  B  be  the  point  so  found  ;  the  fact  that  when  it  is  connected 
with  B  by  the  bridge  BGB'  no  current  passes  from  one  to  the  other, 
proves  that  the  potential  at  B'  is  the  same  as  the  potential  at  B.  From 
this  it  follows,  that  if  r  and  r'  are  the  resistances  of  AB  and  BC  re- 
spectively, and  s  and  s^  the  resistances  of  AB'  and  B'C, 

r  \  r'  =  s  \  s\ 

If  the  conductor  AB'C  is  a  wire  of  uniform  material  and  diameter,  the 
ratio  of  the  resistances  s  and  s^  will  be  the  ratio  of  the  lengths  of  the  corre- 
sponding portions  of  wire,  and  can  therefore  be  at  once  readily  ascertained. 

To  prove  this,  let  MN,  NO,  MN'  and  N'O'  (fig.  746)  be  taken  in  the 


Q 

1 

> 

X           a' 

s 

r 

r'             ^~~"^^^ 

(y 


JM 


Fig.  746. 


same  straight  Hne,  proportional  respectively  to  the  several  resistances 
r,  r^y  Jj  s^ ;  and  let  MP  be  drawn  at  right  angles  to  O'MO  of  a  length 
proportional  to  the  difference  of  potential  between  the  points  A  and  C. 
Then  if  the  straight  lines  PO  and  PO'  be  drawn,  the  potential  at  N  (the 
points  of  junction  of  the  conductor  whose  resistances  r  and  r^  are  to  be 
compared,  the  point  corresponding  to  B  in  the  previous  figure)  will  be 
given  by  the  length  of  the  hne  NQ,  drawn  from  N  at  right  angles  to  NO; 
and  the  point  N'  (corresponding  to  B'  in  the  previous  figure)  where  the 
potential  is  the  same  as  at  N  will  be  found  by  drawing  QQ^  parallel  to 
00',  and  letting  fall  from  Q'  the  perpendicular  Q'N'  upon  O'M.  The 
geometry  of  the  figure  gives  obviously 


r  +  r' 


MP  J  +  J, 


MP' 


and  therefore  since  NQ  =  N^Qp 


887.  Determination  of  the  internal  resistance  of  an  element. — 

The  following  is  a  method  of  determining  the  internal  resistance  of  an 
element.  A  circuit  is  formed  consisting  of  one  element,  a  rheostat  and 
a  galvanometer,  and  the  strength  C  is  noted  on  the  galvanometer.  A 
second  element  is  then  joined  with  the  first,  so  as  to  form  one  of  double 
the  size,  atid  therefore  half  the  resistance,  and  then  by  adding  a  length,  /, 
of  the  rheostat  wire,  the  strength  is  brought  to  what  it  originally  was. 
Then  if  E  is  the  electromotive  force,  and  R  the  resistance  of  an  element, 
r,  the  resistance  of  the  galvanometer  and  the  other  parts  of  the  circuit  j 


-888] 


Electrical  Conductivity. 


825 


the  strength  C  in  the  one  case  is  C 


and  in  the  other : 


R  +  r  ^R  +  r  +  /' 

and  since  the  strength  in  both  cases  is  the  same,  R  =  2/. 

888.  Slectrical  conductivity. — We  can  regard  conductors  in  two 
aspects,  and  consider  them  as  endowed  with  a  greater  or  less  faciUty  for 
allowing  electricity  to  traverse  them,  a  property  which  is  termed  conduc- 
tivity ;  or  we  may  consider  conductors  interposed  in  a  circuit  as  offering 
an  obstacle  to  the  passage  of  electricity — that  is,  a  resistance  which  it  must 
overcome.  A  good  conductor  offers  a  feeble  resistance,  and  a  bad  con- 
ductor a  great  resistance.  Conductivity  and  resistance  are  the  inverse  of 
each  other. 

The  conductivity  of  metals  has  been  investigated  by  many  physicists 
by  methods  analogous  in  general  to  that  described  in  the  preceding  para- 
graph, and  very  different  results  have  been  obtained.  This  arises  mainly 
from  the  different  degrees  of  purity  of  the  specimens  investigated,  but 
their  molecular  condition  has  also  great  influence.  Matthiessen  finds 
the  difference  in  conductivity  between  hard-drawn  and  annealed  silver 
wire  to  amount  to  8-5,  for  copper  2*2,  and  for  gold  1-9  per  cent.  The 
following  are  results  of  a  series  of  careful  experiments  by  Matthiessen 
on  the  electrical  conductivity  of  metals  at  0°  C.  compared  with  silver  as 
a  standard  : — 


Silver 

.     loo-o 

Iron     . 

.       1 6-8 

Copper 

.       99-9 

Tin      .         .         . 

.       131 

Gold 

8o-o 

Lead    . 

•        8-3 

Aluminium 

56-0 

German  Silver     . 

77 

Sodium     . 

37*4 

Antimony    . 

4-6 

Zinc 

29-0 

Mercury 

1-6 

Cadmium. 

237 

Bismuth 

1-2 

Potassium 

20-8 

Graphite 

0-07 

Platinum  . 

i8-o 

The  conductivity  of  metals  is  diminished\y^  an  increase  in. temperature 
The  law  of  this  diminution  is  expressed  by  the  formula 

K-<  =  Kr„  (i  —at  +  bt^) ; 

where  r,  and  k„  are  the  conductivities  at  t  and  0°  respectively,  and  a  and  b 
are  constants,  which  are  probably  the  same  for  all  pure  metals.  For  ten 
metals  investigated  by  Matthiessen  he  found  that  the  conductivity  is 
expressed  by  the  formula 

K,  =K„  (i -0-0037647^  + 0-00000834/2). 

Liquids  are  infinitely  worse  conductors  than  metals.  The  conductivity 
of  a  solution  of  one  part  of  chloride  of  sodium  in  100  parts  of  water  is 
30050000  ^^^^  °f  copper.  In  general  acids  have  the  highest  and  solutions 
of  alkalies  and  neutral  salts  the  lowest  conductivity.  Yet,  in  solutions, 
the  conductivity  does  not  increase  in  direct  proportion  to  the  quantity  of 
salt  dissolved. 

The  following  is  a  list  of  the  conductivity  of  a  few  liquids  as  compared 
with  that  of  pure  silver : — 

N  N  3 


826  Dynamical  Electricity.  [888- 


Pure  silver 

100,000,000-00 

Nitrate  of  copper,  saturated  solution 

8-99 

Sulphate  of  copper            ditto 

5*42 

Chloride  of  sodium            ditto 

31-52 

Sulphate  of  zinc                 ditto 

577 

Sulphuric  acid,  I -lo  sp.  gr.     . 

99-07 

„       i-24sp.  gr.     . 

132-75 

„.         „       i-4osp.gr.     . 

90-75 

Nitric  acid,  commercial 

88-68 

Distilled  water 

o-oi 

Liquids  and  fused  conductors  increase  in  conductivity  by  an  increase 
of  temperature.     This  increase  is  expressed  by  the  formula 

ff  =  fo    (l   +^0> 

and  the  values  of  a  are  considerable.     Thus,  for  a  saturated  solution  of 
sulphate  of  copper,  it  is  0-0286. 

By  most  physicists  the  conductivity  of  liquids  has  been  regarded  as  a 
purely  electrolytic  conductivity,  that  is,  due  to  chemical  decomposition. 
Yet  Faraday,  in  stating  his  law  of  electrolytic  decomposition,  had  an- 
nounced that  it  was  subject  to  certain  restrictions  in  cases  in  which 
liquids  could  conduct  electricity  without  being  decomposed.  Foucault 
has  recently  shown  by  delicate  experiments,  that  liquids  have  a  peculiar 
conductivity,  «^>^jj/Vrt/ conductivity  analogous  to  that  of  metals.  This 
is,  however,  much  less  than  the  electrolytic  conductivity,  but  may  have 
a  distinct  influence  on  the  chemical  effects  of  currents  and  on  Faraday's 
law. 

An  influence  of  light  upon  electrical  conductivity  has  been  ascertained 
to  exist  in  the  case  of  selenium.  A  thin  strip  of  this  metalloid,  about 
38  mm.  in  length  by  13  in  breadth,  was  provided  at  the  ends  with  con- 
ducting wires  and  placed  in  a  box  with  a  draw  lid.  The  selenium,  having 
been  carefully  balanced  in  a  Wheatstone's  bridge,  was  exposed  to 
diffused  light  by  withdrawing  the  lid,  when  the  resistance  at  once  fell  in 
the  ratio  of  1 1  to  9.  On  exposure  to  the  various  spectral  colours,  after 
having  been  in  the  dark,  it  was  found  to  be  most  affected  by  the  red ; 
but  the  maximum  action  was  just  outside  the  red,  where  the  resistance 
fell  in  the  ratio  of  3  to  2.  Momentary  exposure  to  the  light  of  a  gas  lamp . 
or  even  to  that  of  a  candle,  causes  a  diminution  of  resistance.  Exposure 
to  full  sunlight  diminished  the  resistance  to  one  half. 

The  effect  produced  on  exposure  to  light  is  immediate,  while  recurrence 
to  the  normal  state  takes  place  more  slowly. 

A  vessel  of  hot  water  placed  near  the  strip  produced  no  effect,  and 
hence  the  phenomenon  cannot  be  due  to  heat,  but  there  appear  to  be 
certain  rays  which  have  the  power  of  producing  a  molecular  change  in 
the  selenium  by  which  its  conductivity  is  increased. 

889.  Betermination  of  electromotive  force.  IXHieatstone's  metbod. 
— In  the  circuit  of  the  element  whose  electromotive  force  is  to  be  deter- 
mined, a  tangent  compass  and  a  rheostat  are  inserted,  the  latter  being  so 


from  which  we  have 


-890]       Siemens'  Electrical  Resistance  Thermometer.  827 

arranged  that  the  strength  C  of  the  current  is  a  definite  amount ;  for 
example,  the  galvanometer  indicates  45°.  By  increasing  the  amount  of  the 
rheostat  wire  by  the  length  /,  a  diminished  strength,  c  (for  instance,  40°)  is 
obtained. 

A  second  standard  element  is  then  substituted  for  that  under  trial, 
and  by  arranging  the  rheostat,  the  strength  of  the  current  is  first  made 
equal  to  C,  and  then,  by  the  addition  of  /  lengths  of  the  rheostat,  is  made 
=  c. 

Then  if  E  and  E^  are  the  two  electromotive  forces,  R  and  R^,  their  re- 
sistances when  they  have  the  intensity  I,  and  /  and  /^  the  lengths  added, 
we  have 

Trial  element.  Standard  element. 

^"R  ^"r; 

r^^^  C-       ^1       ■ 

R  +  /  Ri  +  ^x' 

Hence  the  electromotive  forces  of  the  elements  compared  are  directly  as 
the  lengths  of  the  wire  interposed. 

Another  method  is  described  by  Wiedemann.  The  two  elements  are 
connected  in  the  same  circuit  with  a  tangent  galvanometer,  or  other  appa- 
ratus for  measuring  strength,  first  in  such  a  manner  that  their  currents  go 
in  the  same  direction,  and,  secondly,  that  they  are  opposed.  Then  if  the 
electromotive  forces  are  E  and  E',  their  resistances  R  and  R'',  the  other 
resistances  in  the  circuits  r,  while  C,  is  the  intensity  when  the  elements 
are  in  the  same  direction,  and  Cj  the  intensity  when  they  go  in  opposite 
directions,  then, 

r  _    E  +  E' 
'"R  +  R'  +  r' 

E  — E' 
and  Cd  =  T5 — ^7 — ) 

R  +  R'  +  r 

whence  ^,^E(C.~Ca)^  • 

890.  Siemens'  electrical  resistance  tbermometer. — Supposing  in  a 
Wheatstone's  bridge  arrangement,  after  the  ratio  r  \r^  =  s  \  s^  has  been 
established,  the  temperature  of  one  of  the  coils,  r,  for  instance,  be  in- 
creased, the  above  ratio  will  no  longer  prevail,  for  the  resistance  of  r. 
will  have  been  altered  by  the  temperature,  and  the  ratio  of  s  and  Jj,  must 
be  altered  so  as  to  produce  equivalence.  On  this  idea  Siemens  has  based 
a  mode  of  observing  the  temperature  of  places  which  are  difficult  of 
direct  access.  He  places  a  coil  of  known  resistance  in  the  particular 
locality  whose  temperature  is  to  be  observed;  it  is  connected  by  means 
of  long  good  conducting  wires  with  the  place  of  observation,  where  it 
forms  part  of  a  Wheatstone's  bridge  arrangement.     The  resistance  of 


828  Dynamical  Electricity.  [890- 

the  coil  is  known  in  terms  of  the  rheostat,  and  by  preliminary  trials  it 
has  been  ascertained  how  much  additional  wire  must  be  introduced  to 
balance  a  given  increase  in  the  temperature  of  the  resistance  coil.  This 
being  knowft,  and  the  apparatus  adjusted  at  the  ordinary  temperature, 
when  the  temperature  .of  the  resistance  coil  varies,  this  variation  in 
either  direction  is  at  once  known  by  observing  the  quantity  which  must 
be  brought  in  or  out  of  the  rheostat  to  produce  equivalence. 

This  apparatus  has  been  of  essential  service  in  watching  the  tempera- 
ture of  large  coils  of  telegraph  wire,  which,  stowed  away  in  the  hold  ot 
vessels,  are  very  liable  to  become  heated.  It  might  also  be  used  for  the 
continuous  and  convenient  observation  of  underground  and  submarine 
temperatures.  If  a  coil  of  platinum  wire  were  substituted  for  the  copper, 
the  apparatus  could  be  used  for  watching  the  temperature  of  the  interior 
of  a  furnace. 

891.  Derived  currents. — In  fig.  747  the  current  from  a  Bunsen's 
element  traverses  the  wire  rqpnm  :  let  us  take  the  case  in  which  any  two 


Fig.  747. 

points  of  this  circuit,  71  and  q,  are  joined  by  a  second  wire,  nxq.  The 
current  will  then  divide  at  the  point  q  into  two  others,  one  of  which 
goes  in  the  direction  qpnm,  while  another  takes  the  direction  qxjtm.  The 
two  points  q  and  n  from  which  the  second  conductor  starts  and  ends  are 
called  the  points  of  derivation,  the  wire  qpn  and  the  wire  qxn  are  derived 
wir-es.  The  currents  which  traverse  these  wires  are  called  the  derived 
or  partial  currerits ;  the  current  which  traversed  the  circuit  rqpnm  before 
it  branches  is  the  primitive  current ;  and  the  name  principal  curre7it  is 
given  to  the  whole  of  the  current  which  traverses  the  circuit  when  the 
derived  wire  has  been  added.  The  principal  current  is  stronger  than  the 
primitive  one,  because  the  interposition  of  the  wire  qxn  lessens  the  total 
resistance  of  the  circuit. 

If  the  two  derived  wires  are  of  the  same  length  and  the  same  section, 
their  action  would  be  the  same  as  if  they  were  juxtaposed,  and  they  might 
be  replaced  by  a  single  wire  of  the  same  length  but  of  twice  the  section, 
and  therefore  with  half  the  resistance.  Hence  the  current  would  divide 
into  two  equal  parts  along  the  two  conductors. 

When  the  two  wires  are  of  the  same  length  but  of  different  sections, 
the  current  would  divide  unequally,  and  the  quantity  which  traversed 
each  wire  would  be  proportional  to  its  section,  just  as  when  a  river 
divides  into  two  branches,  the  quantity  of  water  which  passes  in  each 
branch   is   proportional  to   its   dimensions.      Hence    the   resistance   of 


-891]  Derived  Currents.  829 

the  two  conductors  joined  would  be  the  same  as  that  of  a  single  wire  of 
the  same  length,  the  section  of  which  would  be  the  sum  of  the  two  sections. 

If  the  two  conductors  qpn  and  qxn  are  different,  both  in  kind,  length, 
and  section,  they  could  always  be  replaced  by  two  wires  of  the  same  kind 
and  length,  with  such  sections  that  their  resistances  would  be  equal  to  the 
two  conductors  ;  in  short,  they  might  be  replaced  by  equivalent  conductors. 
These  two  wires  would  produce  in  the  circuit  the  same  effect  as  a  single 
wire,  which  had  this  common  length,  and  whose  section  would  be  the  sum 
of  the  sections  thus  calculated.  The  current  divides  at  the  junction  into 
two  parts  proportional  to  these  sections,  or  inversely  as  the  resistances  of 
the  two  wires. 

Suppose,  for  instance,  qp7i  is  an  iron  wire  5  metres  in  length  and  3  mm 
square  in  section,  and  qxn  a.  copper  wire. 

The  first  might  be  replaced  by  a  copper  wire  a  metre  in  length,  whose 
section  would  be  f  x  i  (taking  the  conductivity  of  copper  at  7  times  that  of 
iron)  or  /g  square  mm.  The  second  wire  might  be  replaced  by  a  copper 
wire  a  metre  in  length  with  a  section  of  |  square  mm.  These  two  wires 
would  present  the  same  resistance  as  a  copper  wire  a  metre  in  length,  and 
with  a  section  of  3^  +  |  =  3Y5  square  millimetres. 

The  principal  current  would  divide  along  the  wires  in  two  portions, 
which  would  be  as  /g :  |. 

The  most  important  laws  of  divided  circuits  are  as  follows  : — 

i.  TAe  sum  of  the  strengths  in  the  divided  parts  of  a  circuit  is  equal 
to  the  strength  of  the  principal  current. 

ii.  The  strengths  of  the  currents  in  the  divided  parts  of  a  circuit  are 
inversely  as  their  resistances  j  or,  what  is  the  same,  the  division  of  a  current 
into  partial  currents  which  lie  between  two  points,  is  directly  as  the  respec- 
tive conductivities  of  these  branches. 

And  as  problems  on  divided  circuits  frequently  occur  in  telegraphy^ 
the  following  formulce,  which  include  these  laws,  are  given  for  a  simple 
case. 

If  C  be  the  strength  of  the  current  in  the  undivided  part  of  the  circuit 
rqpnm,  and  if  c  is  the  strength  in  one  branch  (say -in  the  above  figure  qpn) 
and  c'  in  qx7i ;  if  R,  r,  and  r^  are  the  corresponding  resistances,  the  electro- 
motive force  being  E,  then 

C  =     E(^  +  ^i) 
Rr  +  Rr^  +  rr^ 

Rr  +  Rr^  +  rrl 


Rr  +  R^i  +  rr^ 

The  resistance  R^  of  the  whole  circuit  through  which  the  current  cir- 
culates is 

R^  =  R  +  J*^^„, 

and  therefore  the  total  resistance  of  the  derived  cnrxtnts  qpn  and  qxn  is 

rr. 


830  Dynamical  Electricity,  [892- 


CHAPTER  X. 

ANIMAL  ELECTRICITY. 

892.  Muscular  currents. — The  existence  of  electrical  currents  in 
living  muscle  was  first  indicated  by  Galvani,  but  his  researches  fell  into 
oblivion  after  the  discovery  of  the  Voltaic  pile,  which  was  supposed  to 
explain  all  the  phenomena.  Since  then,  NobiH,  Matteucci,  and  others, 
especially,  in  late  years,  Du  Bois  Reymond,  have  shown  that  electric 
currents  do  exist  in  living  muscles  and  nerves,  and  have  investigated 
their  laws. 

For  investigating  these  currents  it  is  necessary  to  have  a  delicate  gal- 
vanometer, and  also  electrodes  which  will  not  become  polarised  or  give 
a  current  of  their  own,  and  which  will  not  in  any  way  alter  the  muscle 
when  placed  in  contact  with  it ;  the  electrodes  which  satisfy  these  con- 
ditions best  are  those  of  Du  Bois  Reymond,  as  modified  by  Bonders. 
Each  consists  of  a  glass  tube,  one  end  of  which  is  narrowed  and  stopped 
by  a  plug  of  paste  made  by  moistening  china-clay  with  a  half  per  cent, 
solution  of  common  salt ;  the  tube  is  then  partially  filled  with  a  saturated 
solution  of  sulphate  of  zinc,  and  into  this  dips  the  end  of  a  piece  of 
thoroughly  amalgamated  zinc  wire,  the  other  end  of  which  is  connected 
by  a  copper  wire  with  the  galvanometer;  the  moistened  china-clay  is 
a  conducting  medium  which  is  perfectly  neutral  to  the  muscle,  and  amal- 
gamated zinc  in  solution  of  sulphate  of  zinc  does  not  become  polarised. 

893.  Currents  of  muscle  at  rest. — In  describing  these  experiments 
the  surface  of  the  muscle  is  called  the  natural  longitudinal  section ;  the 
tendon,  the  natural  transverse  section;  and  the  surfaces  obtained  by 
cutting  the  muscle  longitudinally  or  transversely  are  respectively  the 
artificial  longitudinal  and  artificial  transverse  sections. 

If  a  living  irritable  muscle  be  removed  from  a  recently  killed  frog,  and 
the  clay  of  one  electrode  be  placed  in  contact  with  its  surface,  and  of 
the  other  with  its  tendon,  the  galvanometer  will  indicate  a  current  from 
the  former  to  the  latter  ;  showing,  therefore,  that  the  surface  of  the 
muscle  is  positive  with  respect  to  the  tendon.  By  varying  the  position 
of  the  electrodes,  and  making  various  artificial  sections,  it  is  found — 

I.  That  any  longitudinal  section  is  positive  to  any  transverse. 
■  2.  That  any  point  of  a  longitudinal  section  nearer  the  middle  of  the 
muscle  is  positive  to  any  other  point  of  the  same  section  farther  from  the 
centre. 

3.  In  any  artificial  transverse  section  any  point  nearer  the  periphery 
is  positive  to  one  nearer  the  centre. 

4.  The  current  obtained  between  two  points  in  a  longitudinal  or  in  a 
transverse  section  is  always  much  more  feeble  than  that  obtained  between 
two  different  sections. 

5.  No  current  is  obtained  if  two  points  of  the  same  section  equidistant 
from  its  centre  be  taken. 


-893] 


Animal  Electricity. 


831 


6.  To  obtain  these  currents  it  is  not  necessary  to  employ  a  whole 
muscle,  or  a  considerable  part  of  one,  but  the  smallest  fragment  that  can 
"be  experimented  with  is  sufficient. 

7.  If  a  muscle  be  cut  straight  across,  the  most  powerful  current  is  that 
from  the  centre  of  the  natural  longitudinal  section  to  the  centre  of  the 
artificial  transverse ;    but  if  the  muscle  be  cut  across  obhquely,  as  in 


Fig.  748. 

fig.  748,  the  most  positive  point  is  moved  from  c  towards  b,  and  the  most 
negative  from  d  towards  a  {'  Currents  of  inclination^). 

To  explain  the  existence  and  relations  of  these  muscular  currents,  it 
may  be  supposed  that  each  muscle  is  made  up  of  regularly  disposed 
electromotor  elements,  which  may  be  regarded  as  cylinders  whose  axis  is 
parallel  to  that  of  the  muscle,  and  whose  sides  are  charged  with  positive 
and  their  ends  with  negative  electricity ;  and,  further,  that  all  are  sus- 
pended and  enveloped  in  a  conducting  medium.  In  such  a  case  (fig.  749) 
it  is  clear  that  throughout  most  of  the  muscle  the  positive  electricities  of 
the  opposed  surfaces  would  neutralise  one  another,  as  would  also  the 
negative  charges  of  the  ends  of  the  cylinders ;  so  that,  so  long  as  the 
muscle  was  intact,  only  the  charges  at  its  sides  and  ends  would  be  left 
free  to  manifest  themselves  by  the  production  of  electromotive  pheno- 
mena; the  whole  muscle  being  enveloped  in  a  conducting  stratum,  a 
current  would  constantly  be  passing  from  the  longitudinal  to  the  trans- 
verse section,  and,  a  part  of  this  being  led  off  by  the  wire  circuit,  would 
manifest  itself  in  the  galvanometer. 

This  theory  also  explains  the  currents  between  two  different  points  on 
the  same  section  ;  the  positive  charge  at  b,  for  instance  (fig.  749),  would 


^^H  ^^H  ^^H  ^^H  ^^B 

+                           +                          +  +                            + 

^+  ^+  ^+  ^+  ^+ 

■+                     4-                   -*-  -4-                     + 

^^H  ^^H  ^^B  ^^H  ^^H 

+                           +                          +  +                           + 

^^H  ^^H  ^^H  ^^M  ^^M 

+                          +                         +  +                           -f- 

^^^  ^^'  ^^^  ^^^  ^^^ 

+                           +                           +  +                           + 
tt h 


Fig.  749. 

have  more  resistance  to  overcome  in  getting  to  the  transverse  section  than 
that  at  d,  therefore  it  has  a  higher  tension ;  and  if  b  and  d  are  connected 
by  the  electrodes,  b  will  be  found  positive  to  d,  and  a  current  will  pass 
from  the  former  to  the  latter. 


832  Dynamical  Electricity.  [893- 

What  are  called  currents  of  inclination  are  also  explicable  on  the  above 
hypothesis,  for  the  obhque  section  can  be  represented  as  a  number  of 
elements  arranged  as  in  fig.  750,  so  that  both  the  longitudinal  surfaces 
and  the  ends  of  the  cylinders  are  laid  bare,  and  it  can  thus  be  regarded 
as  a  sort  of  obhque  pile  whose  positive  pole  is  towards  b  and  its  negative 


Fig.  750. 

at  a,  and  whose  current  adds  itself  algebraically  to  the  ordinary  current 
and  displaces  its  poles  as  above  mentioned. 

.  A  perfectly  fresh  muscle,  very  carefully  removed,  with  the  least  possible 
contact  with  foreign  matters,  sometimes  gives  almost  no  current  loetween 
its  different  natural  sections,  and  the  current  always  becomes  more 
marked  after  the  muscle  has  been  exposed  a  short  time ;  nevertheless, 
the  phenomena  are  vital,  for  the  currents  disappear  completely  with  the 
life  of  the  muscle,  sometimes  becoming  first  irregular  or  even  reversed  in 
direction. 

894.  Rheoscoplc  frog*.  Contraction  \irlthout  metals. — The  exist- 
ence of  the  muscular  currents  can  be  manifested  without  a  galvanometer, 
by  using  another  muscle  as  a  galvanoscope.  Thus  if  the  nerve  of  one 
living  muscle  be  dropped  suddenly  on  another  living  muscle,  so  as  to 
come  in  contact  with  its  longitudinal  and  transverse  sections,  a  contraction 
of  the  first  muscle  will  occur,  due  to  the  stimulation  of  its  nerve  by  the 
passage  through  it  of  the  electric  current  derived  from  the  surface  of  the 
second. 

895.  Currents  in  active  muscle. — When  a  muscle  is-  made  to  con- 
tract there  occurs  a  sudden  diminution  of  its  natural  electric  current,  as  in- 
dicated by  the  galvanometer.  This  is  so  instantaneous  that,  in  the  case 
of  a  single  muscular  contraction  it  does  not  overcome  the  inertia  of  the 
needle  of  the  galvanometer ;  but  if  the  contractions  be  made  to  succeed 
one  another  very  rapidly — that  is,  if  the  muscle  be  tetanised  (778) — then 
the  needle  swings  steadily  back  towards  zero  from  the  position  in  which 
the  current  of  the  resting  muscle  had  kept  it,  often  gaining  such  momen- 
tum in  the  swing  as  to  pass  beyond  the  zero  point,  but  soon  reverting  to 
some  point  between  zero  and  its  original  position. 

The  negative  variation  in  the  case  of  a  simple  muscular  contraction 
can,  however,  be  made  manifest  by  using  another  muscle  as  a  rheoscope; 
if  the  nerve  of  this  second  muscle  be  laid  over  the  first  muscle  in  such  a 
position  that  the  muscular  current  passes  through  it,  and  the  first  muscle 
be  then  made  to  contract,  the  sudden  alteration  in  the  intensity  of  its 
current  stimulates  the  nerve  laid  on  it  (jjZ),  and  so  causes  a  contraction 
of  the  muscle  to  which  the  latter  belongs. 


-897]  Electrical  Fish.  833 

The  same  phenomena  can  be  demonstrated  in  the  muscles  of  warm- 
blooded animals;  but  with  less  ease,  on  account  of  the  difficulty  of  keep- 
ing them  alive  after  they  are  laid  bare  or  removed  from  the  body. 
Experiments  made  by  placing  electrodes  outside  the  skin,  or  passing 
them  through  it,  are  inexact  and  unsatisfactory. 

896.  Electric  currents  In  nerve. — From  nerves  the  same  electro- 
motor indications  can  be  obtained  as  from  muscles  ;  at  least,  as  far  as 
their  smaller  size  will  permit;  the  currents  are  more  feeble  than  the 
muscular  ones,  but  can  be  demonstrated  by  the  galvanometer  in  a  similar 
way.  Negative  variation  has  been  proved  to  occur  in  active  nerve  as  in 
active  muscle.  The  effect  of  a  constant  current  passed  through  one  part 
of  a  nerve  on  the  amount  of  the  normal  nerve  current,  measured  at 
another  part,  has  already  been  described  (Chap.  III.,  Electrotonus). 

897.  Slectrical  flsli. — Electrical  fish  are  those  fish  which  have  the 
remarkable  property  of  giving,  when  touched,  shocks  like  those  of  the. 
Leyden  jar.  Of  these  fish  there  are  several  species,  the  best  known  of 
which  are  the  torpedo,  the  gymnotus,  and  the  silurus.  The  torpedo, 
which  is  very  common  in  the  Mediterranean,  has  been  carefully  studied 
by  MM.  Becquerel  and  Breschet  in  F>ance,  and  by  M.  Matteucci  in 
Italy.  The  gymnotus  has  been  investigated  by  Humboldt  and  Bonpland 
in  South  America,  and  in  England  by  Faraday,  who  had  the  opportunity 
of  examining  live  specimens. 

The  shock  which  they  give  serves  both  as  a  means  of  offence  and  of 
defence.  It  is  purely  voluntary,  and  becomes  gradually  weaker  as  it  is 
repeated  and  as  these  animals  lose  their  vitahty,  for  the  electrical  action 
soon  exhausts  them  materially. 

The  shock  is  very  violent.  According  to  Faraday  the  shock  which 
the  gymnotus  gives  is  equal  to  that  of  a  battery  of  15  jars  exposing  a 
coating  of  25  square  feet,  which  explains  how  it  is  that  horses  frequently 
give  way  under  the  repeated  attacks  of  the  gymnotus. 

Numerous  experiments  show  that  these  shocks  are  due  to  ordinary 
electricity.  For  if,  touching  with  one  hand  the  back  of  the  animal,  the 
belly  is  touched  with  the  other,  or  with  a  metal  rod,  a  violent  shock  is 
felt  in  the  wrists  and  arms :  while  no  shock  is  felt  if  the  animal  is  touched 
with  an  insulating  body.  Further,  when  the  back  is  connected  with  one 
end  of  a  galvanometer  wire  and  the  belly  with  the  other,  at  each  discharge 
the  needle  is  deflected,  but  immediately  returns  to  zero,  which  shows 
that  there  is  an  instantaneous  current ;  and,  moreover,  the  direction  of 
the  needle  shows  that  the  current  goes  from  the  back  to  the  belly  of  the 
fish.  Lastly,  if  the  current  of  a  torpedo  be  passed  through  a  helix,  in  the 
centre  of  which  is  a  small  steel  bar,  the  latter  is  magnetised  by  the 
passage  of  a  discharge. 

By  means  of  the  galvanometer,  Matteucci  has  established  the  follow- 
ing facts : 

I.  When  a  torpedo  is  lively,  it  can  give  a  shock  in  any  part  of  its 
body ;  but  as  its  vitality  diminishes,  the  parts  at  which  it  can  give  a  shock 
are  nearer  the  organ  which  is  the  seat  of  the  development  of  electricity. 


834  Dyjiamical  Electricity.  [897- 

2.  Any  point  of  the  back  is  always  positive  as  compared  with  the  cor- 
responding point  of  the  belly. 

3.  Of  any  two  points  at  different  distances  from  the  electrical  organ, 
the  nearest  always  plays  the  part  of  positive  pole,  and  the  furthest  that 
of  negative  pole.     With  the  belly,  the  reverse  is  the  case. 

The  organ  where  the  electricity  is  produced  in  the  torpedo  is  double, 
and  formed  of  two  parts  symmetrically  situated  on  the  two  sides  of  the 
head,  and  attached  to  the  skull  bone  by  the  internal  face.  Each  part 
consists  of  nearly  parallel  lamellae  of  connective  tissue  inclosing  small 
chambers,  in  which  lie  the  so-called  electrical  ptates^  each  of  which  has 
a  final  nerve  ramification  distributed  on  one  of  its  faces.  This  face, 
on  which  the  nerve  ends,  is  turned  the  same  way  in  all  the  plates,  and 
when  the  discharge  takes  place  is  always  negative  to  the  other. 

Matteucci  investigated  the  influence  of  the  brain  on  the  discharge. 
For  this  purpose  he  laid  bare  the  brain  of  a  living  torpedo,  and  found  that 
the  first  three  lobes  could  be  irritated  without  the  discharge  being  produced, 
and  that  when  they  were  removed  the  animal  still  possessed  the  faculty 
of  giving  a  shock.  The  fourth  lobe,  on  the  contrary,  could  not  be  irritated 
without  an  immediate  production  of  the  discharge ;  but  if  it  was  removed, 
all  disengagement  of  electricity  disappeared,  even  if  the  other  lobes  re- 
mained untouched.  Hence  it  would  appear  that  the  primary  source  of 
the  electricity  elaborated  is  the  fourth  lobe,  whence  it  is  transmitted  by 
means  of  the  nerves  to  the  two  organs  described  above,  which  act  as 
multipliers.  In  the  silurus  the  head  appears  also  to  be  the  seat  of  the 
electricity ;  but  in  the  gymnotus  it  is  found  in  the  tail. 

898.  Application  of  electricity  to  medicine. — The  first  applications 
of  electricity  to  medicine  date  from  the  discovery  of  the  Leyden  jar. 
Nollet  and  Boze  appear  to  have  been  the  first  who  thought  of  the  applica- 
tion, and  soon  the  spark  and  electrical  frictions  became  a  universal 
panacea;  but  it  must  be  admitted  that  subsequent  trials  did  not  come  up 
to  the  hopes  of  the  experimentalists. 

After  the  discovery  of  dynamic  electricity  Galvani  proposed  its  appli- 
cation to  medicine :  since  which  time  many  physicists  and  physiologists 
have  been  engaged  upon  this  subject,  and  yet  there  is  still  much  uncer- 
tainty as  to  the  real  effects  of  electricity,  the  cases  in  which  it  is  to  be 
applied,  and  the  best  mode  of  applying  it.  Practical  men  prefer  the  use 
of  currents  to  that  of  statical  electricity,  and,  except  in  a  few  cases,  dis- 
continuous to  continuous  currents.  There  is,  finally,  a  choice  between 
the  currents  of  the  battery  and  those  of  induction  currents  ;  further,  the 
effects  of  the  latter  differ,  according  as  induction  currents  of  the  first  or 
second  order  are  used. 

In  fact,  since  induction  currents,  although  very  intense,  have  a  very 
feeble  chemical  action,  it  follows  that  when  they  traverse  the  organs,  they 
do  not  produce  the  chemical  effects  of  the  current  of  the  battery,  and 
hence  do  not  tend  to  produce  the  same  disorganisation.  Further,  in 
electrifying  the  muscles  of  the  face,  induction  currents  are  to  be  pre- 
ferred, for  Dr.  Duchenne  has  found  that  these  currents  only  act  feebly  on 
the  retina,  while  the  currents  of  the  battery  act  energetically  on  this  organ. 


-898]  Applicatio7i  of  Electricity  to  Medicine.  835 

and  may  affect  it  dangerously,  as  serious  accidents  have  shown.  There 
is  a  difference  in  the  action  of  induced  currents  of  different  orders  : 
for  while  the  primary  induced  current  causes  lively  muscular  actions, 
but  has  little  action  on  the  cutaneous  sensibility,  the  secondary  induced 
current,  on  the  contrary,  increases  the  cutaneous  sensibility  to  such  a 
point,  that  its  use  ought  to  be  proscribed  to  persons  whose  skin  is  very 
irritable. 

Hence  electrical  currents  should  not  be  applied  in  therapeutics  without 
a  thorough  knowledge  of  their  various  properties.  They  ought  to  be 
used  with  great  prudence,  for  their  continued  action  may  produce  serious 
accidents.  Matteucci,  in  his  lectures  on  the  physical  phenomena  of  living 
bodies,  expresses  himself  as  follows  :  *  In  commencing,  a  feeble  current 
must  always  be  used.  This  precaution  now  seems  to  me  the  more  im- 
portant, as  I  did  not  think  it  so  before  seeing  a  paralytic  person  seized 
with  almost  tetanic  convulsions  under  the  action  of  a  current  formed  of 
a  single  element.  Take  care  not  to  continue  the  application  too  long, 
especially  if  the  current  is  energetic.  Rather  apply  a  frequently-inter- 
rupted current  than  a  continuous  one,  especially  if  it  be  strong  ;  but  after 
20  or  30  shocks  at  most,  let  the  patient  take  a  few  moments'  rest.' 

Of  late  years,  however,  feeble  continuous  currents  have  come  more 
into  use.  They  are  frequently  of  great  service  when  applied  skilfully 
so  as  to  throw  the  nerves  of  the  diseased  part  into  a  state  of  cathelectro- 
tonus  or  analectrotonus,  according  to  the  end  which  is  wished  for  in  any 
given  case. 


836  Meteorology.  [899- 


ELEMENTARY   OUTLINES 
i  OF 

METEOROLOGY  AND  CLIMATOLOGY. 


METEOROLOGY. 


899.  Meteorologry. — The  phenomena  which  are  produced  in  the  at- 
mosphere are  called  fneteors ;  and  meteorology  is  that  part  of  physics 
which  is  concerned  with  the  study  of  these  phenomena. 

A  distinction  is  made  between  aerial  meteors,  such  as  winds,  and 
hurricanes,  and  whirlwinds  ;  aqueous  meteors,  comprising  fogs,  clouds, 
rain,  dew,  snow,  and  hail  ;  and  luminous  meteors,  as  lightning,  the  rain- 
bow, the  aurora  borealis. 

Aerial  Meteors. 

900.  Birection  and  velocity  of  winds. —  Winds  are  currents  moving 
in  the  atmosphere  with  variable  directions  and  velocities.  There  are 
eight  principal  directions  in  which  they  blow — north,  north-east,  east, 
south-east,  south,  south-west,  west,  and  north-west.  Mariners  further 
divide  each  of  the  distances  between  these  eight  directions  into  four  others, 
making  in  all  32  directions,  which  are  csW&d.  points  or  rhumbs.  A  figure 
of  these  '32  rhumbs  on  a  circle,  in  the  form  of  a  star,  is  known  as  the 
mariner's  card. 

The  direction  of  the  wind  is  determined  by  means  of  vanes,  and  its 
velocity  by  means  of  the  anetnometer.  There  are  several  forms  of  this 
instrument  ;  the  most  usual  consists  of  a  small  vane  with  fans,  which  the 
wind  turns  ;  the  velocity  is  deduced  from  the  number  of  turns  made  in  a 
given  time,  which  is  measured  by  means  of  an  endless  screw  and  wheel- 
work.  In  our  climate  the  mean  velocity  is  from  18  to  20  feet  in  a  second. 
With  a  velocity  of  6  or  7  feet,  the  wind  is  moderate  ;  with  30  or  35  feet, 
it  is  fresh  ;  with  60  or  70  feet,  it  is  strong ;  with  a  velocity  of  85  to  90 
feet,  it  is  a  tempest ;  and,  from  90  to  120,  it  is  a  hurricane. 

We  have  but  few  experimental  results  as  to  the  laws  of  the  intensity  of 
the  force  which  wind  exerts  on  surfaces  exposed  to  its  action.  Smeaton 
gives  a  table  compiled  by  Rouse  from  a  considerable  number  of  facts 
and  experiments  ;  he  observes  that  these  experiments  do  not  deserve  as 
much  confidence  for  velocities  above  as  for  velocities  below  50  miles  an 


-902]  Meteorology.  837 

hour.  The  numerical  values  for  the  pressures  given  in  this  table  seem  to 
have  been  calculated  on  the  supposition  that  the  pressure  is  proportional 
to  the  square  of  the  velocity  of  the  wind  ;  they  are  approximately  given 
by  the  formula 

/=  0-002214  V^ 

where  V  being  the  velocity  of  the  wind  in  feet  per  second,/  is  the  pres- 
sure in  pounds  per  square  foot. 

901.  Causes  of  winds. — Winds  are  produced  by  a  disturbance  of 
the  equilibrium  in  some  part  of  the  atmosphere ;  a  disturbance  always 
resulting  from  a  difference  in  temperature  between  adjacent  countries. 
Thus,  if  the  temperature  of  a  certain  extent  of  ground  becomes  higher, 
the  air  in  contact  with  it  becomes  heated,  it  expands  and  rises  towards 
the  higher  regions  of  the  atmosphere  ;  whence  it  flows,  producing  winds 
which  blow  from  hot  to  cold  countries.  But  at  the  same  time  the  equi- 
librium is  destroyed  at  the  surface  of  the  earth,  for  the  barometric  pressure 
on  the  colder  adjacent  parts  is  greater  than  on  that  which  has  been 
heated,  and  hence  a  current  will  be  produced  with  a  velocity  dependent 
on  the  difference  between  these  pressures ;  thus  two  distinct  winds  will 
be  produced,  an  upper  one  setting  outwards  from  the  heated  region,  and 
a  lower  one  setting  i7iwards  towards  it. 

902.  Regrular,  periodical,  and  variable  winds. — According  to  the 
more  or  less  constant  directions  in  which  winds  blow,  they  may  be  classed 
as  regular,  periodical,  and  variable  winds. 

i.  Regular  winds  are  those  which  blow  all  the  year  through  in  a  virtually 
constant  direction.  These  winds,  which  are  also  known  as  the  trade 
winds,  are  uninterruptedly  observed  far  from  the  land  in  equatorial 
regions,  blowing  from  the  north-east  to  the  south-west  in  the  northern 
hemisphere,  and  from  the  south-east  to  the  north-west  in  the  southern 
hemisphere.  They  prevail  on  the  two  sides  of  the  equator  as  far  as  30° 
of  latitude,  and  they  blow  in  the  same  direction  as  the  apparent  motion 
of  the  sun — that  is,  from  east  to  west. 

The  air  above  the  equator  being  gradually  heated,  rises  as  the  sun 
passes  round  from  east  to  west,  and  its  place  is  supplied  by  the  colder  air 
from  the  north  or  south.  The  direction  of  the  wind,  however,  is  modified 
by  this  fact,  that  the  velocity  which  this  colder  air  has  derived  from  the 
rotation  of  the  earth — namely,  the  velocity  of  the  surface  of  the  earth  at 
the  point  from  which  it  started — is  less  than  the  velocity  of  the  surface  of 
the  earth  at  the  point  at  which  it  has  now  arrived  ;  hence  the  currents 
acquire  in  reference  to  the  equator,  the  constant  direction  which  consti- 
tutes the  trade  winds. 

ii.  Periodical  winds  are  those  which  blow  regularly  in  the  same  direc- 
tion at  the  same  seasons,  and  at  the  same  hours  of  the  day  :  the  monsoon, 
simoom,  and  the  land  and  sea  breeze  are  examples  of  this  class.  The 
name  monsoon  is  given  to  winds  which  blow  for  six  months  in  one  direc- 
tion and  for  six  months  in  another.  They  are  principally  observed  in 
the  Red  Sea  and  in  the  Arabian  Gulf,  in  the  Bay  of  Bengal  and  in  the 
Chinese  Sea.  These  winds  blow  towards  the  continents  in  summer,  and 
in  a  contrary  direction  in  winter.     The  simoom  is  a  hot  wind  which  blows 


8sS  Winds,  [902- 

over  the  deserts  of  Asia  and  Africa,  and  which  is  characterised  by  its 
high  temperature  and  by  the  sands  which  it  raises  in  the  atmosphere  and 
carries  with  it.  During  the  prevalence  of  this  wind  the  air  is  darkened, 
the  skin  feels  dry,  the  respiration  is  accelerated,  and  a  burning  thirst  is 
experienced. 

This  wind  is  known  under  the  name  of  sirocco  in  Italy  and  Algiers, 
where  it  blows  from  the  great  desert  of  Sahara.  In  Egypt,  where  it 
prevails  from  the  end  of  April  to  June,  it  is  called  kamsin.  The  natives 
of  Africa,  in  order  to  protect  themselves  from  the  effects  of  the  too 
rapid  perspiration  occasioned  by  this  wind,  cover  themselves  with  fatty 
substances. 

The  /andcind  sea  breeze  is  a  wind  which  blows  on  the  sea  coast,  during 
the  day  from  the  sea  towards  the  land,  and  during  the  night  from  the 
land  to  the  sea.  For  during  the  day  the  land  becomes  more  heated  than 
the  sea,  in  consequence  of  its  lower  specific  heat  and  greater  conduc- 
tivity, and  hence  as  the  superincumbent  air  becomes  more  heated  than 
that  upon  the  sea,  it  ascends  and  is  replaced  by  a  current  of  colder  and 
denser  air  flowing  from  the  sea  towards  the  land.  During  the  night  the 
land  cools  more  rapidly  than  the  sea,  and  hence  the  same  phenomenon 
is  produced  in  a  contrary  direction.  The  sea  breeze  commences  after 
sunrise,  increases  to  three  o'clock  in  the  afternoon,  decreases  towards 
evening,  and  is  changed  into  a  land  breeze  after  sunset.  These  winds 
are  only  perceived  at  a  slight  distance  from  the  shores.  They  are  regular 
in  the  tropics,  but  less  so  in  our  climates  ;  and  traces  of  them  are  seen 
as  far  as  the  coasts  of  Greenland.  The  proximity  of  mountains  also 
gives  rise  to  periodical  daily  breezes. 

iii.  Variable  winds  are  those  which  blow  sometimes  in  one  direction 
and  sometimes  in  another,  alternately,  without  being  subject  to  any  law. 
In  mean  latitudes  the  direction  of  the  winds  is  very  variable  ;  towards 
the  poles  this  irregularity  increases,  and  under  the  arctic  zone  the  winds 
frequently  blow  from  several  points  of  the  horizon  at  once.  On  the  other 
hand,  in  approaching  the  torrid  zone,  they  become  more  regular.  The 
south-west  wind  prevails  in  the  north  of  France,  in  England,  and  in 
Germany  ;  in  the  south  of  France  the  direction  inclines  towards  the 
north,  and  m  Spain  and  Italy  the  north  wind  predominates. 

903.  law  of  tlie  rotation  of  winds. — Spite  of  the  great  irregularity 
which  characterises  the  direction  of  the  winds  in  our  latitude,  it  has  been 
ascertained  that  the  wind  has  a  preponderating  tendency  to  veer  round 
according  to  the  sun's  motion — that  is,  to  pass  from  north,  through  north- 
east, east,  south-east  to  south,  and  so  on  round  in  the  same  direction 
from  west  to  north  ;  that  it  often  makes  a  complete  circuit  in  that  direc- 
tion, or  more  than  one  in  succession,  occupying  many  days  in  doing  so, 
but  that  it  rarely  veers,  and  very  rarely  or  never  makes  a  complete  circuit 
in  the  opposite  direction.  This  course  of  the  winds  is  most  regularly 
observed  in  winter.  According  to  Leverrier,  the  displacement  of  the 
north-east  by  the  south-west  wind  arises  from  the  occurrence  of  a  whirl- 
wind formed  upon  the  Gulf-stream. 

For  a  station  in  south  latitude  a  contrary  law  of  rotation  prevails. 


-905] 


Fogs  and  Mists. 


839 


This  law,  though  more  or  less  suspected  for  a  long  time,  was  first 
formally  enunciated  and  explained  by  Dove,  and  is  known  as  Dove's  law 
of  the  7'otation  of  winds. 

904.  Fogrs  and  mists. — When  aqueous  vapours  rising  from  a  vessel 
of  boiling  water  diffuse  in  the  colder  air,  they  are  condensed ;  a  sort  of 
cloud  is  formed  which  consists  of  a  number  of  small  hollow  vesicles  of 
water,  which  remain  suspended  in  the  air.  These  are  usually  spoken 
of  as  vapours,  yet  they  are  not  so,  at  any  rate  not  in  the  physical  sense  of 
the  word  ;  for  they  are  partially  condensed  vapours. 

When  this  condensation  of  aqueous  vapours  is  not  occasioned  by  con- 
tact with  cold  solid  bodies,  but  takes  place  throughout  large  spaces  of  the 
atmosphere,  they  constitute  fogs  or  mists^  which,  in  fact,  are  nothing 
more  than  the  appearance  seen  over  a  vessel  of  hot  water. 

A  chief  cause  of  fogs  consists  in  the  moist  soil  being  at  a  higher  tem- 
perature than  the  air.  The  vapours  which  then  ascend  condense  and 
become  visible.  In  all  cases,  however,  the  air  must  have  reached  its 
point  of  saturation  before  condensation  takes  place.  Fogs  may  also  be 
produced  when  a  current  of  hot  and  moist  air  passes  over  a  river  at  a 
lower  temperature  than  its  own,  for  then  the  air  being  cooled,  as  soon  as 
it  is  saturated,  the  excess  of  vapour  present  is  condensed. 

The  distinction  between  mists  and  fogs  is  one  of  degree  rather  than  of 
kind.     A  fog  is  a  very  thick  mist. 

905.  Clouds. — Clouds  are  masses  of  vapour,  condensed  into  little  drops 
or  vesicles  of  extreme  minuteness,  like  fogs ;  from  which  they  only  differ 


Fig-  751. 


in  occupying  the  higher  regions  of  the  atmosphere ;  they  always  result 
from  the  condensation  of  vapours  which  rise  from  the  earth.     According 


840  Fogs  and  Mists.     Clouds.  [905- 

to  their  appearance,  they  have  been  divided  by  Howard  into  four  princi- 
pal kinds  :  the  nimbjis,  the  stratus^  the  cumulus,  and  the  cirrus.  These 
four  kinds  are  represented  in  fig.  751,  and  are  designated  respectively  by 
one,  two,  three,  and  four  birds  on  the  wing. 

The  cirrus  consist  of  small  whitish  clouds,  which  have  a  fibrous  or 
wispy  appearance,  and  occupy  the  highest  regions  of  the  atmosphere. 
The  name  of  mare^  tails,  by  which  they  are  generally  known,  well 
describes  their  appearance.  From  the  low  temperature  of  the  spaces 
which  they  occupy,  it  is  more  than  probable  that  cirrus  clouds  consist  of 
frozen  particles ;  and  hence  it  is  that  haloes,  coronas,  and  other  optical 
appearances,  produced  by  refraction  and  reflection  from  ice  crystals, 
appear  almost  always  in  these  clouds  and  their  derivatives.  Their  ap- 
pearance often  precedes  a  change  of  weather. 

The  cumulus  are  rounded  spherical  forms  which  look  like  mountains 
piled  one  on  the  other.  They  are  more  frequent  in  summer  than  in 
winter,  and  after  being  formed  in  the  morning,  they  generally  disappear 
towards  evening.  If,  on  the  contrary,  they  become  more  numerous, 
and  especially  if  surmounted  by  cirrus  clouds,  rain  or  storms  may  be 
expected. 

Stratus  clouds  consist  of  very  large  and  continuous  horizonal  sheets, 
which  chiefly  form  at  sunset,  and  disappear  at  sunrise.  They  are  fre- 
quent in  autumn  and  unusual  in  spring  time,  and  are  lower  than  the 
preceding. 

The  nimbus,  or  rain  clouds,  which  are  sometimes  classed  as  one  of  the 
fundamental  varieties,  are  properly  a  combination  of  the  three  preceding 
kinds.  They  affect  no  particular  form,  and  are  solely  distinguished  by  a 
uniform  grey  tint,  and  by  fringed  edges.  They  are  indicated  on  the  right 
of  the  figure  by  the  presence  of  one  bird. 

The  fundamental  forms  pass  into  one  another  in  the  most  varied 
manner  ;  Howard  has  classed  these  traditional  forms  as  cirro-cumulus, 
cirro-stratus,  and  cumulo-stratus,  and  it  is  often  very  difficult  to  tell  from 
the  appearance  of  a  cloud,  which  type  it  most  resembles.  The  cirro- 
cumulus  is  most  characteristically  known  as  a '  mackerel  sky  ; '  it  consists 
of  small  roundish  masses,  disposed  with  more  or  less  irregularity  and 
connection.  -  It  is  frequent  in  summer,  and  attendant  on  warm  and  dry 
weather.  Cirro-stratus  appears  to  result  from  the  subsidence  of  the 
fibres  of  cirrus  to  a  horizontal  position,  at  the  same  time  approaching 
laterally.  The  form  and  relative  position  when  seen  in  the  distance 
frequently  give  the  idea  of  shoals  of  fish.  The  tendency  of  cmmilo- 
stratus  is  to  spread,  settle  down  into  the  nitnbus,  and  finally  fall  as  rain. 

The  height  of  clouds  varies  greatly ;  in  the  mean  it  is  from  1,300  to 
1,500  yards  in  winter,  and  from  3,300  to  4,400  yards  in  summer.  But 
they  often  exist  at  greater  heights  ;  Gay-Lussac,  in  his  balloon  ascent, 
at  a  height  of  7,650  yards,  observed  cirrus-clouds  above  him,  which 
appeared  still  to  be  at  a  considerable  height.  In  Ethiopia,  M.  d'Ab- 
badie  observed  storm  clouds  whose  height  was  only  230  yards  above  the 
ground. 

In  order  to  explain  the  suspension  of  clouds  in  the  atmosphere,  Halley 


-906]  Formation  of  Clouds,  841 

first  proposed  the  hypothesis  of  vesicular  vapours.  He  supposed  that 
clouds  are  formed  of  an  infinity  of  extremely  minute  vesicles,  hollow, 
like  soap  bubbles  filled  with  air,  which  is  hotter  than  the  surrounding 
air  :  so  that  these  vesicles  float  in  the  air  like  so  many  small  balloons. 
This  theory,  which  was  first  propounded  by  Saussure,  has  been  defended 
by  Kratzenstein,  subsequently  by  Bravais  and  most  physicists;  it  has, 
however,  been  combated  by  Desaguiliers,  and  afterwards  by  Monge,  and 
has  at  present  many  opponents.  These  latter  assume  that  clouds  and 
fogs  consist  of  extremely  minute  droplets  of  water,  which  are  retained 
in  the  atmosphere  by  the  ascensional  force  of  currents  of  hot  air,  just  as 
light  powders  are  raised  by  the  wind.  Ordinarily,  clouds  do  not  appear 
to  descend,  but  this  absence  of  downward  motion  is  only  apparent.  In 
fact,  clouds  do  usually  fall  slowly,  but  then  the  lower  part  is  continually 
dissipated  on  coming  in  contact  with  the  lower  and  more  heated  layers  ; 
at  the  same  time  the  upper  part  is  always  increasing  from  the  condensa- 
tion of  new  vapours  ;  so  that  from  these  two  actions  clouds  appear  to 
retain  the  same  height. 

906.  Formation  of  clouds. — Many  causes  may  concur  in  the  for- 
mation of  clouds,  i.  The  low  temperature  of  the  higher  regions  of 
the  atmosphere.  For,  owing  to  solar  radiation,  vapours  are  constantly 
disengaged  from  the  earth .  and  from  the  waters,  which  from  their 
elastic  force  and  lower  density  rise  in  the  atmosphere;  meeting  there 
continually  colder  and  colder  layers  of  air,  they  sink  to  the  point  of 
saturation,  and  then  condensing  in  infinitely  small  droplets,  they  give 
rise  to  clouds. 

ii.  The  hot  and  moist  currents  of  air  rising  during  the  day  undergo  a 
gradually  feebler  pressure,  and  thus  is  produced  an  expansion  which  is  a 
source  of  intense  cold,  and  produces  a  condensation  of  vapour.  Hence  it 
is  that  high  mountains,  stopping  the  aerial  currents,  and  Jforcing  them  to 
rise,  are  an  abundant  source  of  rain. 

iii.  A  hot,  moist  current  of  air  mixing  with  a  colder  current,  undergoes 
a  cooling,  which  brings  about  a  condensation  of  the  vapour.  Thus  the 
hot  and  moist  winds  of  the  south  and  south-west,  mixing  with  the  colder 
air  of  our  latitudes,  give  rain.  The  winds  of  the  north  and  north-east  tend 
also,  in  mixing  with  our  atmosphere,  to  condense  the  vapours ;  but  as 
these  winds,  owing  to  their  low  temperature,  are  very  dry,  the  mixture 
rarely  attains  saturation,  and  generally  gives  no  rain. 

The  formation  of  clouds  is  thus  explained  by  Hutton.  The  tension 
of  aqueous  vapour,  and  therewith  the  quantity  present  in  a  given  space 
when  saturated,  diminishes  according  to  a  geometric  progression,  while 
the  temperature  falls  in  arithmetical  progression,  and  therefore  the  elas- 
ticity of  the  vapour  present  at  any  time  is  reduced  by  a  fall  of  tempera- 
ture more  rapidly  than  in  direct  proportion  to  the  fall.  Hence  if  a  current 
of  warm  air,  saturated  with  aqueous  vapour,  meet  a  current  of  cold  air 
also  saturated,  the  air  acquires  the  mean  temperature  of  the  two,  but 
can  only  retain  a  portion  of  the  vapour  in  the  invisible  condition,  and  a  cloud 
or  mist  is  formed.  Thus  suppose  a  cubic  metre  of  air  at  10°  C.  mixes 
with  a  cubic  metre  of  air  at  2o°C-j  and  that  they  are  respectively  saturated 

00 


842 


Meteorology. 


[906- 


with  aqueous  vapour.  By  formula  (375)  it  is  easily  calculated  that  the  weight 
of  water  contained  in  the  cubic  metre  of  air  at  10°  C.  is  9-397  grammes, 
and  in  that  at  20°  C.  is  I7-632  grammes,  or  27-029  grammes  in  all.  When 
mixed  they  produce  two  cubic  metres  of  air  at  15°  C.  ;  but  as  the  weight 
of  water  required  to  saturate  this  is  only  2  x  12-8  =  25-6  grammes,  the 
excess,  1-429  grammes,  will  be  deposited  in  the  form  of  mist  or  clouds. 

907.  Rain. — When  by  the  constant  condensation  of  aqueous  vapour 
the  individual  vapour  vesicles  become  larger  and  heavier,  and  when 
finally  individual  vesicles  unite,  they  form  regular  drops  which  fall  as 
rain. 

The  quantity  of  rain  which  falls  annually  in  any  given  place,  or  the 
annual  rainfall,  is  measured  by  means  of  a  rain  gauge  or  pluviometer. 
Ordinarily  it  consists  of  a  cylindrical  vessel  M  (figs.  752  and  753),  closed 


Fig.  752. 


t'ig-  753- 


at  the  top  by  a  funnel-shaped  lid,  in  which  there  is  a  very  small  hole, 
through  which  the  rain  falls.  At  the  bottom  of  the  vessel  is  a  glass  tube, 
A,  in  which  the  water  rises  to  the  same  height  as  inside  the  rain  gauge, 
and  is  measured  by  a  scale  on  the  side,  as  shown  in  the  figures. 

The  apparatus  being  placed  in  an  exposed  situation,  if  at  the  end  of  a 
month  the  height  of  water  in  the  tiihe  is  two  inches  for  example,  it  shows 
that  the  water  has  attained  this  height  in  the  vessel ;  and,  consequently, 
that  a  layer  of  two  inches  in  depth  expresses  the  quantity  of  rain  which 
this  extent  of  surface  has  received. 

It  has  been  noticed  that  the  quantity  of  rain  indicated  by  the  rain 
gauge  is  greater  as  this  instrument  is  nearer  the  ground.  This  has 
been  ascribed  to  the  fact  that  the  rain-drops,,  which  are  generally  colder 
than  the  layers  of  air  which  they  traverse,  condense  the  vapour  in  these 
layers,  and,  therefore,  constantly  increase  in  volume.  Hence  more  rain 
falls  on  the  surface  of  the  ground  than  at  a  certain  height.  But  it  has 
been  objected  that  the  excess  of  the  quantity  of  rain  which  falls,  over 
that  at  a  certain  height,  is  six  or  seven  times  that  which  could  arise 
from  condensation,  even  during  the  whole  course  of  the  rain-drops  from 
the  clouds  to  the  earth.  The  difference  must,  therefore,  be  ascribed  to  purely 
local  causes,  and  it  is  now  assumed  that  the  difference  arises  from  eddies 
produced  in  the  air  about  the  rain  gauge,  which  are  more  perceptible  as 


-909]  Rain,      Waterspouts,  8^3 

it  is  higher  above  the  ground ;  as  these  eddies  disperse  the  drops  which 
would  otherwise  fall  into  the  instrument,  they  diminish  the  quantity  of 
water  which  it  receives. 

In  any  case  it  is  clear  that  if  rain-drops  traverse  moist  air,  they  will, 
from  their  temperature,  condense  vapour  and  increase  in  volume.  If,  on 
the  contrary,  they  traverse  dry  air,  the  drops  tend  to  vaporise,  and  less 
rain  falls  than  at  a  certain  height ;  it  might  even  happen  that  the  rain 
did  not  reach  the  earth. 

Many  local  circumstances  may  affect  the  quantity  of  rain  which  falls 
in  different  countries  ;  but,  other  things  being  equal,  most  rain  falls  in 
hot  climates,  for  there  the  vaporisation  is  most  abundant.  The  rain-fall 
decreases,  in  fact,  from  the  equator  to  the  poles.  At  London  it  is  23-5 
inches;  at  Bordeaux  it  is  25-8;  at  Madeira  it  is  277  ;  at  Havannah  it  is 
91-2,  and  at  St.  Domingo  it  is  107-6.  The  quantity  varies  with  the 
seasons  ;  in  Paris,  in  winter,  it  is  4*2  inches  ;  in  spring  6*9 ;  in  summer 
6'3,  and  in  autumn  4-8  inches.  The  heaviest  annual  rain-fall  at  any 
place  on  the  globe  is  on  the  Khasia  Hills  in  Bengal,  where  it  is  600  inches ; 
of  which  500  inches  fall  in  seven  months. 

The  driest  recorded  place  in  England  is  Lincoln,  where  the  mean 
rainfall  is  20  inches,  and  the  wettest  is  Stye,  at  the  head  of  Borrowdale 
in  Cumberland,  where  it  amounts  to  165  inches. 

An  inch  of  rain  on  a  square  yard  of  surface  expresses  a  fall  of  4674 
pounds,  or  4-67  gallons.  On  an  acre  it  corresponds  to  22,622  gallons,  or 
100-9935  tons.  100  tons  per  inch  per  acre  is  a  ready  way  of  remember- 
ing this. 

908.  "Waterspouts. — These  are  masses  of  vapour  suspended  in  the 
lower  layers  of  the  atmosphere  which  they  traverse,  and  endowed  with  a 
gyratory  motion  rapid  enough  to  uproot  trees,  upset  houses,  and  break 
and  destroy  everything  with  which  they  come  in  contact. 

These  meteors,  which  are  generally  accompanied  by  hail  and  rain, 
often  emit  lightning  and  thunder,  producing  the  sound  of  carriages 
rolling  over  a  stony  road.  Many  of  them  have  no  gyratory  motion, 
and  about  a  quarter  of  those  observed  are  produced  in  a  calm  atmo- 
sphere. 

When  they  take  place  on  the  sea  they  present  a  curious  phenomenon. 
The  water  is  disturbed,  and  rises  in  the  form  of  a  cone,  while  the  clouds 
are  depressed  in  the  form  of  an  inverted  cone ;  the  two  cones  then  unite 
and  form  a  continuous  column  from  the  sea  to  the  clouds  (fig.  754),  which 
are  called  waterspouts.  Even,  however,  on  the  high  seas  the  water  of 
these  waterspouts  is  never  salt,  proving  that  they  are  formed  of  con- 
densed vapours,  and  not  of  sea  water  raised  by  aspiration. 

'the  origin  of  these  is  not  known.  Kaemtz  assumes  that  they  are  due 
principally  to  two  opposite  winds  which  pass  by  the  side  of  each  other,  or 
to  a  very  high  wind  which  prevails  in  the  higher  regions  of  the  atmo- 
sphere. 

Peltier  and  many  others  ascribe  to  them  an  electrical  origin. 

909.  Influence  of  aqueous  vapour  on  climate.-*-One  of  the  most 
important  elements  in  meteorology  is  undoubtedly  the  property  possessed 


844 


Meteorology. 


[909 


by  aqueous  vapour  of  powerfully  absorbing  and  radiating  heat.  The 
same  physicist  who  discovered  this  property  (411)?  has  applied  it  to  the 
explanation  of  some  obscure  points  in  meteorological  science,  and  there 
can  be  no  doubt  that  the  knowledge  of  it  will  gradually  lead  to  a  clearer 
understanding  of  many  inexplicable  and  apparently  capricious  meteorolo- 
gical phenomena. 


Fig.  754- 


Tyndall  has  established  the  fact,  that  in  a  tube  4  feet  long  the  atmo- 
spheric vapour  on  a  day  of  average  dryness  absorbs  10  per  cent,  of  obscure 
heat.  With  the  earth  warmed  by  the  sun,  as  a  source,  there  can  be  no 
doubt  that  at  the  very  least  10  per  cent,  of  its  heat  is  intercepted  within 
10  feet  of  the  surface.  If  aqueous  vapour  be  compared  atom  for  atom 
with  air,  its  power  of  absorption  and  radiation  is  more  than  16,000  times 
that  possessed  by  air.  Such  facts  as  these  are  sufficient  to  show  the 
importance  of  the  small  quantity  of  this  vapour  that  exists  in  our  atmo- 
sphere. 

The  radiative  power  of  aqueous  vapour  may  be  the  main  cause  of  the 
^  torrential  rains  that  occur  in  the  tropics,  and  also  of  the  formation  of 
cumuli  clouds  in  our  own  latitudes.  This  same  property  probably 
causes  the  descent  of  a  very  fine  rain,  called  serei?i,  which  has  more  the 
characteristics  of  falling  dew,  as  it  appears  a  short  time  after  sunset, 
when  the  sky  is  clear  ;  its  production  has  therefore  been  attributed  to  the 
cold,  resulting  from  the  radiation  of  the  air.  It  is  not  the  air,  however, 
but  the  aqueous  vapour  in  the  air,  which  by  its  own  radiation  chills 
itself,  so  that  it  condenses  into  sdreiii. 


-910]  Injiuence  of  A  queoiis  Vapour  on  Climate.  845 

The  absorbejit  power  of  aqueous  vapour  is  even  of  greater  importance. 
Whenever  the  air  is  dry,  terrestrial  radiation  at  night  is  so  rapid  as  to 
cause  intense  cold.  Thus,  in  the  central  parts  of  Asia,  Africa,  and  Aus- 
tralia, the  daily  range  of  the  thermometer  is  enormous;  in  the  interior  of 
the  last  continent  a  difference  in  temperature  of  no  less  than  40°  C.  has 
been  recorded  within  24  hours.  In  India,  and  even  in  the  Sahara,  owing  to 
the  copious  radiation,  ice  has  been  formed  at  night.  But  the  heat  which 
aqueous  vapour  absorbs  most  largely  is  of  the  kind  emitted  from  sources  of 
low  temperature ;  it  is  to  a  large  extent  transparent  to  the  heat  emitted  from 
the  sun,  whilst  it  is  almost  opaque  to  the  heat  radiated  from  the  earth. 
Consequently,  the  solar  rays  penetrate  our  atmosphere  with  a  loss,  as 
estimated  by  Pouillet,  of  only  25  per  cent.,  when  directed  vertically  down- 
wards, but  after  warming  the  earth  they  cannot  retraverse  the  atmosphere. 
Through  thus  preventing  the  escape  of  terrestrial  heat,  the  aqueous 
vapour  in  the  air  moderates  the  extreme  chilling  which  is  due  to  the 
unchecked  radiation  from  the  earth,  and  raises  the  temperature  of  that 
region  over  which  it  is  spread.  Tyndall  has  thus  described  the  action 
of  this  substance  : — *  Aqueous  vapour  is  a  blanket  more  necessary  to  the 
vegetable  life  of  England  than  clothing  is  to  man.  Remove  for  a  single 
summer  night  the  aqueous  vapour  from  the  air  which  overspreads  this 
country,  and  every  plant  capable  of  being  destroyed  by  a  freezing  tempe- 
rature would  perish.  The  warmth  of  our  fields  and  gardens  would  pour 
itself  unrequited  into  space,  and  the  sun  would  rise  upon  an  island  held 
fast  in  the  iron  grip  of  frost.' 

910.  Tyndall's  researclies.— Tyndall  has  recently  examined  the  action 
of  solar  and  of  the  electric  light  on  vapours  under  a  great  degree  of  attenua- 
tion ;  and  has  found  that  under  these  circumstances  they  are  decomposed. 
This  new  reaction  not  only  puts  a  most  powerful  agent  of  chemical  de- 
composition into  the  hands  of  chemists,  which  remains  for  them  to  make 
use  of,  but  it  has  led  Tyndall  to  important  conclusions  regarding  the 
origin  of  the  blue  colour  of  the  sky,  and  the  polarisation  of  daylight 

For  these  experiments  he  used  a  glass  tube  with  glass  ends,  such  as 
he  had  used  for  his  researches  on  radiant  heat.  This  could  be  exhausted 
and  then  filled  with  air  charged  with  the  vapours  of  volatile  liquids,  by 
allowing  the  air  to  pass  through  small  Wolff  bottles  containing  them.  By 
mixing  with  different  proportions  of  pure  air  the  air  charged  with  vapour, 
and  by  varying  the  degree  of  exhaustion,  it  was  possible  to  have  a  vapour 
under  any  degree  of  attenuation.  It  was  also  possible  to  fill  the  tube 
with  the  vapour  of  a  liquid  alone. 

The  tube  having  been  filled  with  air  charged  with  vapours  of  nitrite 
of  amyle,  a  somewhat  convergent  beam  from  the  electric  lamp  was 
passed  into  the  tube.  For  a  moment  the  tube  appeared  optically  empty, 
but  suddenly  a  shower  of  liquid  spherules  was  precipitated  on  the  path 
of  the  beam  forming  a  luminous  white  cloud.  The  nature  of  the  sub- 
stance thus  precipitated  was  not  specially  investigated. 

This  effect  was  not  due  to  any  chemical  action  between  the  vapour  and 
the  air,  for  when  either  dry  oxygen  or  dry  hydrogen  was  used  instead  of 
air,  or  when  the  vapour  was  admitted  alone,  the  effect  was  substantially 


846  Meteorology.  [910- 

the  same.  Nor  was  it  due  to  any  heating  effect,  for  the  beam  had  been 
previously  sifted  by  passing  through  a  solution  of  alum,  and  through  the 
thick  glass  of  the  lens.  The  unsifted  beam  produced  the  same  effect ; 
the  obscure  calorific  rays  did  not  seem  to  interfere  with  the  result. 

The  sun's  hght  also  affects  the  decomposition  of  the  nitrite  of  amyle 
vapour ;  and  this  decomposition  was  found  to  be  mainly  due  to  the  more 
refrangible  rays. 

When  the  electric  light,  before  entering  the  experimental  tube,  was 
made  to  pass  through  a  layer  of  the  liquid  nitrite  of  amyle  an  eighth  of 
an  inch  in  thickness,  the  luminous  effect  was  not  appreciably  diminished, 
but  the  chemical  action  was  almost  entirely  stopped.  Thus  that  special 
constituent  of  the  luminous  radiation  which  effects  the  decomposition  of 
the  vapour  is  absorbed  by  the  liquid.  The  liquid  nitrite  of  amyle  is 
probably  decomposed  by  light;  but  its  decomposition,  if  it  take  place  at 
all,  is  far  less  rapid  and  distinct  than  that  of  the  vapour.  The  circum- 
stance that  the  absorption  is  the  same  whether  the  nitrite  is  in  the  liquid 
or  in  the  vaporous  state,  is  considered  by  Tyndall  as  a  proof  that  the 
absorption  is  not  the  act  of  the  molecule  as  a  whole,  but  that  it  is  atomic, 
that  is,  that  it  is  to  the  atoms  that  the  peculiar  rate  of  vibration  is  trans- 
ferred, which  brings  about  the  decomposition  of  the  body. 

Besides  nitrite  of  amyle,  the  vapour  of  a  number  of  other  substances 
was  examined,  such,  for  example,  as  benzole,  iodide  of  allyle,  bisulphide 
of  carbon.  By  varying  the  nature  of  the  vapour,  the  shape  of  a  cloud 
could  be  greatly  varied,  and  in  many  cases  presented  the  most  fantastic 
and  beautiful  forms. 

It  was  also  found  that  a  vapour  which  when  alone  resists  the  action  of 
light,  may,  by  being  associated  with  another  gas  or  vapour,  exhibit  a 
vigorous  or  even  violent  action. 

Thus,  when  the  tube  was  filled  with  atmospheric  air,  mixed  with  nitrite 
of  butyle  vapour,  the  electric  hght  produced  very  little  effect.  But  with 
half  an  atmosphere  of  this  mixture,  and  half  an  atmosphere  of  air  which 
had  passed  through  hydrochloric  acid,  the  action  of  the  light  was  almost 
instantaneous.  In  another  case  mixed  air  and  nitrite  of  butyle  vapour 
were  passed  into  the  tube  so  as  to  depress  the  barometer  the  j^^th  of  an  inch  ; 
that  is,  the  mixed  air  and  vapour  were  under  a  pressure  of  3^^  of  an 
atmosphere.  Air  passed  through  solution  of  hydrochloric  acid  was  intro- 
duced until  the  pressure  was  3  inches.  The  condensed  beam  passed 
through  for  some  time  without  change,  but  afterwards  a  superbly  blue 
cloud  was  formed. 

In  cases  where  the  vapours  are  under  a  sufficient  degree  of  attenua- 
tion, whatever  otherwise  be  their  nature,  the  visible  action  commences 
with  the  formation  of  a  blue  cloud.  The  term  cloud,  however,  must  not 
be  understood  in  its  ordinary  sense  :  the  blue  cloud  is  invisible  in  ordinary 
daylight,  and  to  be  seen  must  be  surrounded  by  darkness,  it  alone  being 
illuminated  by  a  powerful  beam  of  light.  The  blue  cloud  differs  in  many 
important  particulars  from  the  finest  ordinary  clouds,  and  may  be  con- 
sidered to  occupy  an  intermediate  position  between  these  clouds  and  true 
cloudless  vapour. 


r.911]  Dew.     Hoar  Frost.  ;847 

By  graduating  the  quantity  of  vapour,  the  precipitation  may  be  ob- 
tained of  any  required  degree  of  fineness :  forming  either  particles  dis- 
tinguishable by  the  naked  eye,  or  particles  beyond  the  reach  of  the 
highest  microscopic  power.  There  is  no  reason  to  doubt  that  particles 
may  be  thus  obtained  whose  wave-length  is  but  a  very  small  fraction  of 
the  length  of  a  wave  of  violet  light. 

The  case  is  similar  to  that  of  carbonic  acid  gas,  which,  diffused  in  the 
atmosphere,  resists  the  decomposing  action  of  solar  light,  but  when  in 
contiguity  with  the  chlorophyle  in  the  leaves  of  plants  is  decomposed. 

When  the  blue  cloud  produced  in  these  experiments  was  examined  by 
any  polarising  arrangement,  the  light  emitted  laterally  from  the  beam — 
that  is,  in  a  direction  at  right  angles  to  its  axis — was  found  to  be  perfectly 
polarised.  This  phenomenon  was  observed  in  its  greatest  perfection  the 
more  perfect  the  blue  of  the  sky.  It  is  produced  by  any  particles,  pro- 
vided they  are  sufficiently  fine. 

This  is  quite  analogous  to  the  light  of  the  blue  sky.  When  this  is 
examined  by  a  Nicol's  prism,  or  any  other  analyser,  it  is  found  that  the 
light,  emitted  at  right  angles  to  the  path  of  the  sun's  rays,  is  polarised. 

These  two  phenomena,  the  fundamental  blue,  and  the  polarisation  of 
the  sky  light,  which  have  long  been  the  enigmas  of  meteorologists,  find 
their  definite  solution  in  these  experiments.  We  have  only  to  assume 
the  existence  in  the  higher  regions  of  the  atmosphere  of  excessively  fine 
particles  of  water ;  for  particles  of  any  kind  produce  this  effect.  It  is  not 
difficult  to  conceive  the  existence  of  such  particles  in  the  higher  regions, 
even  on  a  hot  summer's  day.  For  the  vapour  must  there  be  in  a  state  of 
extreme  attenuation ;  and  inasmuch  as  the  oxygen  and  nitrogen  of  the 
atmosphere  behave  like  a  vacuum  to  radiant  heat,  the  extremely  attenu- 
ated particles  of  aqueous  vapour  are  practically  in  contact  with  the  absolute 
cold  of  space. 

'  Suppose  the  atmosphere  surrounded  by  an  envelope  impervious  to 
light,  but  with  an  aperture  on  the  sunward  side,  through  which  a  parallel 
beam  of  solar  light  could  enter  and  traverse  the  atmosphere.  Surrounded 
on  all  sides  by  air  not  directly  illuminated,  the  track  of  such  a  beam 
would  resemble  that  of  the  parallel  beam  of  the  electric  light  through 
an  incipient  cloud.  The  sunbeam  would  be  blue,  and  it  would  discharge 
light  laterally  in  the  same  condition  as  that  discharged  by  the  incipient 
cloud.  The  azure  revealed  by  such  a  beam  would  be  to  all  intents  and 
purposes  a  blue  cloud.' 

911.  Dew.  Hoar  frost. — Dew  is  merely  aqueous  vapour  which  has 
condensed  on  bodies  during  the  night  in  the  form  of  minute  globules. 
It  is  occasioned  by  the  chilling  which  bodies  near  the  surface  of  the  earth 
experience  in  consequence  of  nocturnal  radiation.  Their  temperature 
having  then  sunk  several  degrees  below  that  of  the  air,  it  frequently 
happens,  especially  in  hot  seasons,  that  this  temperature  is  below  that  at 
which  the  atmosphere  is  saturated.  The  layer  of  air  which  is  immediately 
in  contact  with  the  chilled  bodies,  and  which  virtually  has  the  same 
temperature,  then  deposits  a  portion  of  the  vapour  which  it  contains ; 
just  as  when  a  bottle  of  cold  water  is  brought  into  a  warm  room,  it  be- 


848  Meteorology,  [911- 

comes  covered  with  moisture,  owing  to  the  condensation  of  aqueous  vapour 
upon  it. 

According  to  this  theory,  which  was  first  propounded  by  Dr.  Wells,  all 
causes  which  promote  the  cooling  of  bodies  increase  the  quantity  of  dew. 
These  causes  are  the  emissive  power  of  bodies,  the  state  of  the  sky,  and 
the  agitation  of  the  air.  Bodies  which  have  a  great  radiating  power  more 
readily  become  cool,  and  therefore  ought  to  condense  more  vapour.  In 
fact,  there  is  generally  no  deposit  of  dew  on  metals,  whose  radiating 
power  is  very  small,  especially  when  they  are  polished;  while  the  ground, 
sand,  glass,  and  plants,  which  have  a  great  radiating  power,  become 
abundantly  covered  with  dew. 

The  state  of  the  sky  also  exercises  a  great  influence  on  the  formation 
of  dew.  If  the  sky  is  cloudless,  the  planetary  spaces  send  to  the  earth  an 
inappreciable  quantity  of  heat,  while  the  earth  radiates  very  considerably, 
and  therefore  becoming  very  much  chilled,  there  is  an  abundant  deposit 
of  dew.  But  if  there  are  clouds,  as  their  temperature  is  far  higher  than 
that  of  the  planetary  spaces,  they  radiate  in  turn  towards  the  earth,  and 
as  bodies  on  the  surface  of  the  earth  only  experience  a  feeble  chilling,  no 
deposit  of  dew  takes  place. 

Wind  also  influences  the  quantity  of  vapour  deposited.  If  it  is  feeble, 
it  increases  it,  inasmuch  as  it  renews  the  air ;  if  it  is  strong,  it  diminishes 
it,  as  it  heats  the  bodies  by  contact,  and  thus  does  not  allow  the  air  time 
to  become  cooled.  Finally,  the  deposit  of  dew  is  more  abundant  accord- 
ing as  the  air  is  moister,  for  then  it  is  nearer  its  point  of  saturation. 

Hoarfrost  and  rime  are  nothing  more  than  dew  which  has  been  depo- 
sited on  bodies  cooled  below  zero,  and  has  therefore  become  frozen.  The 
flocculent  form  which  the  small  crystals  present,  of  which  rime  is  formed, 
shows  that  the  vapours  solidify  directly  without  passing  through  the 
liquid  state.  Hoar  frost,  like  dew,  is  formed  on  bodies  which  radiate 
most,  such  as  the  stalks  and  leaves  of  vegetables,  and  is  chiefly  deposited 
on  the  parts  turned  towards  the  sky. 

912.  Snow.  Sleet. — Snow  is  water  solidified  in  stellate  crystals, 
variously  modified,  and  floating  in  the  atmosphere.  These  crystals  arise 
from  the  congelation  of  the  minute  vesicles  which  constitute  the  clouds, 
when  the  temperature  of  the  latter  is  below  zero.  They  are  more  regular 
when  formed  in  a  calm  atmosphere.  Their  form  may  be  investigated  by 
collecting  them  on  a  black  surface,  and  viewing  them  through  a  strong 
lens.  The  regularity,  and  at  the  same  time  variety,  of  their  forms  are 
truly  beautiful.  Fig.  755  shows  some  of  the  forms  as  seen  through  a 
microscope. 

It  snows  most  in  countries  near  the  poles,  or  which  are  high  above  the 
sea  level.  Towards  the  poles,  the  earth  is  constantly  covered  with  snow; 
the  same  is  the  case  on  high  mountains,  where  there  are  perpetual  snows 
even  in  equatorial  countries. 

Sleet  is  also  solidified  water,  and  consists  of  small  icy  needles  pressed 
together  in  a  confused  manner.  Its  formation  is  ascribed  to  the  sudden 
congelation  of  the  minute  globules  of  the  clouds  in  an  agitated  atmo- 
sphere. 


-914] 


Ice.     Regelatioii. 


849 


913.  Bail. — Hail  is  a  mass  of  compact  globules  of  ice  of  different 
sizes,  which  fall  in  the  atmosphere.  In  our  chmate  hail  falls  principally 
during  spring  and  summer,  and  at  the  hottest  times  of  the  day ;  it  rarely 
falls  at  night.     The  fall  of  hail  is  always  preceded  by  a  peculiar  noise. 

Hail  is  generally  the  precursor  of  storms,  it  rarely  accompanies  them, 
and  follows  them  more  rarely  still.     Hail  falls  from  the  size  of  small  peas 


Fig.  755- 

to  that  of  an  ^g%  or  an  orange.  The  formation  of  hailstones  has  never 
been  altogether  satisfactorily  accounted  for;  nor  more  especially  their 
great  size. 

914.  Ice.  Hegrelation. — Ice  is  nothing  more  than  an  aggregate  of 
snow  crystals,  such  as  are  shown  in  fig.  755.  The  transparency  of  ice 
is  due  to  the  close  contact  of  these  crystals,  which  causes  the  individual 
particles  to  blend  into  an  unbroken  mass,  and  renders  the  substance 
optically,  as  well  as  mechanically,  continuous.  When  large  masses  of  ice 
slowly  melt  away,  a  crystalline  form  is  sometimes  seeri  by  the  gradual 
disintegration  into  rude  hexagonal  prisms :  a  similar  structure  is  fre- 
quently met  with,  but  in  greater  perfection,  in  the  ice  caves  or  glaciers  of 
cold  regions. 

An  experiment  of  Tyndall  has  more  clearly  revealed  the  beautiful 
structure  of  ice.  When  a  piece  of  ice  is  cut  parallel  to  its  planes  of 
freezing,  and  the  radiation  from  any  source  of  light,  as  the  sun,  a  gas  or 
oil  flame,  is  permitted  to  pass  through  it,  the  disintegration  of  the  sub- 
stance proceeds  in  a  remarkable  way.  By  observing  the  plate  of  ice 
through  a  lens,  numerous  small  crystals  will  be  seen  studding  the  interior 
of  the  block;  as  the  heat  continues  these  crystals  expand,  and  finally 
assume  the  shape  of  six-rayed  stars  of  exquisite  beauty. 

This  is  a  kind  of  negative  crystallisation,  the  crystals  produced  being 
composed  of  water ;  they  owe  their  formation  to  the  molecular  disturbance 
caused  by  the  absorption  of  heat  from  the  source.  Nothing  is  easier 
than  to  reproduce  this  phenomenon,  if  care  be  taken  in  cutting  the  ice. 
The  planes  of  freezing  can  be  found  by  noting  the  direction  of  the  bubbles 

003 


SCO  Meteorology.  [914- 

in  ice,  which  are  either  sparsely  arranged  in  striae  at  right  angles  to  the 
suface,  or  thickly  collected  in  beds  parallel  to  the  surface  of  the  water. 
A  warm  and  smooth  metal  plate  should  be  used  to  level  and  reduce  the 
ice  to  a  slab  not  exceeding  half  an  inch  in  thickness. 

A  still  more  important  property  of  ice  remains  to  be  noticed.  Faraday 
discovered  that  when  two  pieces  of  melting  ice  are  pressed  together  they 
freeze  into  one  at  their  points  of  contact.  This  curious  phenomenon  is 
now  known  under  the  name  of  regeiatioii.  The  cause  of  it  has  been  the 
subject  of  much  controversy,  but  the  simplest  explanation  seems  to  be 
that  given  by  its  discoverer.  The  particles  on  the  exterior  of  a  block  of 
ice  are  held  by  cohesion  on  one  side  only :  when  the  temperature  is  at  o° 
C,  these  exterior  particles  being  partly  free  are  the  first  to  pass  into  the 
liquid  state,  and  a  film  ot  water  covers  the  solid.  But  the  particles  in  the 
interior  of  the  block  are  bounded  on  all  sides  by  the  solid  ice,  the  force  of 
cohesion  is  here  a  maximum,  and  hence  the  interior  ice  has  no  tendency 
to  pass  into  a  liquid,  even  when  the  whole  mass  is  at  o°.  If  the  block  be 
now  split  in  halves,  a  liquid  film  instantly  covers  the  fractured  surfaces, 
for  the  force  of  cohesion  on  the  broken  surfaces  has  been  lessened  by 
the  act.  By  placing  the  halves  together,  so  that  their  original  position 
shall  be  regained,  the  liquid  films  on  the  two  fractured  surfaces  again 
become  bounded  by  ice  on  both  sides.  The  film  being  excessively  thin, 
the  force  of  cohesion  is  able  to  act  across  it;  the  consequence  of  this  is, 
the  liquid  particles  pass  back  into  the  solid  state,  and  the  block  is, 
reunited  by  regelation.  Not  only  do  ice  and  ice  thus  freeze  together, 
but  regelation  also  takes  place  between  moist  ice  and  any  nonconducting 
solid  body,  as  flannel  or  sawdust ;  a  similar  explanation  to  that  just  given 
has  been  apphed  here,  substituting  another  solid  for  the  ice  on  one  side. 
It  must  be  remarked,  however,  that  many  eminent  philosophers  dissent 
from  the  explanation  here  given. 

Whatever  may  be  the  true  cause  of  regelation,  there  can  be  no  doubt 
that  this  interesting  observation  of  Faraday's  explains  many  natural 
phenomena.  For  example,  the  formation  of  a  snowball  depends  on  the 
regelation  of  the  snow  granules  composing  it,  and  as  regelation  cannot 
take  place  at  temperatures  below  o°  C,  for  then  both  snow  and  ice  are  dry, 
it  is  only  possible  to  make  a  coherent  snowball  when  the  snow  is  melting. 

The  snow  bridges,  also,  which  span  wide  chasms  in  the  Alps  and  else- 
where, and  over  which  men  can  walk  in  safety,  owe  their  existence  to  the 
regelation  of  gradually  accumulating  particles  of  snow. 

915.  Glaciers.— Tyndall  has  applied  this  regelating  property  of  ice  to 
the  explanation  of  still  grander  phenomena — the  formation  and  motion 
of  glaciers,  of  which  the  following  is  a  brief  description.  In  elevated 
regions,  what  is  termed  the  snow  line  marks  the  boundary  of  eternal 
snow,  for  above  this  the  heat  of  summer  is  unable  to  melt  the  winter's 
snow.  By  the  heat  of  the  sun  and  the  consequent  percolation  of  water 
melted  from  the  surface,  the  lower  portions  of  the  snow  field  are  raised 
to  0°  C. ;  at  the  same  time  this  part  is  closely  pressed  together  by  the 
weight  of  the  snow  above,  regelation  therefore  sets  in,  converting  the 
loose  snow  into  a  coherent  mass. 


-916]  Atmospheric  Electricity.  851 

By  increasing  pressure  the  intermingled  air  which  renders  snow  opaque 
becomes  ejected  and  transparent ;  ice  then  results.  Its  own  gravity,  and 
the  pressure  from  behind,  urge  downwards  the  glacier  which  has  thus 
been  formed.  In  its  descent  from  the  mountain  the  glacier  behaves  in 
all  respects  like  a  river,  passing  through  narrow  gorges  with  comparative 
velocity,  and  then  spreading"  out  and  moving  slowly  as  its  bed  widens. 
Further,  just  as  the  central  portions  of  a  river  move  faster  than  the  sides, 
so  Professor  Forbes  has  ascertained  that  the  centre  of  a  glacier  moves 
quicker  than  its  margin,  and  from  the  same  reason  (the  difference  in  the 
friction  encountered)  the  surface  moves  more  rapidly  than  the  bottom. 
To  explain  these  facts  Forbes  assumed  ice  to  be  a  viscous  body  capable 
of  flexion,  and  flowing  hke  lava ;  but  as  ice  has  not  the  properties  of  a 
viscous  substance,  the  now  generally  accepted  explanation  of  glacier 
motion  is  that  supplied  by  the  theory  of  regelation.  According  to  this 
theory,  the  brittle  ice  of  the  glacier  is  crushed  and  broken  in  its  passage 
through  narrow  channels,  such  as  that  of  Trelaporte  on  Mont  Blanc  ;  and 
then,  as  it  emerges  from  the  gorge  which  confined  it,  becomes  reunited 
by  virtue  of  regelation ;  in  this  instance  forming  the  well-known  Mer  de 
Glace.  By  numerous  experiments  Tyndall  has  established  that  rege- 
lation is  adequate  to  furnish  this  explanation,  and  with  complete  success 
has  artificially  imitated,  on  a  small  scale,  the  moulding  of  glaciers  by 
the  crushing  and  subsequent  regelation  of  ice. 

LUMINOUS   METEORS., 

916.  Atmospheric  electricity.  Franklin's  experiment. — The  most 
frequent  luminous  phenomena,  and  the  most  remarkable  for  their  effects, 
are  those  produced  by  the  free.electricity  in. the  atmosphere.  The  first 
physicists  who  observed  the  electric  spajrk  compared  it  to  the  gleam  of 
lightning,  and  its  crackling  to  the  sound  of  thunder.  But  Franklin,  by 
the  aid  of  powerful  electrical  batteries,  first  established  a  complete 
parallel  between  lightning  and  electricity;  and  he  indicated,  in  a  memoir 
published  in  1749,  the  experiments  necessary  to  attract  electricity  from 
the  clouds  by  means  of  pointed  rods.  The  experiment  was  tried  by 
Ualibard  in  France;  and  Franklin,  pending  the  erection  of  a  pointed 
rod  on  a  spire  in  Philadelphia,  had  the  happy  idea  of  flying  a  kite, 
provided  with  a  metallic  point,  which  could  reach  the  higher  regions 
of  the  atmosphere.  In  June  1752,  during  stormy  weather,  he  flew 
the  kite  in  a  field  near  Philadelphia.  The  kite  was  flown  with  ordinary 
pack-thread,  at  the  end  of  which  Franklin  attached  a  key,  and  to  the  key 
a  silk  cord,  in  order  to  insulate  the  apparatus  ;  he  then  fixed  the  silk  cord 
to  a  tree,  and  having  presented  his  hand  to  the  key,  at  first  he  obtained  no 
spark.  He  was  beginning  to  despair  of  success,  when,  rain  having  fallen, 
the  cord  became  a  good  conductor,  and  a  spark  passed.  Franklin,  in  his 
letters,  describes  his  emotion  on  witnessing  the  success  of  the  experiment 
as  being  so  great  that  he  could  not  refrain  from  tears. 

Franklin,  who  had  discovered  the  power  of  points  (695),  but  who  did 
not  understand  its  explanation,  imagined  that  the  kite  withdrew  from  the 


852 


Meteorology. 


[916- 


cloud  its  electricity ;  it  is,  in  fact,  a  simple  case  of  induction,  and  depends 
on  the  inductive  action  which  the  thunder-cloud  exerts  upon  the  kite  and 
the  cord. 

917.  Apparatus  to  Investigrate  tbe  electricity  of  the  atmosphere. — 

The  apparatus  used  to  ascertain  the  presence  of  electricity  in  the  atmo- 
sphere are :  the  electroscope,  either  with  pith  balls,  straw,  or  gold  leaf : 
the  apparatus  first  used  by  Dalibard,  and  which  consisted  of  an  insulated 
iron  rod,  36  yards  in  height :  arrows  discharged  into  the  atmosphere,  and 
even  kites  and  captive  balloons. 

To  observe  the  electricity  in  fine  weather,  when  the  amount  is  generally 
small,  an  electrometer  is  used,  as  devised  by  Saussure  for  this  kind  of  in- 
vestigation. It  is  an  electroscope  similar  to  that 
already  described,  but  the  rod  to  which  the  gold 
leaves  are  fixed  is  surmounted  by  a  conductor  2  feet 
in  length,  and  terminating  either  in  a  knob  or  a 
point  (fig,  756).  To  protect  the  apparatus  against 
rain,  it  is  covered  with  a  metallic  shield  4  inches 
in  diameter.  The  glass  case  is  square,  instead  of 
being  round,  and  .a  divided  scale  on  its  inside  face 
indicates  the  divergence  of  the  gold  leaves  or  of  the 
straws.  This  electrometer  only  gives  signs  of  atmo- 
spheric electricity  as  long  as  it  is  raised  in  the 
atmosphere,  so  that  it  is  in  layers  of  air  of  which 
the  electrical  condition  is  superior  to  its  own. 

To  ascertain  the  electricity  of  the  atmosphere, 
Saussure  also  used  a  copper  ball,  which  he  pro- 
jected vertically  with  his  hand.  This  ball  was  fixed 
to  one  end  of  a  metallic  wire,  the  other  end  of 
which  was  attached  to  a  ring,  which  could  glide 
along  the  conductor  of  the  electrometer.  From 
the  divergence  of  the  straws,  or  of  the  gold  leaves, 
the  electrical  condition  of  the  air  at  the  height 
which  the  ball  attained  could  be  determined.  M. 
Becquerel,  in  experiments  made  on  the  St.  Bernard, 
improved  Saussure's  apparatus,  by  substituting  for 
the  knob  an  arrow,  which  was  projected  into  the 
atmosphere  by  means  of  a  bow.  A  gilt  silk  thread, 
88  yards  long,  was  fixed  with  one  end  to  the  arrow, 
while  the  other  end  was  attached  to  the  stem  of  an 
electroscope.  Peltier  used  a  gold-leaf  electroscope, 
at  the  top  of  which  was  a  somewhat  large  copper 
globe.  Provided  with  this  instrument,  the  observer 
stations  himself  in  a  commanding  position — it  is  then  quite  sufficient  to 
raise  the  electroscope  even  a  foot  or  so  to  obtain  signs  of  electricity. 

To  observe  the  electricity  of  clouds,  where  the  tension  is  very  con- 
siderable, use  is  made  of  a  long  bar  terminating  in  a  point.  This  bar, 
which  is  insulated  with  care,  is  fixed  to  the  summit  of  a  building,  and  its 
lower  end  is  connected  with  an  electrometer,  or  even  an  electric  chimes 


Fig.  756. 


-918]  Ordinary  Electricity  of  the  Atmosphere.  853 

(fig.  559),  which  announces  the  presence  of  thunder-clouds.  As,  however, 
the  bar  can  then  give  dangerous  shocks,  a  metalHc  ball  must  be  placed 
near  it,  which  is  well  connected  with  the  ground,  and  which  is  nearer  the 
bar  than  the  observer  himself ;  so  that  if  a  discharge  should  ensue,  it  will 
strike  the  ball  and  not  the  observer.  Professor  Richmann,  of  St.  Peters- 
burg, was  killed  in  an  experiment  of  this  kind,  by  a  discharge  which 
struck  him  on  the  forehead. 

Sometimes  also  captive  balloons  or  kites  have  been  used,  provided 
with  a  point,  and  connected  by  means  of  a  gilt  cord  with  an  electrometer. 

A  good  collector  of  atmospheric  electricity  consists  of  a  fishing-rod 
with  an  insulated  handle  which  projects  from  an  upper  window.  At  the 
summit  is  a  bit  of  lighted  amadou  held  in  a  metallic  forceps,  the  smoke 
of  which,  being  an  excellent  conductor,  conveys  the  electricity  of  the  air 
down  a  wire  attached  to  the  rod.  A  sponge  moistened  with  alcohol,  and 
set  on  fire,  is  also  an  excellent  conductor. 

A  very  convenient  instrument  for  investigating  atmospheric  electricity 
has  been  introduced  by  Sir  W.  Thomson  ;  it  consists  of  an  insulated  can 
of  water  placed  on  a  table  or  on  a  window-sill  on  the  ijiside.  The 
water  discharges  through  a  zinc  nozzle  at  the  end  of  a  narrow  pipe  which 
projects  through  the  partially  open  window  to  a  distance  of  two  or  three 
feet,  with  a  head  of  water  of  about  10  inches,  and  a  discharge  so  slow  that 
there  is  no  trouble  in  replenishing  the  can  ;  the  atmospheric  electricity  is 
quickly  collected  and  may  be  examined  by  connecting  the  can  with  any 
electrometer. 

918.  Ordinary  electricity  of  the  atmosphere. — By  means  of  the  dif- 
ferent apparatus  which  have  been  described,  it  has  been  found  that  the 
presence  of  electricity  in  the  atmosphere  is  not  confined  to  stormy 
weather,  but  that  the  atmosphere  always  contains  free  electricity, 
usually  positive  but  sometimes  negative.  When  the  sky  is  cloudless,  the 
electricity  is  always  positive,  but  it  varies  in  amount  with  the  height  of 
the  locality,  and  with  the  time  of  day.  The  amount  is  greatest  in  the 
highest  and  most  isolated  places.  No  trace  of  positive  electricity  is  found 
in  houses,  streets,  and  under  trees  ;  in  towns  positive  electricity  is  most 
perceptible  in  large  open  spaces,  on  quays,  or  on  bridges.  In  all  cases, 
positive  electricity  is  only  found  at  a  certain  height  above  the  ground. 
On  flat  land,  it  only  becomes  perceptible  at  a  height  of  5  feet ;  above  that 
point  it  increases  according  to  a  law  which  is  not  made  out,  but  which 
seems  to  depend  on  the  hygrometric  state  of  the  air. 

At  sunrise  the  free  positive  electricity  is  feeble  ;  it  increases  up  to 
1 1  o'clock,  according  to  the  season,  and  then  attains  its  first  maximum. 
It  then  decreases  rapidly  until  a  Httle  before  sunset,  and  then  increases 
till  it  reaches  its  second  maximum,  a  few  hours  after  sunset ;  the  re- 
mainder of  the  night  the  electricity  decreases  until  sunrise.  Thus  the 
greatest  amount  of  electricity  is  observed  when  the  barometric  pressure 
is  greatest.  These  increasing  and  decreasing  periods,  which  are  ob- 
served all  the  year,  are  more  perceptible  when  the  sky  is  clearer,  and  the 
weather  more  settled.  The  positive  electricity  of  fine  weather  is  much 
stronger  in  winter  than  in  summer. 


854  Meteorology,  [918- 

In  foggy  weather  the  electricity  of  the  air  is  more  strongly  positive 
than  at  other  times.  When  the  sky  is  clouded,  the  electricity  is  some- 
times positive  and  sometimes  negative.  It  often  happens  that  the 
electricity  changes  its  sign  several  times  in  the  course  of  the  day,  owing 
to  the  passage  of  an  electrified  cloud.  During  storms,  and  when  it  rains 
or  snows,  the  atmosphere  may  be  positively  electrified  one  day,  and 
negatively  the  next,  and  the  numbers  of  the  two  sets  of  days  are  virtually 
equal. 

The  electricity  of  the  ground  has  been  found  by  Peltier  to  be  always 
negative,  but  to  different  extents,  according  to  the  hygrometric  state  and 
temperature  of  the  air. 

919.  Causes  of  the  atmosplierie  electricity. — Many  hypotheses  have 
been  propounded  to  explain  the  origin  of  the  atmospheric  electricity. 
Some  have  ascribed  it  to  the  friction  of  the  air  against  the  ground,  some 
to  the  vegetation  of  plants,  or  to  the  evaporation  of  water.  Some,  again, 
have  compared  the  earth  to  a  vast  voltaic  pile,  and  others  to  a  thermo- 
electrical  apparatus.  Many  of  these  causes  may,  in  fact,  concur  in  pro- 
ducing the  phenomena. 

Volta  first  showed  that  the  evaporation  of  water  produced  electricity. 
Pouillet  and  others  have  subsequently  shown  that  no  electricity  is  pro- 
duced by  the  evaporation  of  distilled  water ;  but  if  an  alkali  or  a  salt  is 
dissolved,  even  in  small  quantity,  the  vapour  is  positively  and  the  solution 
is  negatively  electrified.  The  reverse  is  the  case  if  the  water  contains 
acid.  Hence  it  has  been  assumed  that  as  the  waters  which  exist  on  the 
surface  of  the  earth  and  on  the  sea  always  contain  salt  dissolved,  the 
vapours  disengaged  ought  to  be  positively  and  the  earth  negatively  elec- 
trified. 

The  development  of  electricity  by  evaporation  may  be  observed  by 
heating  strongly  a  platinum  dish,  adding  to  it  a  small  quantity  of  liquid, 
and  placing  it  on  the  upper  plate  of  the  condensing  electroscope  (fig.  567), 
taking  care  to  connect  the  lower  plate  with  the  ground.  When  the 
water  of  the  capsule  is  evaporated,  the  connexion  with  the  ground  is 
broken,  and  the  upper  plate  raised.  The  gold  leaves  then  diverge  if  the 
water  contained  salts,  but  remain  quiescent  if  the  water  was  pure. 

Reasoning  from  this  experiment,  Pouillet  has  ascribed  the  development 
of  electricity  by  evaporation  to  the  separation  of  particles  of  water  from 
the  substances  dissolved  ;  but  Reich  and  Riess  have  shown  that  the  elec- 
tricity disengaged  during  evaporation  could  be  attributed  to  the  friction 
which  the  particles  of  water  carried  away  in  the  current  of  vapour  exercise 
against  the  sides  of  the  vessel,  just  as  in  Armstrong's  electrical  machine. 
By  a  recent  series  of  experiments,  Gaugain  has  arrived  at  the  same  result : 
and  thinks  it  no  longer  allowable  to  ascribe  the  atmospheric  electricity 
to  any  changes  that  take  place  during  the  tranquil  evaporation  of  sea 
water. 

In  support  of  the  hypothesis  which  considers  the  earth  as  an  immense 
source  of  voltaic  electricity  due  to  chemical  actions,  Becquerel  has  re- 
cently published  numerous  experiments  to  show  that  when  earth  and 
water  come  in  contact  electricity  is  always  produced  :  the  earth  taking  a 


-921]  Electricity  of  Clouds.     Lightning.  855 

considerable  excess  of  positive  or  negative  electricity,  and  the  water  a 
corresponding  excess  of  the  opposite  electricity,  according  to  the  nature 
of  the  salts  or  other  compounds  which  the  water  held  dissolved.  This 
is  a  general  fact  which,  according  to  M.  Becquerel,  is  liable  to  no  ex- 
ception. 

Becquerel  experimented  with  an  ordinary  multiplier,  the  wire  of  which 
was  connected  with  two  platinum  plates  immersed  in  the  pieces  of  ground, 
or  the  water  whose  electrical  condition  he  wished  to  investigate.  He 
thus  found  that  when  two  moist  pieces  of  ground  are  connected,  that 
which  contained  the  strongest  solution  took  an  excess  of  positive  elec- 
tricity. He  found  that  in  the  neighbourhood  of  a  river,  even  at  some 
distance,  the  land  and  objects  placed  on  the  surface  possessed  an  excess 
of  negative  electricity,  while  the  water  and  the  aquatic  plants  which 
swam  on  the  surface  where  charged  with  positive  electricity.  But  accord- 
ing to  the  nature  of  the  substances  dissolved  in  the  water,  different  effects 
were  produced.  As  from  Becquerel's  experiments,  the  waters  are  some- 
times positive  and  sometimes  negative,  and  the  earth  in  a  contrary  con- 
dition, it  follows  that  water  in  evaporating  must  constantly  send  into  the 
atmosphere  an  excess  of  positive  or  negative  electricity,  while  the  earth, 
by  the  vapours  disengaged  on  its  surface,  allows  an  excess  of  the  contrary 
electricity  to  escape.  Now  this  excess  of  electricity  ought  necessarily  to 
influence  the  distribution  of  the  electricity  in  the  atmosphere,  and  may 
serve  to  explain  how  it  is  that  the  clouds  are  sometimes  positively  and 
sometimes  negatively  electrified. 

920.  Electricity  of  clouds. — In  general  the  clouds  are  all  electrified, 
sometimes  positively  and  sometimes  negatively,  and  only  differ  in  their 
greater  or  less  tension.  The  formation  of  positive  clouds  is  usually 
ascribed  to  the  vapours  which  are  disengaged  from  the  ground,  and  con- 
dense in  the  higher  regions.  Negative  clouds  are  supposed  to  result  from 
fogs,  which,  by  their  contact  with  the  ground,  become  charged  with  nega- 
tive fluid,  which  they  retain  on  rising  into  the  atmosphere  ;  or  that, 
separated  from  the  ground  by  layers  of  moist  air,  they  have  been  nega- 
tively electrified  by  induction  from  the  positive  clouds,  which  have  re- 
pelled into  the  ground  positive  electricity. 

921.  Iiigrlitningr. — This,  as  is  well  known,  is  the  dazzling  light  emitted 
by  the  electric  spark  when  it  shoots  from  clouds  charged  with  electricity. 
In  the  lower  regions  of  the  atmosphere  the  light  is  white,  but  in  the 
higher  regions,  where  the  air  is  more  rarefied,  it  takes  a  violet  tint ;  as 
does  the  spark  of  the  electrical  machine  in  a  rarefied  medium  (740). 

The  flashes  of  lightning  are  sometimes  several  leagues  in  length  ;  they 
generally  pass  through  the  atmosphere  in  a  zigzag  direction :  a  phenome- 
non ascribed  to  the  resistance  offered  by  the  air  condensed  by  the  passage 
of  a  strong  discharge.  The  spark  then  diverges  from  a  right  line,  and 
takes  the  direction  of  least  resistance.  In  vacuo  electricity  passes  in  a 
straight  line. 

Several  kinds  of  Hghtning  flashes  may  be  distinguished — i.  the  zigzag 
flashes  which  move  with  extreme  velocity  in  the  form  of  a  fine  of  fire 
with  sharp  outlines,  and  which  entirely  resemble  the  spark  of  an  clec- 


856  Meteorology.  [921- 

trical  machine  ;  2.  the  flashes  which,  instead  of  being  linear,  like  the 
preceding,  fill  the  entire  horizon  without  having  any  distinct  shape.  This 
kind,  which  is  most  frequent,  appears  to  be  produced  in  the  cloud  itself, 
and  to  illuminate  the  mass.  According  to  Kundt  the  number  of  sheet 
discharges  are  to  the  zigzag  discharges  as  11:6;  and  from  spectrum 
observations  it  would  appear  that  the  former  are  brush  discharges 
between  clouds,  while  the  latter  are  true  electrical  discharges  between 
the  clouds  and  the  earth.  Another  kind  is  called  heat  lightning,  because 
it  -illuminates  the  summer  nights  without  the  presence  of  any  clouds 
above  the  horizon,  and  without  producing  any  sound.  The  most  prob- 
able of  the  many  hypotheses  which  have  been  proposed  to  account  for  its 
origin,  is  that  which  supposes  it  to  consist  of  ordinary  lightning  flashes, 
which  strike  across  the  clouds  at  such  distances  that  the  rolling  of 
thunder  cannot  reach  the  ear  of  the  observer.  There  is  further  the  very 
unusual  phenomenon  oi globe  light ni?tg,  or  the  flashes  which  appear  in  the 
form  of  globes  of  fire.  These,  which  are  sometimes  visible  for  as  much 
as  ten  seconds,  descend  from  the  clouds  to  the  earth  with  such  slowness 
that  the  eye  can  follow  them.  They  often  rebound  on  reaching  the  ground  ; 
at  other  times  they  burst  and  explode  with  a  noise  like  that  of  the  report 
of  many  cannon. 

The  duration  of  the  light  of  the  first  three  kinds  does  not  amount  to  a 
thousandth  of  a  second,  as  has  been  determined  by  Mr.  Wheatstone  by 
means  of  a  rotating  wheel,  which  was  turned  so  rapidly  that  the  spokes 
were  invisible :  on  illuminating  it  by  the  Hghtning  flash,  its  duration  was 
so  short  that,  whatever  the  velocity  of  rotation  of  the  wheel,  it  appeared 
quite  stationary;  that  is,  its  displacement  is  not  perceptible  during  the 
time  the  lightning  exists. 

922.  Tbunder. — The  thunder  is  the  violent  report  which  succeeds 
lightning  in  stormy  weather.  The  lightning  and  the  thunder  are  always 
simultaneous,  but  an  interval  of  several  seconds  is  always  observed 
between  these  two  phenomena,  which  arises  from  the  fact  that  sound 
only  travels  at  the  rate  of  about  1,100  feet  in  a  second  (216),  while  the 
passage  of  light  is  almost  instantaneous.  Hence  an  observer  will  only 
hear  the  noise  of  thunder  five  or  six  seconds,  for  instance,  after  the 
lightning,  according  as  the  distance  of  the  thunder-cloud  is  five  or  six 
times  1,100  feet.  The  noise  of  thunder  arises  from  the  disturbance  which 
the  electric  discharge  produces  in  the  air,  and  which  may  be  witnessed 
in  Kinnersley's  thermometer.  Near  the  place  where  the  lightning  strikes, 
the  sound  is  dry  and  of  short  duration.  At  a  greater  distance  a  series 
of  reports  are  heard  in  rapid  succession.  At  a  still  greater  distance  the 
noise,  feeble  at  the  commencement,  changes  into  a  prolonged  rolling  sound 
of  varying  intensity.  If  the  lightning  is  at  a  greater  distance  than  14  or 
1 5  miles,  it  is  no  longer  heard,  for  sound  is  more  imperfectly  propagated 
through  air  than  through  solid  bodies ;  hence,  there  are  lightning 
discharges  without  thunder;  these  occur  at  times  when  the  sky  is  cloud- 
less. 

Some  attribute  the  noise  of  the  rolling  of  thunder  to  the  reflection  of 
sound  from  the  ground  and  from  the  clouds.     Others  have  considered 


-924]  Effects  of  L ighUting.  857 

the  lightning  not  as  a  single  discharge,  but  as  a  series  of  discharges, 
each  of  which  gives  rise  to  a  particular  sound.  But  as  these  partiaL 
discharges  proceed  from  points  at  different  distances,  and  from  zones  of 
unequal  density,  it  follows  not  only  that  they  reach  the  ear  of  the  observer 
successively,  but  that  they  bring  sounds  of  unequal  density,  which  occasion 
the  duration  and  inequality  of  the  rolling.  The  phenomenon  has  finally 
been  ascribed  to  the  zigzags  of  lightning  themselves,  assuming  that  the  air 
at  each  salient  angle  is  at  its  greatest  compression,  which  would  produce 
the  unequal  intensity  of  the  sound. 

923.  Effects  of  lig^btningr. — The  lightning  discharge  is  the  electric 
discharge  which  strikes  between  a  thunder-cloud  and  the  ground.  The 
latter,  by  the  induction  from  the  electricity  of  the  cloud,  becomes  charged 
with  contrary  electricity ;  and  when  the  tendency  of  the  two  electricities 
to  combine  exceeds  the  resistance  of  the  air,  the  spark  passes,  which  is 
often  expressed  by  saying  that  a  thunder-belt  has  fallen.  Lightning  in 
general  strikes  from  above,  but  ascending  lightning  is  also  sometimes 
observed ;  probably  this  is  the  case  when  the  clouds  being  negatively  the 
earth  is  positively  electrified,  for  all  experiments  show  that  at  the  ordinary 
pressure  the  positive  fluid  passes  through  the  atmosphere  more  easily 
than  negative  electricity. 

From  the  first  law  of  electrical  attraction,  the  discharge  ought  to  fall 
first  on  the  nearest  and  best-conducting  objects,  and,  in  fact,  trees, 
elevated  buildings,  metals,  are  more  particularly  struck  by  the  discharge. 
Hence  it  is  imprudent  to  stand  under  trees  during  a  thunder-storm. 

The  effects  of  lightning  are  very  varied,  and  of  the  same  kind  as  those 
of  batteries  (736),  but  of  far  greater  intensity.  The  lightning  discharge 
kills  men  and  animals,  inflames  combustible  matters,  melts  metals,  breaks 
bad  conductors  in  pieces.  When  it  penetrates  the  ground  it  melts  the 
siliceous  substance  in  its  way,  and  thus  produces  in  the  direction  of  the 
discharge  those  remarkable  vitrified  tubes  c^W^di  fulgurites,  some  of  which 
are  as  much  as  12  yards  in  length.  When  it  strikes  bars  of  iron,  it  mag- 
netises them,  and  often  inverts  the  poles  of  compass  needles. 

After  the  passage  of  lightning,  a  highly  peculiar  odour  is  generally 
produced,  like  that  perceived  in  a  room  in  which  an  electrical  machine 
is  being  worked.  This  "odour  was  first  attributed  to  the  formation  of  an 
oxygenised  compound,  to  which  the  name  ozone  was  given :  but  S-chonbein, 
in  1840,  has  shown  that  ozone  is  a  peculiar  allotrophic  modification  of 
oxygen. 

924.  Return  sbock. — This  is  a  violent  and  sometimes  fatal  shock 
which  men  and  animals  experience,  even  when  at  a  great  distance  from 
the  place  where  the  lightning  discharge  passes.  This  is  caused  by  the 
inductive  action  which  the  thunder-cloud  exerts  on  bodies  placed  within 
the  sphere  of  its  activity.  These  bodies  are  then,  like  the  ground,  charged 
with  the  opposite  electricity  to  that  of  the  cloud ;  but  when  the  latter  is 
discharged  by  the  recombination  of  its  electricity  with  that  of  the  ground 
the  induction  ceases,  and  the  bodies  reverting  rapidly  from  the  electrical 
state  to  the  neutral  state,  the  concussion  in  question  is  produced,  the  return 
shock.     A  gradual  decomposition  and  reunion  of  the  electricity  produces 


858  Meteorology.  [924- 

invisible  effects ;  yet  it  appears  that  such  disturbances  of  the  electrical 
equilibrium  are  perceived  by  nervous  persons. 

The  return  shock  is  always  less  violent  than  the  direct  one ;  there  is 
no  instance  of  its  having  produced  any  inflammation,  yet  plenty  of  cases 
in  which  it  has  killed  both  men  and  animals  ;  in  such  cases  no  broken 
limbs,  wounds,  or  burns,  are  observed. 

The  return  shock  may  be  imitated  by  placing  a  gold  leaf  electroscope 
connected  by  a  wire  with  the  ground  near  an  electrical  machine ;  when 
the  machine  is  worked  at  each  spark  taken  from  it  the  gold  leaves 
diverge. 

925.  Xlgrhtning  conductor. — The  ordinary  form  of  this  instrument  is 
an  iron  rod,  through  which  passes  the  electricity  of  the  ground  attracted 
by  the  opposite  electricity  of  the  thunder-clouds.  It  was  invented  by 
Franklin  in  1755. 

There  are  two  principal  parts  in  lightning  conductors ;  the  rod  and 
the  conductor.  The  rod  is  a  pointed  bar  of  iron,  fixed  vertically  to  the 
roof  of  the  edifice  to  be  protected;  it  is  from  6  to  10  feet  in  height,  and 
its  basal  section  is  about  2  or  3  inches  in  diameter.  The  conductor  is 
a  bar  of  iron  which  descends  from  the  bottom  of  the  rod  to  the  ground, 
which  it  penetrates  to  some  distance.  As,  in  consequence  of  their 
rigidity,  iron  bars  cannot  always  be  well  adapted  to  the  exterior  of 
buildings,  they  are  best  formed  of  wire  cords,  such  as  are  used  for  rigging 
and  for  suspension  bridges.  In  a  report  made  by  the  Academy  of 
Sciences  on  the  construction  of  lightning  conductors,  the  use  of  copper 
instead  of  iron  wire  in  these  conductors  is  recommended,  inasmuch  as 
copper  is  a  better  conductor  than  iron.  The  metallic  section  of  the 
cords  ought  to  be  about  ^  a  square  inch,  and  the  individual  wires  0-04  to 
o-o6  inch  in  diameter;  they  ought  to  be  twisted  in  three  strands,  like  an 
ordinary  cord.  The  point  of  the  lightning  conductor  ought  to  be  of 
copper  instead  of  platinum,  for  the  sake  of  better  conductivity.  The 
conductor  is  usually  led  into  a  well,  and  to  connect  it  better  with  the 
soil  it  ends  in  two  or  three  ramifications.  If  there  is  no  well  in  the 
neighbourhood,  a  hole  is  dug  in  the  soil  to  the  depth  of  6  or  7  yards, 
and  the  foot  of  the  conductor  having  been  introduced,  the  hole  is  filled 
with  wood  ashes,  which  conduct  very  well  and  preserve  the  metal  from 
oxidation.     Powdered  coke  serves  the  same  purpose. 

The  action  of  a  lightning  conductor  depends  on  induction  and  the 
power  of  points  (695);  when  a  storm-cloud,  positively  electrified,  for 
instance,  rises  in  the  atmosphere,  it  acts  inductively  on  the  earth,  repels 
the  positive  and  attracts  the  negative  fluid,  which  accumulates  in  bodies 
placed  on  the  surface  of  the  soil,  the  more  abundantly  as  these  bodies  are 
at  a  greater  height.  The  tension  is  then  greatest  on  the  highest  bodies, 
which  are  therefore  most  exposed  to  the  electric  discharge  ;  but  if  these 
bodies  are  provided  with  metal  points,  like  the  rods  of  conductors,  the  nega- 
tive electricity,  withdrawn  from  the  soil  by  the  influence  of  the  cloud,  flows 
into  the  atmosphere,  and  neutralises  the  positive  electricity  of  the  cloud. 
Hence,  not  only  does  a  lightning  conductor  tend  to  prevent  the  acumu- 


-926]  -  Rainbow,  859 

lation  of  electricity  on  the  surface  of  the  earth,  but  it  also  tends  to  restore 
the  clouds  to  their  natural  state,  both  which  concur  in  preventing  light- 
ning discharges.  The  disengagement  of  electricity  is,  however,  some- 
times so  abundant,  that  the  lightning  conductor  is  inadequate  to  discharge 
the  ground,  and  the  lightning  strikes  ;  but  the  conductor  receives  the 
discharge,  in  consequence  of  its  greater  conductivity,  and  the  edifice  is 
preserved. 

Experiment  has  shown  that,  approximately,  a  lightning  conductor 
protects  a  circular  space  around  it,  the  radius  of  which  is  double  its 
height.  Thus,  a  building,  64  yards  in  length,  would  be  preserved  by  two 
rods  8  yards  in  height,  at  a  distance  of  32  yards. 

A  conductor,  to  be  efficient,  ought  to  satisfy  the  following  conditions  : 
i.  the  rod  ought  to  be  so  large  as  not  to  be  melted  if  the  discharge  passes  ; 
ii.  it  ought  to  terminate  in  a  point  to  give  readier  issue  to  the  electricity 
disengaged  from  the  ground,  hence  the  rod  is  usually  provided  with  a 
point  of  platinum  or  of  gilt  copper  ;  iii.  the  conductor  must  be  continuous 
from  the  point  to  the  ground,  and  the  connexion  between  the  rod  and 
the  ground  must  be  as  intimate  as  possible  ;  iv.  if  the  building  which  is 
provided  with  a  lightning  conductor  contains  metallic  surfaces  of  any 
extent,  such  as  zinc  roofs,  metal  gutters,  or  iron  work,  these  ought  to  be 
connected  with  the  conductor.  If  the  last  two  conditions  are  not  ful- 
filled, there  is  a  great  danger  of  lateral  discharges  :  that  is  to  say,  that  the 
discharge  takes  place  between  the  conductor  and  the  edifice,  and  then  it 
only  increases  the  danger. 

926.  Rainbow. — The  rainbow  is  a  luminous  meteor  which  appears  in 
the  clouds  opposite  the  sun  when  they  are  resolved  into  rain.  It  consists 
of  seven  concentric  arcs,  presenting  successively  the  colours  of  the  solar 
spectl-um.  Sometimes  only  a  single  bow  is  perceived,  but  there  are 
usually  two  \  a  lower  one,  the  colours  of  which  are  very  bright,  and  an 
external  or  secondary  one,  which  is  paler,  and  in  which  the  order  of  the 
colours  is  reversed.  In  the  interior  rainbow  the  red  is  the  highest 
colour  ;  in  the  other  rainbow  the  violet  is.  It  is  seldom  that  three  bows 
are  seen ;  theoretically  a  greater  number  may  exist,  but  their  colours  are 
so  feeble  that  they  are  not  perceptible. 

The  phenomenon  of  the  rainbow  is  produced  by  the  decomposition  of 
the  white  light  of  the  sun  when  it  passes  into  the  drops  and  by  its  reflec- 
tion from  their  inside  face.  In  fact,  the  same  phenomenon  is  witnessed  in 
dewdrops  and  in  jets  of  water  ;  in  short,  wherever  solar  light  passes  into 
drops  of  water  under  a  certain  angle. 

The  appearance  and  the  extent  of  the  rainbow  depend  on  the  position 
of  the  observer,  and  on  the  height  of  the  sun  above  the  horizon  ;  hence 
only  some  of  the  rays  refracted  by  the  rain  drops,  and  reflected  in  their 
concavity  to  the  eye  of  the  spectator,  are  adapted  to  produce  the  pheno- 
menon.    Those  which  do  so  are  called  elective  rays. 

To  explain  this  let  «  (fig.  757)  be  a  drop  of  water,  into  which  a  solar 
ray  S^:  penetrates.  At  the  point  of  incidence,  a,  part  of  the  light  is  re- 
flected from  the  surface  of  the  liquid  ;  another,  entering  it,  is  decomposed 


86o  Meteorology.  [926- 

and  traverses  the  drop  in  the  direction  ab.  Arrived  at  b  part  of  the  light 
emerges  from  the  rain  drop,  the  other  part  is  reflected  from  the  concave 
surface,  and  tends  to  emerge  at^.  At  this  point  the  light  is  again  par- 
tially reflected,  the  remainder  emerges  in  a  direction  gO,  which  forms 
with  the  incident  ray,  S^:,  an  angle,  called  the  angle  of  deviation.  It  is 
such  rays  as^O,  proceeding  from  the  side  next  the  observer,  -jvhich  pro- 


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Fig-  757. 

duce  on  the  retina  the  sensation  of  colours,  provided  the  light  is  suffi- 
ciently intense. 

It  can  be  shown  mathematically  that  in  the  case  of  a  series  of  rays 
which  impinge  on  the  same  drop,  and  only  undergo  a  reflection  in  the 
interior,  the  angle  of  deviation  increases  from  the  ray  ^"n,  for  which  it  is 
zero,  up  to  a  certain  limit,  beyond  which  it  decreases,  and  that  near  this 
limit  rays  passing  parallel  into  a  drop  of  rain,  also  emerge  parallel.  From 
this  parallelism  a  beam  of  light  is  produced  sufficiently  intense  to  impress 
the  retina  ;  these  are  the  rays  which  emerge  parallel  and  are  efficient. 

As  the  different  colours  which  compose  white  light  are  unequally  re- 
frangible, the  maximum  angle  of  deviation  is  not  the  same  for  all.  For 
red  rays  the  angle  of  deviation  corresponding  to  the  active  rays  is  42°  2', 
and  for  violet  rays  it  is  40°  17'.  Hence,  for  all  drops  placed  so  that  rays 
proceeding  from  the  sun  to  the  drop  make,  with  those  proceeding  from 
the  drop  to  the  eye,  an  angle  of  42°  2',  this  organ  will  receive  the  sen- 
sation of  red  light ;  this  will  be  the  case  with  all  drops  situated  on  the 
circumference  of  the  base  of  a  cone,  the  summit  of  which  is  the  spectator's 
eye  ;  the  axis  of  this  cone  is  parallel  to  the  sun's  rays,  and  the  angle 
formed  by  the  two  opposed  generating  lines  is  84°  4'.  This  explains  the 
formation  of  the  red  band  in  the  rainbow  :  the  angle  of  the  cone  in  the 
case  of  the  violet  band  is  80°  34'. 

The  cones  corresponding  to  each  band  have  a  common  axis  called  the 
visual  axis.  As  this  right  line  is  parallel  to  the  rays  of  the  sun,  it  follows 
that  when  this  axis  is  on  the  horizon,  the  visual  axis  is  itself  horizontal, 
and  the  rainbow  appears  as  a  semicircle.  If  the  sun  rises,  the  visual  axis 
sinks,  and  with  it  the  rainbow.     Lastly,  when  the  sun  is  at  a  height  of 


-927]  Aurora  Borealis.  86 1 

42°  2',  the  arc  disappears  entirely  below  the  horizon.  Hence  the  phe- 
nomenon of  the  rainbow  never  takes  place  except  in  the  morning  and 
evening. 

What  has  been  said  refers  to  the  interior  arc.  The  secondary  bow  is 
formed  by  rays  which  have  undergone  two  reflections,  as  shown  by  the 
ray  S^i  dfeO,  in  the  drop  p.  The  angle  S'lO  formed  by  the  emergent 
and  incident  ray  is  called  the  angle  of  deviation.  This  angle  is  no  longer 
susceptible  of  a  maximum,  but  of  a  minimum,  which  varies  for  each  kind 
of  rays,  and  to  which  also  efficient  rays  correspond.  It  is  calculated  that 
the  minimum  angle  for  violet  rays  is  54°  7',  and  for  red  rays  only  50°  57'; 
hence  it  is  that  the  red  bow  is  here  on  the  inside,  and  the  violet  arc  on 
the  outside.  There  is  a  loss  of  light  for  every  internal  reflection  in  the 
drop  of  rain,  and,  therefore,  the  colours  of  the  secondary  bow  are  always 
feebler  than  those  of  the  internal  one.  The  secondary  bow  ceases  to  be 
visible  when  the  sun  is  54°  above  the  horizon. 

The  moon  sometimes  produces  rainbows  like  the  sun,  but  they  are 
very  pale. 

927.  Aurora  borealis. — The  aurora  bo7'ealis,  or  northern  light,  or 
more  properly,  pola?'  aurora,  is  a  remarkable  luminous  phenomenon  which 
is  frequently  seen  in  the  atmosphere  at  the  two  terrestrial  poles.  The 
following  is  a  description  of  an  aurora  borealis  observed  at  Bossekop,  in 
Lapland,  lat.  70°,  in  the  winter  of  1 838-1839. 

In  the  evening,  between  4  and  8  o'clock,  the  upper  part  of  the  fog 
which  usually  prevails  to  the  north  of  Bossekop  became  coloured.  This 
light  became  more  regular,  and  formed  an  indistinct  arc  of  a  pale  yellow, 
with  its  concave  side  turned  towards  the  earth,  while  its  summit  was  in 
the  magnetic  meridian. 

Blackish  rays  soon  separated  the  luminous  parts  of  the  arc.  Luminous 
rays  formed,  becoming  alternately  rapidly  and  slowly  longer  and  shorter, 
their  lustre  suddenly  increasing  and  diminishing.  The  bottom  of  these 
rays  always  showed  the  brightest  light,  and  formed  a  more  or  less  regular 
arc.  The  length  of  the  rays  was  very  variable,  but  they  always  con- 
verged towards  the  same  point  of  the  horizon,  which  was  in  the  prolon- 
gation of  the  north  end  of  the  dipping  needle;  sometimes  the  rays  were 
prolonged  as  far  as  their  point  of  meeting,  and  thus  appeared  like  a  frag- 
ment of  an  immense  cupola. 

The  arc  continued  to  rise  in  an  undulatory  motion  towards  the  zenith. 
Sometimes  one  of  its  feet  or  even  both  left  the  horizon ;  the  folds  became 
more  distinct  and  more  numerous ;  the  arc  was  now  nothing  more  than 
a  long  band  of  rays  convoluted  in  very  graceful  shapes,  forming  what  is 
called  the  boreal  crown.  The  lustre  of  the  rays  varied  suddenly  in  in- 
tensity, and  attained  that  of  stars  of  the  first  magnitude  ;  the  rays  darted 
with  rapidity,  the  curves  formed  and  reformed  like  the  folds  of  a  serpent 
(fig.  758),  the  base  was  red,  the  middle  green,  while  the  remainder  re- 
tained its  bright  yellow  colour.  Lastly,  the  lustre  diminished,  the  colours 
disappeared  :  everything  became  feebler  or  suddenly  went  out. 

A  French  scientific  commission  to  the  North  observed  150  auroras 
boreales  in  200  days;  it  appears  that  at  the  poles,  nights  without  an  aurora 


862 


Meteorology, 


[927- 


borealis  are  quite  exceptional,  so  that  it  may  be  assumed  that  they  take 
place  every  night,  though  with  varying  intensity.  They  are  visible  at  a 
considerable  distance  from  the  poles,  and  over  an  immense  area.     Some- 


Fig.  758. 


times  the  same  aurora  borealis  has  been  seen  at  the  same  time  at  Moscow, 
Warsaw,  Rome,  and  Cadiz. 

Numerous  hypotheses  have  been  devised  to  account  for  the  aurorae 
boreales.  The  constant  direction  of  their  arc  as  regards  the  magnetic 
meridian,  and  their  action  on  the  magnetic  needle  (663),  show  that  they 
ought  to  be  attributed  to  electric  currents  in  the  higher  regions  of  the 
atmosphere.  This  hypothesis  is  confirmed  by  the  circumstance  observed 
in  France  and  other  countries  on  August  29  and  September  i,  1859,  that 
two  brilliant  auroras  boreales  acted  powerfully  on  the  wires  of  the  electric 
telegraph  ;  the  alarums  were  for  a  long  time  violently  rung,  and  despatches 
were  frequently  interrupted  by  the  spontaneous  abnormal  working  of  the 
apparatus. 

The  spectrum  of  the  aurora  borealis  has  been  found  by  Vogel  to  consist 
of  five  lines  in  the  green,  and  of  an  indistinct  line  in  the  blue :  to  which 
must  be  added  a  red  line  due  to  the  red  protuberances ;  these  lines  are 
the  same  as  those  of  nitrogen  greatly  rarefied  and  at  a  low  temperature. 

According  to  M.  dela  Rive  the  aurorae  boreales  are  due  to  electric  dis- 
charges which  take  place  in  polar  regions  between  the  positive  electricity 
of  the  atmosphere  and  the  negative  electricity  of  the  terrestrial  globe  ; 
electricities  which  themselves  are  separated  by  the  action  of  the  sun, 
principally  on  the  equatorial  regions. 

The  occurrence  of  irregular  currents  of  electricity  which  manifest  them- 
selves by  abnormal  disturbances  of  telegraphic  communications  is  not  in- 
frequent ;  such  currents  have  received  the  name  of  earth  currents.    Sabine 


-929]  Climatology.  863 

has  found  that  these  magnetic  disturbances  are  due  to  a  peculiar  action  of 
the  sun,  and  probably  independently  of  its  radiant  heat  and  light.  It  has 
also  been  ascertained  that  the  aurora  borealis  as  well  as  earth  currents  in- 
variably accompany  these  magnetic  disturbances.  According  to  Balfour 
Stewart,  aurorse  and  earth  currents  are  to  be  regarded  as  secondary  cur- 
rents due  to  small  but  rapid  changes  in  the  earth's  magnetism ;  he  likens 
the  body  of  the  earth  to  the  magnetic  core  of  a  Ruhmkorff' s  machine,  the 
lower  strata  of  the  atmosphere  forming  the  insulator,  while  the  upper  and 
rarer,  and  therefore  electrically  conducting  strata,  may  be  considered  as 
the  secondary  coil. 

On  this  analogy  the  sun  may  perhaps  be  likened  to  the  primary  cur- 
rent which  performs  the  part  of  producing  changes  in  the  magnetic  state 
of  the  core.  Now  in  Ruhmkorff's  machine  the  energy  of  the  secondary 
current  is  derived  from  that  of  the  primary  current.  Thus  if  the  analogy 
be  correct,  the  energy  of  the  aurora  borealis  may  in  like  manner  come 
from  the  sun ;  but  until  we  know  more  of  the  connection  between  the 
sun  and  terrestrial  magnetism  these  ideas  are  to  be  accepted  with  some 
reserve. 

CLIMATOLOGY. 

928.  »Kean  temperature. — The  inean  daily  tejnper attire,  or  simply 
temperature,  is  that  obtained  by  adding  together  24  hourly  observations, 
and  dividing  by  24.  A  very  close  approximation  to  the  mean  temperature 
is  obtained  by  taking  the  mean  of  the  maxima  and  minima  temperatures 
of  the  day  and  of  the  night,  which  are  determined  by  means  of  the  maxi- 
mum and  minimum  thermometers.  These  ought  to  be  protected  from  the 
solar  rays,  raised  above  the  ground,  and  far  from  all  objects  which  might 
influence  them  by  their  radiation. 

The  temperatures  of  a  month  is  the  mean  of  those  of  30  days,  and  the 
temperature  of  the  year  is  the  mean  of  those  of  12  months.  Finally,  the 
temperature  of  a  place  is  the  mean  of  its  annual  temperature,  for  a  great 
series  of  years.  The  mean  temperature  of  London  is  8*28°  C,  or  46-9°  F. 
The  temperatures  in  all  cases  are  those  of  the  air  and  not  those  of  the 
ground. 

929.  Causes  wbicb  modify  the  temperature  of  ttae  air.  —  The 
principal  causes  which  modify  the  temperature  of  the  air  are  the  latitude 
of  a  place,  its  height,  the  direction  of  the  winds,  and  the  proximity  of 
seas. 

Influence  of  the  latitude.  The  influence  of  the  latitude  arises  from  the 
greater  or  less  obliquity  of  the  solar  rays,  for  as  the  quantity  of  heat 
absorbed  is  greater  the  nearer  the  rays  are  to  the  normal  incidence  (382), 
the  heat  absorbed  decreases  from  the  equator  to  the  poles,  for  the  rays 
are  then  more  oblique.  This  loss  is,  however,  in  summer,  in  the  tem- 
perate and  arctic  zones,  partially  compensated  by  the  length  of  the  days. 
Under  the  equator,  where  the  length  of  the  days  is  constant,  the  tem- 
perature is  almost  invariable ;  in  the  latitude  of  London,  and  in  more 
northerly  countries,  where  the  days  are  very  unequal,  the  temperature 


864  Meteorology.  [929- 

varies  greatly  ;  but  in  summer  it  sometimes  rises  almost  as  high  as  under 
the  equator.  The  lowering  of  the  temperature  produced  by  the  latitude 
is  small ;  thus  in  a  latitude  of  115  miles  north  of  France,  the  temperature 
is  only  1°  C.  lower. 

hifltience  of  altitude.  The  height  of  a  place  has  a  much  more  consider- 
able influence  on  the  temperature  than  its  latitude.  In  the  temperate  zone 
a  diminution  of  1°  C.  corresponds  in  the  mean  to  an  ascent  of  180  yards. 

The  cooling  on  ascending  in  the  atmosphere  has  been  observed  in 
balloon  ascents,  and  a  proof  of  it  is  seen  in  the  perpetual  snows  which 
cover  the  highest  mountains.  ]t  is  caused  by  the  greater  rarefaction  of 
the  air,  which  necessarily  diminishes  its  absorbing  power ;  besides  which 
the  air  is  at  a  greater  distance  from  the  ground,  which  heats  it  by  con- 
tact ;  and  finally  dry  air  is  very  diathermanous. 

The  law  of  the  diminution  of  temperature  corresponding  to  a  greater 
height  in  the  atmosphere  has  not  been  made  out,  in  consequence  of  the 
numerous  perturbing  causes  which  modify  it,  such  as  the  prevalent  winds, 
the  hygrometric  state,  the  time  of  day,  etc.  The  difference  between  the 
temperature  of  two  places  at  unequal  heights  is  not  proportional  to  the 
difference  of  level,  but  for  moderate  heights  an  approximation  to  the  law 
may  be  made.  As  the  mean  of  a  series  of  very  careful  observations  made 
by  Mr.  Walsh  during  balloon  ascents,  a  diminution  of  1°  C.  corresponded 
to  an  increase  m  height  of  232  yards. 

Direction  of  winds.  As  winds  share  the  temperature  of  the  countries 
which  they  have  traversed,  their  direction  exercises  great  influence  on 
the  air  in  any  place.  In  Paris,  the  hottest  winds  are  the  south,  then 
come  the  south-east,  the  south-west,  the  west,  the  east,  the  north-west, 
north,  and,  lastly,  the  north-east,  which  is  the  coldest.  The  character  of 
the  wind  changes  with  the  seasons  ;  the  east  wind,  which  is  cold  in  winter, 
is  hot  in  summer. 

Proximity  of  the  seas.  The  neighbourhood  of  the  sea  tends  to  raise 
the  temperature  of  the  air,  and  to  render  it  uniform.  The  average  tem- 
perature of  the  sea  in  equatorial  and  polar  countries  is  always  higher  than 
that  of  the  atmosphere.  With  reference  to  the  uniformity  of  the  tem- 
perature, it  has  been  found  that  in  temperate  regions — that  is,  from  25°  to 
50°  of  latitude,  the  difference  between  the  maximum  and  minimum  tem- 
perature of  a  day  does  not  exceed,  on  the  sea,  2°  to  3°;  while  upon  the 
continent  this  amounts  to  12°  to  15°.  In  islands  the  uniformity  of  tem- 
perature is  very  perceptible,  even  during  the  greatest  heats.  In  con- 
tinents, on  the  contrary,  the  winters  for  the  same  latitudes  become  colder, 
and  the  difference  between  the  temperature  of  summer  and  winter  be- 
comes greater. 

930.  Culf  stream. — A  similar  influence  to  that  of  the  winds  is  exerted 
by  currents  of  warm  water.  To  one  of  these,  the  Gulf  stream,  the  mild- 
ness of  the  climate  in  the  north-west  of  Europe  is  mainly  due.  This 
great  body  of  water,  taking  its  origin  in  equatorial  regions,  flows  through 
the  Gulf  of  Mexico,  from  whence  it  derives  its  name  ;  passing  by  the 
southern  shores  of  North  America,  it  makes  its  way  in  a  north-westerly 
direction  across  the  Atlantic,  and  finally  washes  the  coast  of  Ireland  and 


-933]  IsotJiermal  lines.     Cliviate.  865 

the  north-west  of  Europe  generally.  Its  temperature  in  the  Gulf  is  about 
28°  C.  (and  generally  it  is  a  little  more  than  5°  C.)  higher  than  the  rest  of 
the  ocean  on  which  it  floats,  owing  to  its  lower  specific  gravity.  To  its  in- 
fluence is  due  the  milder  climate  of  west  Europe  as  compared  with  that  of 
the  opposite  coast  of  America ;  thus  the  river  Hudson,  in  the  latitude  of 
Rome,  is  frozen  over  three  months  in  the  year.  It  also  causes  the  polar 
regions  to  be  separated  from  the  coasts  of  Europe  by  a  girdle  of  open  sea  ; 
and  thus  the  harbour  of  Hammerfest  is  open  the  year  round.  Besides  its 
influence  in  thus  moderating  climate,  the  Gulf  stream  is  an  important  help 
to  navigators. 

931.  Isothermal  lines. — When  on  a  map  aW  the  points  whose  tem- 
perature is  known  to  be  the  same  are  joined,  curves  are  obtained  which 
Humboldt  first  noticed,  and  which  he  called  isothermal lities.  If  the  tem- 
perature of  a  place  only  varied  with  the  obliquity  of  the  sun's  rays,  that  is, 
with  the  latitude,  isothermal  lines  would  all  be  parallel  to  the  equator  ;  but 
as  the  temperature  is  influenced  by  many  local  causes,  especially  by  the 
height,  the  isothermal  lines  are  always  more  or  less  curved.  On  the  sea, 
however,  they  are  almost  parallel.  A  distinction  is  made  between  isothcr- 
?nal  lilies,  isotheral  lines,  and  isochimenal  lines,  where  the  m.&2in  general ,, 
the  mean  summer,  and  the  mean  winter  temperatures  are  respectively  con- 
stant. An  isothermal  zone  is  the  space  comprised  between  two  isothermal 
lines.  Kupffer  also  distinguishes  isogeothermic  lines  where  the  mean  tem- 
perature of  the  soil  is  constant. 

932.  Climate.— By  the  climate  of  a  place  is  understood  the  whole  of  the 
meteorological  conditions  to  which  a  place  is  subjected  ;  its  mean  annual 
temperature,  summer  and  winter  temperatures,  and  by  the  extremes  within 
which  these  are  comprised.  Some  writers  distinguish  seven  classes  of 
climates  according  to  their  mean  annual  temperature  :  a  hot  climate  from 
29°  5'  to  25°  C.  ;  a  warm  cliinate  from  25°  to  20°  C. ;  a  inild  climate  horn 
20°  to  15°  ;  a  temperate  climate  from  15°  to  10°  C.  ;  a  cold  climate  from 
10°  to  5°  ;  a  very  cold  climate  from  5°  to  zero  ;  and  an  arctic  climate  where 
the  temperature  is  below  zero. 

Those  climates,  again,  are  classed  as  constant  clzjnates,  where  the  dif- 
ference between  the  mean  and  summer  and  winter  temperature  does  not 
exceed  6°  to  8° ;  variable  climates,  where  the  difference  amounts  to  from 
16°  to  20°  ;  and  extreme  climates,  where  the  difference  is  greater  than  30° 
The  climates  of  Paris  and  London  are  variable  ;  those  of  Pekin  and  New 
York  are  extreme.  Island  climates  are  generally  little  variable,  as  the 
temperature  of  the  sea  is  constant ;  and  hence  the  distinction  between  land 
and  sea  climates.  Marine  climates  are  characterised  by  the  fact  that  the 
difference  between  the  temperature  of  summer  and  winter  is  always  less 
than  in  the  case  of  continental  climates.  But  the  temperature  is  by 
no  means  the  only  character  which  influences  climates  ;  there  are  in 
addition,  the  humidity  of  the  air,  the  quantity  and  frequency  of  the  rains 
the  number  of  storms,  the  direction  and  intensity  of  the  winds,  and  the 
nature  of  the  soil. 

933.  Bistribution  of  temperature  on  the  surface  of  the  globe. 

The  temperature  of  the  air  on  the  surface  of  the  globe  decreases  from  the 

PP 


S66 


Meteorology. 


[933 


equator  to  the  poles  ;  but  it  is  subject  to  perturbing  causes  so  numerous 
and  so  purely  local,  that  its  decrease  cannot  be  expressed  by  any  law.  It 
has  hitherto  not  been  possible  to  do  more  than  obtain  by  numerous  obser- 
vations the  mean  temperature  of  each  place,  or  the  maximum  and  minimum 
temperatures.  The  following  table  gives  a  general  idea  of  the  distribution 
of  heat  in  the  northern  hemisphere  :— 

Mean  temperature  at  different  latitudes. 


Abyssinia     . 

3i-o°C. 

Paris 

io-8°  C 

Calcutta 

.        28-5 

London 

8-3 

Jamaica 

.    •        26-1 

Brussels 

IO'2 

Senegal 

24-6 

Strasburg    . 

9-8 

Rio  de  Janeiro     . 

23-1 

Geneva 

97 

Cairo  . 

22-4 

Boston 

9-3 

Constantino . 

17-2 

Stockholm . 

5-6 

Naples . 

.            167 

Moscow 

3-6 

Mexico 

i6-6 

St.  Petersburg    . 

3-5 

Marseilles     . 

14-1 

St.  Gothard 

-ro 

Constantinople     . 

137 

Greenland . 

-77 

Pekin   . 

127 

Melville  Island  . 

-187 

These  are  mean  temperatures.  The  highest  temperature  which  has 
been  observed  on  the  surface  of  the  globe  is  47*4°  at  Esne,  in  Egypt,  and 
the  lowest  is  —  567  at  Fort  Reliance,  in  North  America  ;  which  gives  a 
difference  of  io4'i°  between  the  extreme  temperatures  observed  on  the 
surface  of  the  globe. 

The  highest  temperature  observed  at  Paris  was  38*4°  on  July  8,  1793, 
and  the  lowest  -23-5  on  December  26,  1798.  The  highest  observed  at 
Greenwich  was  35°  C.  in  1808,  and  the  lowest  —20°  C.  in  1838. 

No  arctic  voyagers  have  succeeded  in  reaching  the  poles,  in  conse- 
quence of  these  seas  being  completely  frozen,  and  hence  the  temperature 
is  not  known.  In  our  hemisphere  the  existence  of  a  single  glacial  pole, 
that  is,  a  place  where  there  was  the  maximum  cold,  has  been  long  assumed. 
But  the  bendings  which  the  isothermal  lines  present  in  the  northern 
hemisphere  have  shown  that  in  this  hemisphere  there  are  two  cold  poles, 
one  in  Asia,  to  the  north  of  Gulf  Taymour,  and  the  other  in  America, 
north  of  Barrow's  Straits,  about  1 5°  from  the  earth's  north  pole.  The 
mean  temperature  of  the  first  of  these  poles  has  been  estimated  at 
—  17°,  and  that  of  the  second  at  — 19°.  With  respect  to  the  austral 
hemispheres,  the  observations  are  not  sufficiently  numerous  to  tell 
whether  there  are  one  or  two  poles  of  greatest  cold,  or  to  determine  their 
position. 

934.  Temperature  of  lakes,  seas,  and  springrs. — In  the  tropics  the 
temperature  of  the  sea  is  generally  the  same  as  that  of  the  air ;  in  polar 
regions  the  sea  is  always  warmer  than  the  atmosphere. 

The  temperature  of  the  sea  under  the  torrid  zone  is  always  about  26° 
to  27°  at  the  surface ;  it  diminishes  as  the  depth  increases,  and  in  tempe- 
rate as  well  as  in  tropical  regions  the  temperature  of  the  sea  at  great 
depths  is  between  2-5°  and  3-5°.     The  temperature  of  the  lower  layers  is 


-935] 


Distribution  of  Land  and  Water. 


S67 


caused  by  submarine  currents  which  carry  the  cold  water  of  the  polar 
seas  towards  the  equator. 

The  variations  in  the  temperature  of  lakes  are  more  considerable ;  their 
surface,  which  becomes  frozen  in  winter,  may  become  heated  to  20°  or  25° 
in  summer.  The  temperature  of  the  bottom,  on  the  contrary,  is  virtually 
4°,  which  is  that  of  the  maximum  density  of  water. 

Springs  which  arise  from  rain  water  which  has  penetrated  into  the 
crust  of  the  globe  to  a  greater  or  less  depth  necessarily  tend  to  assume 
the  temperature  of  the  terrestrial  layers  which  they  traverse;  Hence 
when  they  reach  the  surface  their  temperature  depends  on  the  depth 
which  they  have  attained.  If  this  depth  is  that  of  the  layer  of  invari- 
able temperature,  the  springs  have  a  temperature  of  10°  or  11°  in  this 
country,  for  this  is  the  temperature  of  this  layer,  or  about  the  mean 
annual  temperature.  If  the  springs  are  not  very  copious,  their  tempera- 
ture is  raised  in  summer  and  cooled  in  winter,  by  that  of  the  layers  which 
they  traverse  in  passing  from  the  invariable  layer  to  the  surface.  But  if 
they  come  from  below  the  layer  of  invariable  temperature,,  their  tempera- 
ture may  considerably  exceed  the  mean  temperature  of  the  place,  and 
they  are  then  called  thermal  springs.  The  following  list  gives  the  tem- 
perature of  some  of  them : 

C. 


Wildbad            .            .... 

37-5' 

Vichy 

4P 

Bath      ...... 

46 

Ems       .             .             .             . 

56 

Baden-Baden   ... 

67-5 

Chaudes-Aigues            .... 

88 

Trincheras 

97 

Great  Geyser,  in  Iceland,  at  a  depth  of  66  ft. 

124 

From  their  high  temperature  they  have  the  property  of  dissolving 
many  mineral  substances  which  they  traverse  in  their  passage,  and  hence 
form  jnmeral  waters.  The  temperature  of  mineral  waters  is  not  modified 
m  general  by  the  abundance  af  rain  or  of  dryness ;  but  it  is  by  earth- 
quakes, after  which  they  have  sometimes  been  found  to  rise  and  at  others 
to  sink. 

935.  Distribution  of  land  and  water. — The  distribution  of  water  on 
the  surface  of  the  earth  exercises  great  influence  on  climate.  The  area 
covered  by  water  is  considerably  greater  than  that  of  the  dry  land ;  and 
the  distribution  is  unequal  in  the  two  hemispheres.  The  entire  surface 
of  the  globe  occupies  about  200  millions  of  square  miles,  nearly  |  of  which 
is  covered  by  water ;  that  is,  the  extent  of  the  water  is  nearly  three  times 
as  great  as  that  of  the  land.  The  surface  of  the  sea  in  the  southern 
hemisphere  is  to  that  in  the  northern  in  about  the  ratio  of  13,10  9. 

The  depth  of  the  open  sea  is  very  variable,  the  lead  generally  reaches 
the  bottom  at  about  300  to  450  yards  ;  in  the  ocean  it  is  often  1,300  yards 
and  instances  are  known  in  which  a  bottom  has  not  been  reached  at  a 
depth  of  4,500.  It  has  been  computed  that  the  total  mass  of  the  water 
does  not  exceed  that  of  a  liquid  layer  surrounding  the  earth  with  a  depth 
of  about  1,100  yards. 


PROBLEMS    AND    EXAMPLES 
IN    PHYSICS. 


1.  A  body  being  placed  successively  in  the  two  pans  of  a  balance,  requires  i8o 
grammes  to  hold  it  in  equilibrium  in  one  pan,  and  i8i  grammes  in  the  other ;  required 
the  weight  of  the  body  to  a  milligramme. 

From  the  formula  deduced  (72)  we  have 

X  =    a/i8o  X  181   =   180S',  499. 

2.  What  resistance  does  a  nut  offer  when  placed  in  a  pair  of  nutcrackers  at  a 
distance  of  |  of  an  inch  from  the  joint  if  a  pressure  of  5  pounds  applied  at  a  distance 
of  4  inches  from  the  joint  is  just  sufficient  to  crack  it?  Ans.  26^  pounds. 

3.  What  force  is  required  to  raise  a  cask  weighing  6  cwt.  into  a  cart  o"8  metre 
high  along  a  ladder  275  metres  in  length  ?  Ans.  195^  pounds. 

4.  If  a  horse  can  move  30  cwt.  along  a  level  road,  what  can  it  move  along  a  road 
the  inclination  of  which  is  i  in  80?  Ans.  26§  cwt. 

5.  The  piston  of  a  force-pump  has  a  diameter  of  8  centimetres,  and  the  arms  of 
the  lever  by  which  it  is  worked  are  respectively  12  and  96  centimetres  in  length,  what 
force  must  be  exerted  at  the  longer  arm  if  a  pressure  of  12  "36  pounds  on  a  square  cen- 
timetre is  to  be  applied  ?  Ans.  78  pounds. 

6.  A  stone  is  thrown  from  a  balloon  with  a  velocity  of  50  metres  in  a  second.  How 
soon  will  the  velocity  amount  to  99  metres  in  a  second,  and  through  what  distance 
will  the  stone  have  fallen  ? 

To  find  the  time  requisite  for  the  body  to  have  acquired  the  velocity  of  99  metres  in 
a  second,  we  have 

V  =   V  +  gt', 

in  which  V  is  the  initial  velocity,  g  the  acceleration  of  gravity  which,  with  sufficient 
approximation,  is  equal  to  9 '8  metres  in  a  second,  and  t  the  time.  Substituting  these 
values,  we  have 

t  =  99-50  =    49    =,  5  seconds. 
9-8  9-8        ^ 

For  the  space  traversed  we  have 

s  =:   Vt  +  ^gi^  =  50  X  5  +  4'9  X  25  =372*5  metres. 

7.  A  projectile  was  thrown  vertically  upwards  to  a  height  of  5io™-22,  Disregard- 
ing the  resistance  of  the  air,  what  was  the  initial  velocity  of  the  body  ? 

The  velocity  is  the  same  as  that  which  the  body  would  have  acquired  on  falling 
from  a  height  of  5 10 "22  metres. 

From  the  formula  t^  =   v^2^.yweget 

V  =  sj'z  X  9-8  X  510*22  =   \/ioooo  =  100  metres. 

8.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  100  metres. 
After  what  time  would  it  return  to  its  original  position  ? 

In  this  cas-a  since  its  velocity  at  its  highest  point  is  null,  we  have,  from  the  formula 
V  =   V  -  gt, 

V  =  100  —  gt,  whence  t  =    —  =  io"2  seconds. 

The  time  required  for  the  body  to  fall  is  that  in  which  it  would  have  acquired 
the  velocity  of  100,  that  is  100  =  ^/  or  /  =  10-2,  and  therefore  the  whole  time  is 
2  X  io'2  =  2o"4  seconds. 


8/0  Problems  and  Examples  in  Physics. 

9.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  loo  metres  ;  after 
X  seconds  a  second  stone  is  thrown  with  the  same  velocity.  The  second  stone  is  rising 
87  seconds  before  it  meets  the  first.     What  interval  separated  the  throws? 

The  rising  stone  will  have  the  velocity  v  =  V  —  gt,  whence  v  =  too  —  9-8  x  87. 
On  the  other  hand,  the  falling  stone,  at  the  moment  the  stones  meet,  will  have  the  velocity 
given  by  the  equation  v  =  gt'  in  which  t'  is  the  time  during  which  the  stone  falls 

before  it  meets  the  second  one.    This  time  is  equal  to  87  seconds  +  x  —  ^^.    Hence 

9-8 
its  velocity  is  ^  v 

.  =  9-8  (8-7  +  -  -   P). 

Equating  the  two  values  of  v  and  reducing,  we  obtain  ^-  =  3  seconds. 

10.  A  body  moving  with  a  uniformly  accelerated  motion  traverses  a  space  of  1000 
metres  in  10  seconds.  What  would  be  the  space  traversed  during  the  eighteenth 
second  if  the  motion  continued  in  the  same  manner  ? 

The  formula  J  =  ^^/'^  gives. for  the  accelerating  force  ^.f  =  20  metres  per  second. 
The  space  traversed  during  the  eighteenth  second  will  be  equal  to  the  difference  of 
the  space  traversed  in  18  seconds  and  that  traversed  at  the  end  of  the  seventeenth. 

350  metres. 


11.  A  cannon-ball  has  been  shot  vertically  upwards  with  a  velocity  of  250  metres  in 
a  second.  After  what  interval  of  time  would  its  velocity  have  been  reduced  to  54  metres 
under  the  retarding  influence  of  gravity,  and  what  space  would  have  been  traversed  by 
the  ball  at  the  end  oi  this  time  ? 

If  /  be  the  time,  then  at  the  end  of  each  second  the  initial  velocity  would  be  dimi- 
nished by  9"' •8.     Hence  we  shall  have 


54 

=   250- 

t   X 

9-8, 

whence  t 

=  20 

seconds 

and  for  the 

space 

traversed 

t 

==   250  X 

20  - 

-9:8 

X    20'2    _ 

3040 

metres. 

12.  Required  the  time  in  which  a  body  would  fall  through  a  height  of  2000  metres, 
neglecting  the  resistance  of  the  air. 

From  J  =  5  gfi  and  substituting  the  values,  we  have 

^000  =  5_  /2^  whence  t  =  20*2  seconds. 
2 

13.  A  body  falls  in  air  from  a  height  of  4000  metres.  Required  the  time  of  its  fall 
and  its  velocity  when  it  strikes  the  ground. 

From  the  formula  s  =  \i  gf^  we  have  for  the  time  /  =       /  —  ;    and,  on  the  other 

V    g 

hand,  from  the  formula  for  velocity  v  =  gt  we  have  t  =  ^. 

Hence  '^  =  ^—,  from  which  l^  =  y/2  sg,  and  substituting  the  values  for  s  and 
g,  V  =  200  metres. 

14.  A  stone  is  thrown  into  a  pit  150  metres  deep  and  reaches  the  bottom  in  4 
seconds.  With  what  velocity  was  it  thrown,  and  what  velocity  had  it  acquired  on 
reaching  the  ground  ?  Ans.  The  stone  was  thrown  with  a  velocity  of  17-9,  and  on 
reaching  the  ground  had  acquired  the  velocity  57-1. 

15.  A  stone  is  thrown  downwards  from  a  height  of  150  metres  with  a  velocity  of  10 
metres  per  second.     How  long  will  it  require  to  fall  ? 

The  distance  through  which  the  stone  falls  is  equal  to  the  sum  of  the  distances 
through  which  it  would  fall  in  virtue  of  its  initial  impulse  and  of  that  which  it  would 

traverse  under  the  influence  of  gravity  alone  :  that  is,  150  =  10  ^  +  ^'^^^. 

2 
Taking  the  positive  value  only  we  get  ^  =  4-61  seconds. 


Problems  and  Examples  in  Physics.  87 1' 

16.  Required  the  time  of  oscillation  of  a  single  pendulum  whose  length  is  0-99384 
and  in  a  place  where  the  intensity  of  gravity  is  9-81. 

From  the  general  formula  t  =  v     /-,  in  which  /  expresses  the  time  of  one  oscil- 
lation, /  the  length  of  the  pendulum,  and'^  the  intensity  of  gravity,  we  have 

/  =   ■5"i4i6       /  -°?3  -4  =    I  second. 

17.  What  is  the  intensity  of  gravity  in  a  place  in  which  the  length  of  the  seconds 
pendulum  is  o™"99i  ?  _ 

In  this  case  zf  =  tt     /  _  ;  and  also  t  =  i.-     /      ■,  and  therefore    ■     =    -  ,    from 
^,  ^  g  V    g'  g' 

which  g'  =  *— .     Substituting  in  this  latter  equation  the  values  of  g'  I  and  /',  we 
have^'  =  9°i7o8. 

18.  In  a  place  at  which  the  length  of  the  seconds  pendulum  is  "99384,  it  is  required 
to  know  the  length  of  a  pendulum  which  makes  one  oscillation  in  5  seconds. 

In  the  present  case,  as  g  remains  the  same  in  the  general  formula,  and  t  varies,  the 
length  /  must  vary  also.       We  shall  have,  then. 


^-s/'-A 


from  which,  reducing  and  introducing  the  values,  we  have 
/'  =  5-  X  0*99384  =  24-846. 

19.  A  pendulum,  the  length  of  which  is  1^-95,  makes  61,682  oscillations  in  a  day. 
Required  the  length  of  the  seconds  pendulum..  Ans.  0-99385  metres. 

20.  A  pendulum  clock  loses  5  seconds  in  a  day.  By  how  much  must  it  be 
shortened  to  keep  correct  time  ?  Ans.  By  0-0001157  of  its  original  length. 

21.  What  is  the  normal  acceleration  of  a  body  which  traverses  a  circle  of  4-2 
metres  diameter  with  a  rectangular  velocity  of  3  metres  ?  Ans.  4-286  metres. 

22.  An  iron  ball  falls  from  a  height  of  68  cm.  on  a  horizontal  iron  plate,  and 
rebounds  to  a  height  of  27  cm.     Required  the  co-efficient  of  elasticity  of  the  iron  ? 

If  an  imperfectly  elastic  ball  with  the  velocity  v  strikes  against  a  plate,  it  rebounds 

with  the  velocity  v    =^    —  k  v,  from  which,  disregarding  the  sign,  k  =  -'.     Now  we 

V 

have   the  velocity  t/^  =    '^2.  gh^  and  v  =    \J -z  gh,  from  which  ^  = '-.    Substitut- 

\/  h 
ing  the  corresponding  values,  we  get  k  =   0-63. 

23.  Two  inelastic  bodies,  weighing  respectively  100  and  200  pounds,  strike  against 
each  other  with  velocities  of  50  and  20  feet,  what  is  their  common  velocity  after  the 
impact?  Ans.  30,  or  3 -3,  according  as  they  move  in  the  same  or  in  opposite  directions 
before  impact. 

24.  The  force  with  which  a  hydraulic  press  is  worked  is  20  pounds  ;  the  arm  of  the 
lever  on  which  this  force  acts  is  5  times  as  long  as  that  of  the  resistance ;  lastly,  the 
area  of  the  large  piston  is  70  times  that'  of  the  smaller  one.  Required  the  pressure 
transmitted  to  the  large  piston. 

If  /''  be  the  power,  and  p  the  pressure  transmitted  to  the  smaller  piston,  we  have 
from  the  principle  of  the  lever  {40)  /  x  i  =  /■"  x  5.  Moreover,  from  the  principle  of 
the  equality  of  pressure  (93) 

P  X  1   =/X70  =  5X20X70  =  7000  pounds. 

25.  The  force  with  which  a  hydraulic  press  is  worked  being  30  kilos,  and  the  arm 
of  the  lever  by  which  this  force  is  applied  being  10  times  as  long  as  that  of  the  resist- 
ance, and  the  diameter  of  the  small  piston  being  two  centimetres  ;  find  the  diameter  of 
the  large  piston,  in  order  that  a  pressure  of  2000  kilos,  may  be  produced. 

Ans.  16-33  centimetres. 


8/2  Problems  and  Examples  in  Physics.  ; 

26.  One  of  the  limbs  of  a  U-shaped  glass  tube  contains  mercury  to  a  height  of 
©■"•lys  ;  the  other  contains  a  different  hquid  to  a  height  of  o'»*42  ;  the  two  columns 
being  in  equilibrium,  required  the  density  of  the  second  hquid  with  reference  to  mer- 
cury and  to  water. 

If  d  is  the  density  of  the  liquid  as  compared  with  mercury  and  d^  the  density  com- 
pared with  water,  then  i*  x  0-175  =  0*42  x  d\  and  13-6  x  0-175  =  0-42  x  d/, 
whence  d  =  0-416  and  d^  =  5-66. 

27.  What  force  would  be  necessary  to  support  a  cubic  decimetre  of  platinum  in 
mercury  at  zero  ?     Density  of  mercury  13-6  and  that  of  platinum  21-5. 

From  the  formula  P  =  VD  the  weight  of  a  cubic  decimetre  of  platinum  is 
I  X  21-5  =  21'' -5  and  that  of  a  cubic  decimetre  of  mercury  is  i  x  13-6  =  13^-6. 
From  the  principle  of  Archimedes  the  immersed  platinum  loses  part  of  its  weight 
-equal  to  that  of  the  mercury  which  it  displaces.  Its  weight  in  the  hquid  is  therefore 
21-5  —  13-6  =  7-9,  and  this  represents  the  force  required. 

28.  Given  a  body  A  which  weighs  7-55  grammes  in  air,  5-17  gr.  in  water,  and 
6-35  gr.  in  another  liquid,  B  ;  required  from  these  data  the  density  of  the  body  A  and 
that  of  the  liquid  B. 

The  weight  of  the  body  A  loses  in  water  7 '55  —  5-17  =  2-38  grammes  ;  this  repre- 
sents the  weight  of  the  displaced  water.  In  the  liquid  B  it  loses  7-55  —  6-35  =  1-2  gr. ; 
this  is  the  weight  of  the  same  volume  of  the  body  B,  as  that  of  A  and  of  the  displaced 
water.     The  specific  gravity  of  A  is  therefore 

755  =  3-172,  and  that  of  .g  -^  =  0-504. 
238  238 

29.  A  cube  of  lead,  the  side  of  which  is  4  cm.,  is  to  be  supported  in  water  by 
being  suspended  to  a  sphere  of  cork.  What  must  be  the  diameter  of  the  latter,  the 
specific  gravity  of  cork  being  0-24,  and  that  of  lead  11-35? 

The  volume  of  the  lead  is  64  cubic  centimetres  ;  its  weight  in  air  is  therefore 
64  X  11-35  and  its  weight  in  water  64  ^   11 '35  -  64  =  662-4  gr. 

If  r  be  the  radius  of  the  sphere  in  centimetres  its  volume  in  cubic  centimetres  will 

be  ^-^~,  and  its  weight  in  grammes  is  ^^ °  ^'^.     Now,  as  the  weight  of  the 

3  3 

displaced  -water  is  obviously  -  w  r^  in  grammes,  there  will  be  an  upward  buoyancy 

represented  by  ^^ —  —  ^-^ ^  ^    \  =  ^— ^1^7  ^  which  must  be  equal  to  the 

3                  ^  r5  X  o-  6  ^ 

weight  of  the  lead  :  that  is  ^^ ^^  =  662-5,  from  which  r  =  5'^™-925  and  the 

diameter  =   11-85. 

30.  A  cylindrical  steel  magnet  15  cm.  in  length  and  1-2  mm.  in  diameter  is  loaded 
at  one  end  with  a  cylinder  of  platinum  of  the  same  diameter  and  of  such  a  length  th»t 
when  the  .solid  thus  formed  is  in  mercury,  the  free  end  of  the  steel  projects  10  mm. 
above  the  surface.  Required  the  length  of  this  platinum.  Specific  gravity  of  steel 
being  7-8  and  of  platinum  21-5. 

The  weight  of  the  steel  in  grammes  will  be  15  w  r'^  x  7-8  and  of  the  platinum 
X  ir  r"^  X  21-5. 

These  are  together  equal  to  the  weight  of  the  displaced  mercury,  which  is 
w  7-2  (j^^  ^  ^)  j^.^  fi-QiYi  which  X  =  9-01  cm. 

31.  A  cylindrical  silver  wire  o'°-ooi5  in  diameter  weighs  3-2875  grammes  ;  it  is  to 
be  covered  with  a  layer  of  gold  o'n-0002  in  thickness.  Required  the  weight  of  the  gold  ; 
the  specific  gravity  of  silver  being  10-47  and  that  of  gold  19-26. 

If  r  is  the  radius  of  the  silver  wire  and  ^  its  radius  when  covered  with  gold,  then 
r  =  o'=-075  and  J?  =  o<=-095.  The  volume  of  the  silver  wire  will  be  n  r"^  I  and  its 
weight  TT  r^  1 10-26,  from  which  /  =   xT'-jeZ. 

The  volume  of  the  layer  of  gold  is 

n  [R-i  _  ^2)  17-768, 
and  its  weight 

IT  (0-0952  —  0-0752)  X  17768  X  19-26  =  3-657  nearly. 

32.  A  kilogramme  of  copper  is  to  be  drawn  into  wire  having  a  diameter  of  0-16 
centimetre.     What  length  will  it  yield  ?    Specific  gravity  of  copper  8-88. 


Problems  and  Examples  in  Physics.     '  873 

The  wire  produced  represents  a  cylinder  /cm.  in  length,  the  weight  of  which  is 
T  r^  /  8  88,  and  this  is  equal  to  looo  grammes.     Hence  /  =  56">*oo85. 

33.  Determine  the  volumes  of  two  liquids,  the  densities  of  which  are  respectively 
1-3  and  07,  and  which  produce  a  mixture  of  three  volumes  having  the  density  o'g. 

If  X  and  y  be  the  volumes,  then  from  P  =  FD,  1-3  jc  +  o'jjv  =  3  x  0*9  and 
AT  +  J)/  =  3,  from  which  x   —   1  and  /  =  2. 

34.  The  specific  gravity  of  zinc  being  7  and  that  of  copper  9,  what  weight  of  each 
metal  must  be  taken  to  form  50  grammes  of  an  alloy  having  the  specific  gravity  8-2  ;  it 
being  assumed  that  the  volume  of  the  alloy  is  exactly  the  sum  of  the  alloyed  metals  ? 

Let  :*:  =  the  weight  of  the  zinc,  and  j>  that  of  the  copper,  then  x  +  y  =  ^o,  and 

p 
from  the  formula  P  =   VD,  which  gives  f^  =  7^.  the  volumes  of  the  two  metals  and  of 

the  alloy  are  respectively  -+'''=  ^°  ,     From  these  two  equations  we  get  x  =   17  "07 

and  J  =  32-93. 

35.  A  platinum  sphere  3  cm.  in  diameter  is  suspended  to  the  beam  of  a  very  ac- 
curate balance,  and  is  completely  immersed  in  mercury.  It  is  exactly  counterbalanced 
by  a  copper  cylinder  of  the  same  diameter  completely  immersed  in  water.  Required 
the  height  of  the  cylinder.  Specific  gravity  of  mercury  13-6,  of  copper  8-8,  and  of 
platinum  21  "5.  Ans.    2-025  centimetres. 

36.  To  balance  an  ingot  of  platinum  27  grammes  of  brass  are  placed  in  the  other 
pan  of  the  balance.  What  weight  would  have  been  necessary  if  the  weighing  had  been 
effected  in  vacuo?    The  density  of  platinum  is  21-5,  that  of  brass  8-3,  and  air  under 

a  pressure  of  760  mm.  and  at  the  temperature  0°  has  the  density  of  water. 

770 
The  weight  of  brass  in  air  is  not  27  grammes,  but  this  -veight  minus  the  weight  of 
a  volume  of  air  equal  to  its  own. 

Since  P  =    VD  .• .  V  =   -  and  the  weight  of  the  air  is  -^-^^^^ =  =Z , 

D  D  X  770        8-3  X  770 

By  similar  considerations,  if  x  is  the  weight  of  platinum  in  vacuo,  its  weight  in  air 

will  be  x  minus  the  weight  of  air  displaced,  that  is  :*:  — ,   and  this  weight 

21-5  X  770 
is  equal  to  that  of  the  true  weight  of  the  brass  ;  and  we  have 

27  —  ^ — ?Z ;  from  which  x  =  26-996. 


21-5  X  770  8-3  X  770 

37.  A  body  loses  in  carbonic  acid  1-15  gr.  of  its  weight.  What  would  be  its  loss 
of  weight  in  air  and  in  hydrogen  respectively  ? 

Since  a  litre  of  air  at  0°  and  760  mm.  weighs  1-293  gramme,  the  same  volume  of 
carbonic  acid  weighs  1-293  ^  i"524  =  1-97  gramme.  We  shall,  therefore,  obtain  the 
volume  of  carbonic  acid  corresponding  to  1-15  gr.  by  dividing  this  number  by  1-97, 
which  gives  0-5837  litre.  This  being  then  the  volume  of  the  body,  it  displaces  that 
volume  of  air,  and  therefore  its  loss  of  weight  in  air  is  0-5837  x  1-293  =  0-7547  grammes, 
and  in  hydrogen  0*5837  x  1-293  ^  0*069  =  0*052076. 

38.  Calculate  the  ascensional  force  of  a  spherical  balloon  of  oiled  silk  which,  when 
empty,  weighs  62-5  kilos,  and  which  is  filled  with  impure  hydrogen,  the  density  of 

which  is   ?     that  of  air.     The  oiled  silk  weighs  0*250  kilo  the  square  metre. 
13 

The  surface  of  the  balloon  is  ^  =  250  square  metres.  This  surface  being  that  of 

0-25 

a  sphere,  is  equal  to  4  tt  R-,  whence  4  tt  i??2  =  250  and  R  =  4*459  ;  therefore  V  —  ^~— 

3 
=  371-52  cubic  metres. 

The  weight  of  air  displaced  is  371*52  x  1-293  ^i^o  =  480-375  kilos  ;  the  weight  of 
the  hydrogen  is  39-88  kilos,  and  therefore  the  ascensional  force  is 

480*375  -  (36-88  +  62-5)   =  38o*995- 

39.  A  balloon  4  metres  in  diameter  is  made  of  the  same  material  and  filled  with 
the  same  hydrogen  as  above.  How  much  hydrogen  is  required  to  fill  it,  and  what 
weight  can  it  support  ? 


8/4  *      Problems  and  Examples  in  Physics. 

The  volume  is   ^  „  K^  =  33*5 1  cubic  metres,  and  the  surface  4  «•  i?2  ^  50-265  square 
3 
metres.     The  weight  of  the  air  displaced  is  33-51  x  1-293  =  43'328  kilos,  and  that  of 
the  hydrogen  is  from  the  above  data  3*33  kilos,  while  the  weight  of  the  material  is  12-566 
kilos.     Hence  the  weight  which  the  balloon  can  support  is 

43-328  -  (12-566  +  3-33)   =  27-432  kil. 

40.  Under  the  receiver  of  an  air-pump  is  placed  a  balance,  to  which  are  suspended 
two  cubes;  one  of  these  is  3  centimetres  in  the  side,  and  weighs  26-324  gr.,  and  the  other 
is  5  centimetres  in  the  side,  and  weighs  26-2597  grammes.  When  a  partial  vacuum  is 
made  these  cubes  just  balance  each  other.     What  is  the  pressure?  Ans.  0^-374. 

41.  A  soap  bubble  8  centimetres  in  diameter  was  filled  with  a  mixture  of  one 
volume  of  hydrogen  gas  and  15  volumes  air.  The  bubble  just  floated  in  the  air ;  re- 
quired the  thickness  of  the  film. 

The  weight  of  the  volume  of  air  displaced  is  ^  t  r^  x  0-001293  grammes,  and  that 

3 

of  the  mixture  of  gases   "^  ^  ^^  x  0-001293  x  ^■^ o_2_93  .  ^nd  the  difference   of 

3  10 

these  will  equal  the  weight  of  the  soap  bubble. 

This  weight  is  that  of  a  spherical  shell,  which,  since  its  thickness  /  is  very 
small,  is  with  sufficient  accuracy  4  if  r^  t  s  va.  grammes,  where  s  is  the  specific  gravity 
=  1-1.     Hence 

-ttr^  \  -001293  —  -001293  X    ii^  93  \    _  ^  ^  ,,0  ^  j,j 
3  \  16     y 

Dividing  each  side  by  '^  w  r^,  and  putting  r  =  4,  we  get 
3 


4  X   -001293  {t.  -  ^1^^)  =  3'3  t\ 


•001293  X  -23^  _  2-3  ^ 


whence  /  =   -00009116629  cm. 


42.  In  a  vessel  wliose  capacity  is  3  litres,  there  are  introduced  2  litres  of  hydrogen 
under  the  pressure  5  atmospheres  ;  3  htres  of  nitrogen  under  the  pressure  of  half  an 
atmosphere,  and  4  htres  of  carbonic  acid  under  the  pressure  4  atmospheres.  What  is 
the  final  pressure  of  the  gas,  the  temperature  being  supposed  constant  during  the 
experiment  ? 

The  pressure  of  the  hydrogen,  from  Dalton's  law,  will  be  ?-AJ,  that  of  the  nitro- 

3 
gen  will  remain  imchanged,  and  that  of  the  carbonic  acid  will  be  l^Li.     Hence  the 

3 
total  pressure  will  be 

=  9^  atmospheres. 


%  ^^  +  L 


2 


43,  A  vessel  containing  10  litres  of  water  is  first  exposed  in  contact  with  oxygen 
under  a  pressure  of  78  cm.  until  the  water  is  completely  saturated.     It  is  then  placed 
in  a  confined  space  containing  100  litres  of  carbonic  acid  under  a  pressure  of  72   cm 
Required  the  volumes  of  the  two  gases  when  equilibrium  is  established.     The  coeffi- 
cient of  absorption  of  oxygen  is  0-042,  and  that  of  carbonic  acid  unity. 

The  volume  of  oxygen  dissolved  is  0-42.  Being  placed  in  carbonic  acid  it  will 
act  as  if  It  alone  occupied  the  space  of  the  carbonic  acid,  and  its  pressure  will  be 

78    X    -^-^ —  =  0-326  cm. 
100-42 

Similarly  the  10  litres  of  water  will  dissolve  10  litres  of  carbonic  acid  gas  the  total 
volume  of  which  will  be  no,  of  which  100  are  in  the  gaseous  state  and  10  are  dissolved. 
Its  pressure  is  therefore  72  x  ^  =  65-454  cm. 


Problems  and  Exaniples  in  Physics,  875 

Hence  the  total  pressure  when  equihbrium  is  established  is 
o'326  +  65"454  =  6578  cm.  ; 
and  the  volume  of  the  oxygen  dissolved  reduced  to  the  pressure  6578  is 

o"'*42"x  °  3^  _  o"'*oo2o8,  and  that  of  the  carbonic  acid  10  x  -5^:54  _  q.q- 
6578  4578 

44.  In  a  barometer  which  is  immersed  in  a  deep  bath  the  mercury  stands  743 
mm.  above  the  level  of  the  bath.  The  tube  is  lowered  until  the  barometric  spape, 
which  contains  air,  is  reduced  to  one-third,  and  the  mercury  is  then  at  a  height  of  701 
mm.     Required  the  atmospheric  piessure  at  the  time  of  observation. 

Ans.   —  764. 

45.  What  is  the  pressure  on  the  piston  of  a  steam  boiler  of  8  decimetres  diameter 
if  the  pressure  in  the  boiler  is  3  atmospheres  ?  Ans.  10385 "8. 

46.  What  is  the  pressure  of  that  height  at  which  an  ascent  of  21  metres  corre- 
spond to  a  diminution  of  t^"^  in  the  barometric  height  ?  Ans.  380""". 

47.  What  would  be  the  height  of  the  atmosphere  if  its  density  were  everywhere 
uniform?  Ans.  7987  metres,  or  nearly  5  miles. 

48.  How  high  must  we  ascend  at  the  sea  level  to  produce  a  depression  of  i  mm. 
in  the  height  of  the  barometer  ? 

Taking  mercury  as  10500  times  as  heavy  as  air,  the  height  will  be  10*5  metres. 

49.  Mercury  is  poured  into  a  barometer  tube  so  that  it  contains  15  cc.  of  air  under 
the  ordinary  atmospheric  pressure.  The  tube  is  then  inverted  in  a  mercury  bath  and 
the  air  then  occupies  a  space  of  25  cc.  ;  the  mercury  occupying  a  height  of  302  mm. 
What  is  the  pressure  of  the  atmosphere  ? 

Let  X  be  the  amount  of  this  pressure,  the  air  in  the  upper  part  of  the  tube  will  have 

a  pressure  represented  by     ^- ,  and  this,  together  with  the  height  of  the  mercurial 

25 
column  302,  will  be  the  pressure  exerted  in  the  interior  of  the  tube  on  the  level   of  the 

mercury  in  the  bath,  which  is  equal  to  the  atmospheric  pressure  ;  that  is  ^-^-  +  302 

=  X,  from  which  x  =  755  mm. 

50.  What  effort  is  necessary  to  support  a  cylindrical 
bell-jar  full  of  mercury  immersed  in  mercury  ;  its  internal 
diameter  being  6  centimetres,  its  height  oi>  above  the  surface 
of  the  mercury  (fig.  i)  18  centimetres,  and  the  pressure  of  the 
atmosphere  077  centimetre? 

The  bell-jar  supports  on  the  outside  a  pressure  equal  to 
that  of  a  column  of  mercury,  the  section  of  whose  base  is  cd, 
and  the  height  that  of  the  barometer.  This  pressure  is  equal  to 

y?2  X  077  X   13-6. 

The  pressure  on  the  inside  is  that  of  the  atmosphere 
less  the  weight  of  a  column  of  mercury  whose  base  is  cd 
andheight^^.  This  is  equal  to  tt  7?^  x  (077  — o'i8)  x  I3'6; 
and  the  effort  necessary  is  the  difference  of  these  two  pres- 
sures. Making  ^  =  3  cm.,  this  is  found  to  be  6"92i6  kilo- 
grammes. 

51.  A  barometer  is  placed  within  a  tube  which  is  after- 
wards hermetically  closed.     At  the  moment  of  closing,  the  ^^'^'  ^• 
temperature  is  15°  and  the  pressure  750  mm.     The  external  space  is  then  heated 
to  30°.     What  will  be  the  height  of  the  barometer  ? 

The  effect  of  the  increase  of  temperature  would  be  to  raise  the  mercury  in  the  tube 

in  the  ratiai  +  -^°-  to  i  +  -^-^-,    and  the  height  k  would  therefore  be 
5550  55SO 

5550 
and  since  in  the  closed  space,  the  elastic  force  of  the  air  increases  in   the  ratio 
I  +  15  a :  I  +  30  *  we  shall  have  finally  A  =  30174  mm. 


8/6 


Problems  and  Examples  in  Physics. 


52.  The  heights  of  two  barometers  A  and  B  have  been  observed  at  —  lo'^  and 
+   15^,  respectively,  to  be  yi   =  737  and  B  =  763.     Required  their  corrected  heights 

at  oP.  Ans.  A   =   738'33.     B  —  jSog^. 

53.  A  voltaic  current  gives  in  an  hour  840  cubic  centimetres  of  detonating  gas 
under  a  pressure  of  760  and  at  the  temperature  12° -5  ;  a  second  voltaic  current  gives 
in  the  «ame  time  960  cubic  centimetres  under  a  pressure  of  755  and  at  the  temperature 
i5°'5-      Compare  the   quantities  of  gas  given  by  the  two  currents.     Ans.  1  :  i'i25. 


54.  The  volume  of  air  in  the  pressure  gauge  of  an 
apparatus  for  compressing  gases  is  equal  to  152  parts. 
By  the  working  of  the  machine  this  is  reduced  to 
37  parts,  and  the  mercury  is  raised  through  ©•48 
metres.     What  is  the  pressure  of  the  gas  ? 

Here  AB  =  152,  AC  =  37 parts,  and  BC  =  ©'"•48. 
The  pressure  of  air  therefore  in  AC  is,  from  Boyle's 
law, 

^?    =    4atm-io8    =     3™ -122. 

37  r 

The  pressure  in  the  receiver  is  therefore 

3'i22  +  0*48  =  3»n-6o2, 
which  is  equal  to  474  atmospheres. 


Flo.  2. 


55.  An  air-tight  bladder  holding  two  litres  of  air  at  the  standard  pressure  and 
temperature  is  immersed  in  sea  water  to  a  depth  of  100  metres  where  the  temperature 
is  4°.     Required  the  volume  of  the  gas. 

The  specific  gravity  of  sea  water  being  i  '026,  the'  depth  of  100  metres  will  repre- 
sent a  column  of  pure  water  102-6  metres  in  height.  As  the  pressure  of  an  atmo- 
sphere is  equal  to  a  pressure  of  io'33  metres  of  pure  water,  the  pressure  of  this  column 

102 -68 
= =  Q  94  atm. 

10-33 

Hence,  adding  the  atmospheric  pressure,  the  bladder  is  now  under  a  pressure  of  10  "94 

atmospheres,  and  its  volume  being  inversely  as  the  pressure  will  be  — ^  -^  =  0"'i83  litre, 

10-94 
if  the  temperature  be  unaltered.    But  the  temperature  is  increased  by  4°,  and  therefore 
the  volume  is  increased  in  the  ratio  277  to  273,  and  becomes 


0-183 


277  _ 


273 


=  0-1855  litres. 


56.  To  what  height  will  water  be  raised  in  the  tube  of  a  pump  by  the  first  stroke 
of  the  piston,  which  is  o-5m.  in  diameter,  the  height  of  the  tube  6  metres,  and  its  section 
iV  that  of  the  piston?    At  starting  the  air  in  the  tube  is  under  a  pressure  of  10  metres. 

If  we  take  the  section  of  the  tube  as  unity,  that  of  the  body  of  the  pump  is  10  ;  and 
the  volumes  of  the  tube  and  of  the  body  of  the  pump  are  in  the  ratio  of  6  to  5.  Then 
if  X  is  the  height  to  which  the  water  is  raised  in  the  pipe,  the  volumes  of  air  in  the 
pump  before  and  after  the  working  of  the  pump  are  6  at  the  pressure  10,  and  5  +  6  -  jr 
at  the  pressure  10  —  x. 

Forming  an  equation  from  these  terms,  and  solving,  we  have  two  values,  x'  =  18™  26 
and  x"  =  2-74.  The  first  of  these  must  be  rejected  as  being  physically  impossible  ; 
and  the  true  height  is  j:  =  2*74  metres. 

57.  A  receiver  with  a  capacity  of  10  litres  contains  air  under  the  pres.sure  76  cm. 
It  is  closed  by  a  valve,  the  section  of  which  is  32  square  centimetres,  and  is  weighted 
with  25  kilogrammes.     The  temperature  of  the  air  is  30°  ;  its  density  at  0==  and  76  cm. 

pressure  is that  of  water.    The  coefficient  of  the  expansion  of  gases  is  0-00366. 

Required  the  weight  of  air  which  must  be  admitted  to  raise  the  valve. 

The  air  already  present  need  not  be  taken  into  account  as  it  is  under  the  pressure 


Problems  and  Examples  in  Physics. 


877 


of  the  atmosphere.     Let  x  be  the  pressure  in  centimetres  of  mercury  of  that  which  is 


admitted, 


X  X  i3"6 


will  represent  in  kilogrammes   its  pressure  on  a  square  centi- 


metre ;  and  therefore  the  internal  pressure  on  the  valve,  and  which  is  equal  to  the  ex- 

X  X   I3'6  X  32 
1000 


temal  pressure  of  25  kilogrammes,  is 
For  the  weight  we  shall  have 


25  k.    From  which  jr  =  57*44. 


P  =  ^' 


0-00I293      ^  57-44  ^  8 -8055  grammes. 


I  +  o  "00366  X  30       76*00 

58.  A  bell-jar  contains  3*17  litres  of  air;  a 
pressure  gauge  connected  with  it  marks  zero  when 
in  contact  with  the  air  (fig.  3).  The  jar  is  closed 
and  the  machine  worked  ;  the  mercury  rises  to  65  cm. 
A  second  barometer  stands  at  76  cm.  during  the 
experiment.  Required  the  weight  of  air  withdrawn 
from  the  bell-jar  and  the  weight  of  that  which  re- 
mains. 

At  0°  and  76  cm.  the  weight  of  air  in  the  bell-jar  is 

1*293  X  3*17  =  4*09881. 

At  0°  and  under  the  pressure  76  —  65  the  weight 
of  the  residual  air  is 


4*09881    X    II 

76 


=  0*5932, 


and  therefore  the  weight  of  that  which  is  withdrawn 
is  4*0988  -  0*5932  =  3-5056  gr. 


1 

^IE13^^^^H 

H 

jjjjjJSllllB 

[M^^^Mj 

IhhihhI 

Fig.  3. 


59.  The  capacity  of  the  receiver  of  an  air-pump  is  7*53  ;  it  is  full  of  air  under  the 
ordinary  atmospheric  pressure  and  at  0°.  Required  the  weight  of  air  when  the  pressure 
is  reduced  to  0*21  ;  the  weight  withdrawn  by  the  piston  ;  and  the  weight  which  would 
be  left  at  15°. 

The  weight  of  7*53  litres  of  air  under  the  ordinary  conditions  is  9*736  grammes. 

Under  a  pressure  of  0*21  it  will  be  2  69  grammes,  and  at  the  temperature  15°  it  will 
2*69 


be 


I  +  0*00366  X  15 


=  0*255  gramme. 


60.  In  a  theoretically  perfect  air  pump,  how  great  is  the  rarefaction  after  10  strokes, 
if  the  volumes  of  the  barrel  and  the  receiver  are  respectively  2  and  3  ? 


Ans. 


4-59" 


or  about  -  -  of  an  atmosphere. 
166 


61.  What  must  be  the  capacity  of  the  barrel  of  an  air-pump  if  the  air  in  a  re- 
ceiver of  4  litres  is  to  be  reduced  to  ^  the  density  in  two  strokes  ?  Ans.  2*9. 

62.  The  reservoir  of  an  air-gun,  the  capacity  of  which  is  40  cubic  inches,  con- 
tains air  whose  density  is  8  times  that  of  the  mean  atmospheric  pressure.  A  shot  is 
fired  when  the  pressure  is  741  cm.  and  the  gas  which  escapes  occupies  a  volume  of  80 
cubic  inches.  What  is  the  elastic  force  of  the  residual  air?     Ans.  6*05 atmospheres. 

63.  If  water  is  continually  flowing  through  an  aperture  of  3  square  inches  with  a 
velocity  of  10  feet,  howmany  cubic  feet  will  flow  out  inanhour  ?  Ans.  750  cubic  feet. 

64.  With  what  velocity  does  water  flow  from  an  aperture  of  3  square  inches,  if 
37*5  cubic  feet  flow  out  every  minute?  Ans.  30  feet. 

65.  What  is  the  ratio  of  the  pressure  in  the  above  two  cases?  Ans.  i  :  9. 

66.  What  is  the  theoretical  velocity  of  water  from  an  aperture  which  is  9  feet 
below  the  surface  of  water  ?  ■  Ans.  24  feet. 

67.  In  a  cylinder,  water  stands  2  feet  above  the  aperture  and  is  loaded  by  a  piston 
which  presses  with  a  force  of  6  pounds  on  the  square  inch.  Required  the  velocity  of 
the  effluent  water.  Ans.  32  feet. 


SyS  Problems  and  Examples  in  Physics. 

68.  How  deep  must  the  aperture  of  the  longer  leg  of  a  syphon,  which  has  a  sec- 
tion of  4  square  centimetres,  be  below  the  surface  of  the  water  in  order  that  25  litres 
may  flow  out  in  a  minute?  Ans.   104  cm. 

69.  Through  a  «>^«/ar  aperture  having  an  area  of  o'oiqS  square  cm.  in  the  bottom 
of  a  reservoir  of  water  which  was  kept  at  a  constant  level,  55  cm.  above  the  bottom, 
it  was  found  that  98  "5  grammes  of  water  flowed  in  22  seconds.  Required  the  coeffi- 
cient of  efflux. 

Since  the  velocity  of  efflux  through  an  aperture  in  the  bottom  of  a  vessel  is  given  by 
the  formula  v  =  J  agh,  it  will  readily  be  seen  that  the  weight  .in  grammes  of  water 
which  flows  in  a  given  time,/,  will  be  given  by  the  formula  w  =  a  at  \/  2gh,  where  (2  is 
the  area  in  square  centimetres,  a  the  coefficient  of  efflux,  t  the  time  in  seconds  and  h 
the  height  in  centimetres.     Hence  in  this  case  a  =  0-69609. 

70.  Similarly  through  a  square  aperture,  the  area  of  which  was  almost  exactly  the 
same  as  the  above,  and  at  the  same  depth,  104 '4  grammes  flowed  out  in  21 '6  seconds. 
In  this  case  a  =  073. 

71.  A  stone  is  dropped  into  a  well,  and  4  seconds  afterwards  the  report  of  its 
striking  the  water  is  heard.  Required  the  depth,  knowing  that  the  temperature  of  the 
air  in  the  pit  was  1074°.  

From  the  formula  v  =  333  s/i  +  a/  we  get  for  the  velocity  of  sound  at  the  tem- 
perature in  question  343  metres. 

Let  /  be  the  time  which  the  stone  occupies  in  falling ;  then  \  gfi  =  x  will  represent 
the  depth  of  the  well ;  on  the  other  hand,  the  time  occupied  by  the  report  will  be  4  —  /, 
and  the  distance  will  be  {\  —  t)v  =  x  (i)  ;  thus  [^  —  t)  v  =  ^  gf-  (ii),  from  which, 
substituting  the  values, 

(4-0  343  =  4*9  f^ 

t  =  3793  seconds,  andl  substituting  this  value  in  either  of  the  equations  (i)  or  (ii), 
we  have  the  depth  =  70*5  metres  nearly. 

72.  A  bullet  is  fired  from  a  rifle  with  a  velocity  of  414  metres,  and  is  heard  to  strike 
a  target  4  seconds  afterwards.  Required  the  distance  of  the  target  from  the  marks- 
man ;  the  temperature  being  assumed  to  be  zero. 

- —   + =  a;  X  =  738 "2. 

414       333 

73.  At  what  distance  is  an  observer  from  an  echo  which  repeats  a  sound  after  3 
seconds  ;  the  temperature  of  the  air  being  10°  ? 

In  these  3  seconds  the  sound  traverses  a  distance  of  3  x  337  =  im  metres  ;  this 
distance  is  twice  that  between  the  observer  and  the  reflecting  surface  ;  hence  the  dis- 
tance is 

— ^  =  505  metres. 
2 

74.  Between  a  flash  of  lightning  and  the  time  at  which  the  corresponding  thunder 
is  first  heard  two  beats  of  the  pulse  are  counted.  Knowing  that  the  pulse  makes  80 
beats  in  a  minute,  what  is  the  distance  of  the  discharge  ?  Ans.  222  metres. 

75.  A  stone  is  thrown  into  a  well  with  a  velocity  of  12  metres  ;  and  strikes  the 
water  4  seconds  afterwards.  Required  the  depth  of  the  well.    Ans.  About  no  metres. 

76.  What  is  the  velocity  of  sound  in  coal  gas  at  0°,  the  density  being  0-5? 

Afis,  475  metres. 

77.  What  must  be  the  temperature  of  air  in  order  that  sound  may  travel  in  it  with 
the  same  velocity  as  in  hydrogen  at  0°  ?  Ans.  About  3650°  C. 

78.  What  must  be  the  temperature  of  air  in  order  that  the  velocity  of  sound  may 
be  the  same  as  in  carbonic  acid  at  0°  ?  Ans.  —  io5°5'C. 

79.  The  report  of  a  cannon  is  heard  15  seconds  after  the  flash  is  seen.  Required 
the  distance  of  the  cannon,  the  temperature  of  the  air  being  22°. 

From  the  formula  for  the  velocity  of  sound  we  have 

15  X  333  \/i  +  0-003665  X  22  =  5175  metres. 


Prohlems  and  Examples  in  Physics.  Sf^ 

80.  A  person  stands  150  feet  on  one  side  of  the  line  of  fire  of  a  rifle  range  450  feet 
in  length  and  at  right  angles  to  a  point  150  feet  in  front  of  the  target.     What  is  the 

velocity  of  the  bullet  if  the  person  hears  it  strike  ^  of  a  second  later  than  the  report 

9 
of  the  gun?  Ans.  2013  feet. 

81.  An  echo  repeats  five  syllables,  eagh  of  which  requires  a  quarter  of  a  second  to 
pronounce,  and  half  a  second  elapses  between  the  time  the  last  syllable  is  heard,  and 
the  first  syllable  is  repeated.  What  is  the  distance  of  the  echo,  the  temperature  of 
the  air  being  10°  C.  ?  Afzs.  295  seconds. 

82.  The  note  given  by  a  silver  wire  a  millimetre  in  diameter  and  a  metre  in 
length  being  the  middle C,  what  is  the  tension  of  the  wire?    Ans.  zz'Sj  kilogrammes, 

83.  The  density  of  iron  being  7 '8  and  that  of  copper  8*8,  what  must  be  the 
thickness  of  wires  of  these  materials  of  the  same  length  and  equally  stretched  so  that 
they  may  give  the  same  sound  ? 

From  the  formula  for  the  transverse  vibration  of  strings  we  have  for  the  number  of 

vibrations  n  =  ^      /  —  .     As  in  the  present  case,  the  tensions,  the  length  of  the 

rl^    ft  d 
strings,  and  the  number  of  vibrations  are  the  same,  we  have 

^       /^  =  -,     /Z",  from  which  i       A=i     /I; 

r"-         d'         8-8     ,  r  /8^     .  , 

whence  —   =     ,    =  —  ;  hence  -  =   ^  /  —  =   1  062. 
r,2         d         7*8  r,         V    7-8 

84.  A  wire  stretched  by  a  weight  of  13  kilos  sounds  a  certain  note.  What  must 
be  the  stretching  weight  to  produce  the  major  third  ? 

The  major  third  having  ^  the  number  of  vibrations  of  the  fundamental  note,  and  as 
4 
all  other  things  being  the  same,  the  numbers  of  vibrations  are  directly  as  the  square 
roots  of  the  stretching  weight,  we  shall  have  x  =  20'3i2  kilos. 

85.  The  diameters  of  two  wires  of  the  same  length  and  material  are  0*0015  and 
0-0038  m. ;  and  their  stretching  weights  400  and  1600  grammes  respectively.  Required 
the  ratio  of  the  numbers  of  their  vibrations.  Ans.  n  :  n,  =   1-266  :  i. 

86.  A  brass  wire  i  metre  in  length  stretched  by  a  weight  of  2  kilogrammes,  and  a 
silver  wire  of  the  same  diameter,  but  3  "165  metres  in  length,  give  the  same  number  of 
vibrations.     What  is  the  stretching  weight  in  the  latter  case  ? 

Since  the  number  of  vibrations  is  equal,  we  shall  have 


ris/      d        rl\/  n  d/ 


from  which,  replacing  the  numbers,  we  get  ^  =  25  kilos. 

87.  A  brass  and  a  silver  wire  of  the  same  diameter  are  stretched  by  the  weights  of  2 
and  25  kilogrammes  respectively,  and  produce  the  same  note.  What  are  their  lengths, 
knowing  that  the  density  of  brass  is  8-39,  and  of  silver  10-47. 

Ans.     The  length  of  the  silver  wire  is  3-16  times  that  of  the  brass. 

88.  A  copper  wire  1-25  mm.  in  diameter  and  a  platinum  one  of  0*75  mm.  are 
stretched  by  equal  weights.  What  is  the  ratio  of  their  lengths,  if,  when  the  copper 
wire  gives  the  note  C  the  platinum  gives  F  on  the  diatonic  scale  ? 

Ans.  The  length  of  the  copper  is  to  the  length  of  the  platinum  =   1-264  :  i- 

89.  An  organ  pipe  gives  the  note  C  at  a  temperature  0°  ;  at  what  temperature 
will  it  yield  the  major  third  of  this  note?  Ans.   153O  C. 

90.  A  brass  wire  a  metre  in  length  and  stretched  by  a  weight  of  a  kilogramme, 
yields  the  same  note  as  a  silver  wire  of  the  same  diameter  but  2-5  metres  in  length  and 
stretched  by  a  weight  of  7-5  kilogrammes.    Required  the  specific  gravity  of  the  silver. 

Ans.  10  32, 

91.  Two  mercurial  thermometers  are  constructed  of  the  same  glass  ;  the  internal 
diameter  of  one  of  the  bulbs  is  7™™ '5  and  of  its  tube  2-5  ;  the  bulb  of  the  other  is 


88o 


Problems  and  Examples  in  Physics, 


6-2  in  diameter  and  its  tube  1-5.     What  is  the  ratio  of  the  length  of  a  degree  of  the 

first  thermDmeter  to  a  degree  of  the  second  ? 

Let  A  and  B  be  the  two  thermometers,  D  and  D' 
the  diameters  of  the  bulbs,  and  d  and  d'  the  dia- 
meters of  the  tubes.  Let  us  imagine  a  third  thermo- 
meter C  with  the  same  bulb  as  B  and  the  same  tube 
as  A,  and  let  /,  /',  and  /"  denote  the  length  of  a 
degree  in  each  of  the  thermometers  respectively. 
Since  the  stems  of  A  and  C  have  the  equal  dia- 
meters, the  lengths  /  and  /"  are  directly  as  the 
volumes  of  the  tubes,  or  what  is  the  same,  as  the 
cubes  of  their  diameters  ;  and  as  B  and  C  have  the 
same  bulk,  the  lengths  /'  and  /"  are  inversely  pro- 
portionate to  the  sections  of  the  stems,  or  what 
amounts  to  the  same,  to  the  squares  of  their  dia- 
meters.    We  have  then 


Fig. 


introducing  the  values  and  solving,  we  have 
J,  =  0-638. 


92.  A  capillary  tube  is  divided  into  180  parts  of  equal  capacity,  25  of  which  weigh 
1*2  gramme.  What  must  be  the  radius  of  a  spherical  bulb  to  be  blown  to  it  so  that 
180  divisions  correspond  to  150  degrees  centigrade? 

Since  25    divisions  of  the    tube    contain    12    gramme,     180   divisions    contain 

'  ^  ^  ^  °    =  8?''*64.     And  since  these  180  divisions  are  to  represent  150  degrees,  the 
25 

weight  of  mercury  corresponding  to  a  single  degree  is 


8^64 
[50* 


But  as  the  expansion  cor- 
responding to  one  degree  is  only  the  apparent  expansion  of  mercury  in  glass,  the  weight 

— 4-  jg      I  _  Qf  tj^g mercury  in  the  reservoir,  which  is  ^  irR^.    From  this  ^  =  I'Sy  centi- 

150       6480  3 

metre. 

93.  By  how  much  is  the  circumference  of  an  iron  wheel,  whose  diameter  is  6  feet, 
increased  when  its  temperature  is  raised  400  degrees  ?  Co-efficient  of  expansion  of 
iron  =  o'ooooi22.  Ans.   By  0*092  foot. 

94.  What  must  be  the  length  of  a  wire  of  this  metal  which  for  a  temperature  of 
1°  expands  by  one  foot  ?  Ans.    =  81967  feet. 

95.  A  pendulum  consists  of  a  platinum  rod,  on  a  flattening  at  the  end  of  which 
rests  a  spherical  zinc  bob.  The  length  of  the  platinum  is  /  at  0°.  What  must  be  the 
diameter  of  the  bob,  so  that  its  centre  is  always  at  the  same  distance  from  the  point  of 
suspension  wliatever  be  the  temperature  ?  Coefficient  of  expansion  of  platinum 
o  •0000088  and  of  zinc  o  •0000294. 

Ans.  The  diameter  of  the  bob  must  be  ^  of  the  length  of  the  platinum. 

96.  At  the  temperature  zero  a  solid  is  immersed  0*975  of  its  total  volume  in 
alcohol.  At  the  temperature  25°  the  solid  is  wholly  immersed.  The  coefficient  of 
expansion  of  the  solid  being  o •000026,  required  the  coefficient  of  expansion  of  the 
alcohol.  Ans.  o •001052. 

97.  Into  a  glass  globe,  the  capacity  of  which  at  0°  is  250  cc,  are  introduced 
25  cc.  of  air  measured  at  0°  and  76  cm.     The  flask  being  closed  and  heated  to  100° 


required  the  internal  pressure.     Coefficient  of  cubical  expansion  of  glass 


38700' 


At  100^  the  capacity  of  the  flask  is  250  (i  +  — -22_^  ;  again  at  100°  the  volume  of 

V         38700/ 

X  o  •00366). 


the  free  air  under  the  pressure  76  is  25  (i  +  0100 

250  y  ^—  under  a  pressure  x.     Hence 
387 

76    :  ;»;  =  250  x  ■^^^    :  25  x  1-366,  from  which 


.But  its  real  volume  is 


388 
387 


10-3548  cm. 


Problems  and  Examples  in  Physics.  88  r 

98.  The  specific  gravity  of  mercury  at  o°  being  i3'6,  required  the  volume  of  3c 
kilogrammes  at  85°.     Coefficient  of  expansion 

The  volume  at  0°  will  be    3°    and  at  85°  -22.    x  (  i  +  — ^^-  )  =  2-239  litres. 

13-6  13-6    V      5550  >' 

99.  A  hollow  copper  sphere  20  cm.  in  diameter  is  filled  with  air  at  0°  under  a 
pressure  of  i^  atmosphere  ;  what  is  the  total  pressure  on  the  interior  surface  when  the 
enclosed  air  is  heated  to  a  temperature  of  600°?  Ans.  6226*5  kilogrammes. 

100.  Between  the  limits  of  pressure  700  to  780mm.  the  boiling  point  of  water  varies 
o°'0375  C.  for  each  mm.  of  pressure.  Between  what  limits  of  temperature  does  the 
boiling  point  vary,  when  the  height  of  the  barometer  is  between  735  and  755  mm. 

Ans.   Between  99*^-0625  and  99°  "8125. 

101.  Liquid  phosphorus  cooled  down  to  30°,  is  made  to  solidify  at  this  tempera- 
ture. Required  to  know  if  the  solidification  will  be  complete,  and  if  not,  what 
weight  will  remain  melted  ?  The  melting  point  of  phosphorus  is  44*2  ;  its  latent  heat 
of  fusion  5-4,  and  its  specific  heat  0*2. 

Let  X  be  the  weight  of  phosphorus  which  solidifies  ;  in  so  doing  it  will  give  out  a 
quantity  of  heat  =  5'4  •*■ ;  this  is  expended  in  raising  the  whole  weight  of  the  phos- 
phorus from  30  to  44-2.     Hence  we  have  5-4  jr  =   i   x  (44-2  -  30)  0*2,   from  which 

X  —  "^A  =  0*526,  so  that  0*474  of  phosphorus  will  remain  liquid. 
5 '4 

102.  A  pound  of  ice  at  o*^  is  placed  in  two  pounds  of  water  at  0°  ;  required  the 
weight  of  steam  at  100°  which  will  melt  the  ice  and  raise  the  temperature  of  the  mix- 
ture to  30°.  The  latent  heat  of  the  liquefaction  of  ice  is  79*2  and  that  of  the  vaporisa- 
tion of  water  536.  Ans.   *279  pounds. 

103.  65*5  grammes  of  ice  at  —  20°  having  been  placed  in  x  grammes  of  oil  of 
turpentine  at  -  3°,  the  final  temperature  is  found  to  be  —  1°.  The  specific  heat  of 
turpentine  is  0*4,  and  it  is  contained  in  a  vessel  weighing  25  grammes,  whose  specific 
heat  is  o*i.     The  specific  heat  of  ice  is  0*5.     Required  the  value  of  x. 

Ans.  x  =  382*0  grammes. 

104.  In  what  proportion  must  water  at  a  temperature  of  30°  and  linseed  oil  (sp 
heat  =  0*5)  at  a  temperature  of  50°  be  mixed  so  that  there  are  20  kilogrammes  of  the 
mixture  at  40°?  Ans.  Water  =   6*66  kilos,  and  linseed  oil   =   13*34. 

105.  By  how  much  will  mercury  at  0°  be  raised  by  an  equal  volume  of  water  at 
100°  ?  Ans.  6%°-SC. 

106.  The  specific  heat  of  gold  being  0*03244,  what  weight  of  it  at  45°  will  raise  a 
kilogramme  of  water  from  i2°*3  to  i5°*7? 

Let  X  be  the  weight  sought  ;  then  x  kilogrammes  of  gold  in  sinking  from  45°  tc 
1 5°  7  will  give  out  a  quantity  of  heat  represented  by  x  (45°  —  15° '7)  0*0324,  and  this  is 
equal  to  the  heat  gained  by  the  water  that  is  to  i  (15*7  —  12*3)  =  3*4,  that  is  :*:•  =  3*58. 

107.  The  specific  heat  of  sulphide  of  copper  is  0*1212  and  that  of  sulphide  of  silver 
0*0846.  5  kilos,  of  a  mixture  of  these  two  bodies  at  40°,  when  immersed  in  16  kilos,  of 
water  at  7*66  degrees,  raises  its  temperature  to  10°.  How  much  of  each  sulphuret  did 
the  mixture  contain  ? 

The  weight  of  the  copper  sulphuret  =  2  and  that  of  the  silver  sulphuret  3. 

108.  Into  a  mass  of  water  at  0°,  100  grammes  of  ice  at  —  12°  are  introduced  ;  a 
weight  of  7*2  grammes  of  water  at  0°  freezes  about  the  lump  immersed,  while  its 
temperature  rises  to  zero.  Required  the  specific  heat  of  ice.  Latent  heat  of  water 
79*2.  Ans.  0*48114. 

109.  Four  pounds  of  copper  filings  at  130°  are  placed  in  20  pounds  of  water  at  20°, 
the  temperature  of  which  is  thereby  raised  2  degrees.  What  is  the  specific  heat,  c,  of 
copper?  Ans.  c  =  0*0926. 

110.  Two  pieces  of  metal  weighing  300  and  350  grammes,  heated  to  a  temperature 
X,  have  been  immersed,  the  former  in  9408  grammes  of  water  at  10°,  and  the  latter  in 
546  grammes  at  the  same  temperature.  The  temperature  in  the  first  case  rises  to  20"^ 
and  in  the  second  to  30°.  Required  the  original  temperature  and  the  specific  heat  of 
the  metal.  Ans.  x  the  temperature  =  1908°  ;     c  the  specific  heat   =    •1038. 

111.  In  what  proportions  must  a  kilogramme  of  water  at  50°  be  divided  in  order  that 
the  heat  which  one  portion  gives  out  in  cooling  to  ice  at  zero  may  be  sufficient  to  change 
the  other  into  steam  at  100®  ?  Ans.  x  =  0*830. 


882  Problems  and  Examples  in  Physies. 

112.  In  25-45  kilogrammes  of  water  at  i2°-5^  are  placed  6-17  kilos  of  a  body  at  a 
temperature  of  80°  ;  the  mixture  acquires  the  ternperature  14° 'i.  Required  the  specific 
heat  of  the  body. 

If  c  is  the  specific  heat  required,  then  mc  [f  —  6)  represents  the  heat  lost  by  the  body 
in  cooling  from  80°  to  i^P'i ;  and  that  absorbed  by  the  water  in  rising  from  12"^ -5  to 
i4°'i  is  m'  (B  —  i).     These  two  values  are  equal.     Substituting  the  numbers,  we  have 

c    =   O'OII. 

113.  Equal  lengths  of  the  same  thin  wire  traversed  by  the  same  electrical  current  are 
placed  respectively  in  i  kilogramme  of  water  and  in  3  kilogrammes  of  mercury.  The 
water  is  raised  10°  in  temperature,  by  how  much  will  the  mercury  be  raised  ? 

Ans.  100° '04. 

114.  How  many  cubic  feet  of  air  under  constant  pressure  are  heated  through  1°  C. 
by  one  thermal  unit  ?  Ans.  52  cubic  feet. 

115.  Given  two  pieces  of  metal,  one  x  weighing  2  kilos  heated  to  80°,  and  the  other 
y  weighing  3  kilos  and  at  the  temperature  50^.  To  determine  their  specific  heats 
they  are  immersed  in  a  kilogramme  of  water  at  10°,  which  is  thereby  raised  to  26°-3. 

The  experiment  is  repeated,  the  two  metals  being  at  the  temperature  100°  and  40° 
respectively,  and,  as  before,  they  are  placed  in  a  kilogramme  of  water  at  10°,  which 
this  time  is  raised  to.  28°*4.     Required  the  specific  heats  of  the  two  metals. 

Ans.  X  =    -115  ;  y  =   0-0555. 

116.  For  high  temperatures  the  specific  heat  of  iron  is  o"io53  +  o  •000071  /.  What 
is  the  temperature  of  a  red-hot  iron  ball  weighing  a  kilogramme  which,  plunged  in  16 
kilogrammes  of  water,  raises  its  temperature  from  12°  to  24°  ?  What  was  the  tempe- 
rature of  the  iron  ? 

(0*1053  -^  o"ooooi7/)  (/  —  24)   =   16  (24  —  12), 
or  •000017  fi  +   "1048892  t  —  2*5272  =   192  ; 

transposing  and  dividing  by  the  coefficient  of  fi,  we  get 
^2  +  6170  /  =   1 1442776, 
/2  +  6170  t  +  (3085)-  =  20960001 ; 
hence  /  +  3085  =  4578^3  nearly  ;    .-.  t  =   1493.3. 

117.  A  kilogramme  of  the  vapour  of  alcohol  at  80°  passes  through  a  copper  worm 
placed  in  io-8  kilogrammes  of  water  at  12°,  the  temperature  of  which  is  thereby  raised 
to  36°.  The  copper  worm  and  copper  vessel  in  which  the  water  is  contained  weigh 
together  3  kilogrammes.     Required  the  latent  heat  of  alcohol  vapour.      Ans.  210-4^. 

118.  Determine  the  temperature  of  combustion  of  charcoal  in  burning  to  form  car- 
bonic acid. 

We  know  from  chemistry  that  one  part  by  weight  of  carbon  in  burning  unites 
with  2§  parts  by  weight  of  oxygen  to  form  3§  parts  by  weight  of  carbonic  acid. 
Again  the  number  of  thermal  units  produced  by  the  combustion  of  a  pound  of  charcoal 
is  8080  ;  the  whole  of  this  heat  is  contained  in  the  3§  parts  of  carbonic  acid  produced, 
and  if  its  specific  heat  were  the  same  as  that  of  water,  its  temperature  would  be 

— —  =  2204°  C. ;  but  since  the  specific  heat  of  carbonic  acid  is  0-2163  that  of  an  equal 

weight  of  water,  the  temperature  will  be  .^?21    =  10189  C. 

0^2163 

119.  Through  a  U-tube  containing  pumice  saturated  with  sulphuric  acid  a  cubic 
metre  of  air  at  15°  is  passed,  and  the  tube  is  found  to  weigh  3^95  grammes  more. 
Required  the  hygrometric  state  of  the  air. 

The  pressure  of  aqueous  vapour  at  15°  is  12^699 ;  hence  the  weight  of  a  cubic 
metre  of  aqueous  vapour  saturated  at  15°  is    1293  x  i2^699  x  5  ^   ^^.^^  grammes, 

I  +  ^^  760  X  8 
273/ 

and  the  hygrometric  state  is  -3 '95    _  o-qoo 
12-79 

120.  The  quantity  of  water  given  out  by  the  lungs  and  skin  may  be  taken  at 
30  ounces  m  24  hours.  How  many  cubic  inches  of  air  already  half  saturated  at  10°  will 
be  fully  saturated  by  the  moisture  exhaled  from  the  above  two  sources  by  one  man  ? 
Tension  of  aqueous  vapour  in  inches  =  0-532.    Pressure  of  the  atmosphere  =  30  inches. 

Ans.  328782-5  c.i.  =  a  cube  5-752  feet  in  the  side. 


*  Problems  and  Examples  in  Physics.  883 

121.  A  mass  of  air  extending  over  an  area  of  60,000  square  metres  to  a  height  of 
300  metres  has  the  dew  point  at  15°  its  temperature  being  20°.  How  much  rain  will 
fall  if  the  temperature  sinks  to  10°  ? 

The  weight  of  vapour  condensed  from  one  cubic  metre  under  these  circumstances 
will  be  3*1435  grammes  and  therefore  from  18,000,000  cubic  metres  it  will  be  56,583 
kilogrammes,  which  is  equal  to  a  rainfall  0*0943  mm.  in  depth. 

122.  When  3  cubic  metres  of  air  at  10°  and  5  cubic  metres  at  18°,  each  saturated 
with  aqueous  vapour  at  those  temperatures,  are  mixed  together  is  any  water  precipi- 
tated ?    And  if  so  how  much  ? 

The  weight  of  water  contained  in  the  two  masses  under  the  given  conditions  are 
respectively  28"i8  and 76*59  grammes  ;the  weight  required  to  saturate  the  mixture  at  the 
temperature  of  15°  is  102*39  grammes,  and  therefore  2*38  grammes  will  be  precipitated. 

123.  The  temperature  of  the  air  at  sunset  being  10°,  what  must  be  the  lowest  hygro- 
metric  state,  in  order  that  dew  may  be  deposited,  it  being  assumed  that  in  conse- 
quence of  nocturnal  radiation  the  temperature  of  the  ground  is  7°  below  that  of  the  air  ? 

Atts.  The  hygrometric  state  must  be  at  least  0*62  of  total  saturation. 

124.  A  raindrop  falls  to  the  ground  from  a  height  of  a  mile.  By  how  much  would 
its  temperature  be  raised,  assuming  that  it  imparts  no  heat  to  the  air  or  to  the  ground? 

Ans.  30*8  C. 

125.  A  lead  bullet  falls  through  a  height  of  10  metres  ;  by  what  amount  will  its 
temperature  have  been  raised  when  it  reaches  the  ground,  if  all  the  heat  is  expended  in 
raising  the  temperature  of  the  bullet  ?  Ans.  0744°  Centigrade. 

126.  From  what  height  must  a  lead  bullet  fall  in  order  that  its  temperature  may 
be  raised  ;/  degrees  ? — and  what  velocity  will  it  have  acquired  ?  It  is  assumed  that  all  the 
heat  is  expended  in  raising  the  temperature  of  the  bullet,  the  specific  heat  of  lead  is 
taken  at  0*0314  and  Joule's  equivalent  in  metres  at  424. 

Ans.  13*31  X  n  metres  ;  ?7  =   16*2  y/ n. 

127.  How  much  heat  is  disengaged  if  a  bullet  weighing  50  grammes  and  having 
a  velocity  of  50  metres  strikes  a  target  ? 

Atis.  Sufficient  to  raise  one  gramme  of  water  through  15°  C. 

128.  How  much  heat  is  produced  in  the  room  of  a  manufactory  in  which  i  2.  horse- 
power of  the  motor  is  consumed  each  hour  in  overcoming  the  resistance  of  friction? 

Ans.  A  quantity  sufficient  to  raise  41,024  pounds  of  water  one  degree  centigrade. 

129.  What  is  the  ratio  between  the  quantities  of  heat  which  are  respectively  pro- 
duced, when  a  bullet  weighing  50  grammes  and  having  a  velocity  of  500  metres, 
and  a  cannon  ball  weighing  40  kilogrammes  with  a  velocity  of  400  metres,  strike  a 
target?  A71S.   i  :  512. 

130.  How  many  candles  are  required  to  produce  at  a  distance  of  2*5  metres,  the 
same  illuminating  effect  as  one  candle  at  a  distance  of  0*45  m.  ?  Am.  31. 

131.  Two  sources  of  light  whose  intensities  are  as  i  :  2  are  two  metres  apart.  At 
what  position  is  a  space  between  them  equally  illuminated  ? 

Ans.  0*82  metres  from  the  less  intense  light. 

132.  A  candle  sends  its  rays  vertically  against  a  plane  surface.  When  the  candle  i? 
removed  to  thrice  the  distance  and  the  surface  makes  an  angle  of  60°  with  the  original 

position,  what  is  the  ratio  of  the  illuminations  in  the  two  cases  ?  Ans.  i  :  — 

i8- 

133.  An  observer,  whose  eye  is  6  feet  above  the  ground,  stands  at  a  distance  of  18 
feet  from  the  near  edge  of  a  still  pond,  and  sees  there  the  image  of  the  top  of  a  tree, 
the  base  of  which  is  at  a  distance  of  100  yards  from  the  place  at  which  the  image  is 
formed.     Required  the  height  of  the  tree.  Ans.  100  feet. 

134.  What  is  the  height  of  a  tower  which'  casts  a  shadow  56*4  in  length  when  a 
vertical  rod  0*95  m.  in  height  produces  a  shadow  1*38  in  length?  Ans.  38 -8. 

135.  A  minute  hole  is  made  in  the  shutter  of  a  dark  room  ;  and  at  a  distance  of 
2*5  metres  a  screen  is  held.  What  is  the  size  of  the  image  of  a  tree  which  is  15-3 
metres  high  and  is  at  a  distance  of  40  metres?  Ans.  0*95625  metres. 

136.  What  is  the  length  of  the  shadow  of  a  tree  50  feet  high  when  the  sun  is  30° 
above  the  horizon?  What  when  it  is  45°  and  60°?    Ans,  86*6  ;  50  and  28*867  feet. 


884  Problems  and  Examples  in  Physics,  ♦ 

137.  Under  what  visual  angle  does  a  line  of  30  feet  appear  at  a  distance  of  18  feet  ? 

Atis.  79° '36. 

138.  The  apparent  diameter  of  the  moon  amounts  to  31'  3".  What  is  its  real  dia- 
meter if  its  distance  from  the  earth  is  taken  at  51535  geographical  miles? 

A7ts.  465  geographical  miles. 

139.  For  an  ordinary  eye  an  object  is  visible  with  a  moderate  illumination  and  pure 
air  under  a  visual  angle  of  40  seconds.  At  what  distance,  therefore,  can  a  black  circle 
(6  inches  in  diameter)  be  seen  on  a  white  ground  ?  Ans.  2578  feet. 

140.  At  what  distance  from  a  circle  with  a  diameter  of  one  foot  is  the  visual  angle  a 
second?  Ans.  206265  feet. 

141.  At  what  distance  would  a  circular  disc  i  inch  in  diameter,  of  the  same  bright- 
ness as  the  sun's  surface,  illuminate  a  given  object  to  the  same  extent  as  a  vertical  sun 
in  the  tropics,  the  light  absorbed  by  the  air  being  neglected  ? 

Ans.  Taking  the  sun's  angular  diameter  at  30',  j;  =  38  inches. 

142.  What  is  the  minimum  deviation  for  a  glass  prism  «  =  i  •53,  whose  refracting 
angle  is  60°?  Ans.  39°  48'. 

143.  What  is  the  minimum  deviation  for  a  prism  of  the  same  substance  when  the 
refracting  angle  is  45°  ?  Ans.  63°  38'. 

144.  The  refracting  angle  of  a  prism  of  silicate  of  lead  has  been  found  by  measure- 
ment to  be  21° "1 2,  and  the  minimum  deviation  to  be  24° "46.  Required  the  refractive 
index  of  the  substance.  Atis.  2*122. 

145.  Construct  the  path  of  a  ray  which  falls  on  an  equiangular  crown-glass  prism 
at  an  angle  of  30°  ;  and  find  its  deviation.  Ans.  70° "45. 

146.  What  are  the  angles  of  refraction  upon  a  ray  which  passes  from  air  into  glass 
at  an  angle  of  40°  ;  from  air  into  water  at  an  angle  of  65°  ;  and  from  air  into  diamond 
at  an  angle  of  80°?  Ans.  25° '22  ;  43° '49  ;  23° -12. 

147.  The  focal  distance  of  a  concave  mirror  is  8  diameters.  What  is  the  distance 
of  the  image  from  the  mirror  when  the  object  is  respectively  at  12,  5,  and  7  diameters 
distance?  Ans.  24;   —  13-3  and  —  56. 

148.  An  object  at  a  distance  of  10  feet  produces  a  distinct  image  at  a  distance  of  3 
feet.     What  is  the  focal  distance  of  the  mirror?  Ans.  2 '3077  feet. 

149.  Required  the  focal  distance  of  a  crown  glass  meniscus,  the  radius  of  curvature 
of  the  concave  face  being  45  mm.,  and  that  of  the  convex  face  30  mm. 

Ans.  f  =   180  mm. 

150.  What  is  the  principal  focal  distance  of  a  double-convex  lens  of  diamond,  the 
radius  of  curvature  of  each  of  whose  faces  is  4  mm.,  and  the  refractive  index  of  dia- 
mond 2*487?  Ans.   1*34  mm. 

151.  A  watch-glass  with  ground  edges,  the  curvature  of  which  was  4*5  cm.,  was 
filled  with  water  and  a  glass  plate  slid  over  it.  The  focus  of  the  plano-convex  lens 
thus  formed  was  found  to  be  13*5  cm.     Required  the  refractive  index  of  the  water. 

Ans.  n   =   i'33- 

152.  What  is  the  focal  distance  of  a  double-convex  lens  when  the  distances  of  the 
image  and  object  are  respectively  5  and  36  centimetres?  Ans.  4*4  centimetres. 

153.  The  radii  of  curvature  of  a  double-convex  lens  of  crown  glass  are  six  and 
eight  inches.     What  is  the  focal  distance?  Ans.  6*85  inches. 

154.  The  focal  distance  pf  a  double-convex  lens  is  4  inches,  the  radius  of  cur- 
vature of  one  of  its  faces  is  3  inches.     What  is  that  of  the  second?   Ans.  6  inches. 

155.  The  radius  of  curvature  of  a  plano-convex  lens  is  12  inches.  Required  its 
focal  distance.  Ans.  24  inches. 

156.  If  the  focal  distance  of  a  double-convex  lens  is  r  centimetre,  at  what  distance 
must  a  luminous  object  be  placed  so  that  its  image  is  formed  at  2  centimetres  dis- 
tance from  the  lens.  Ans.  2  centimetres. 

157.  A  candle  at  a  distance  of  120  centimetres  from  a  lens  forms  an  image  on  the 
other  side  of  the  lens  at  a  distance  of  200  feet.  Required  the  nature  of  the  lens  and 
its  focal  distance.  Ans.  It  is  a  convex  lens,  and  its  focal  distance  is  75  cm. 

158.  A  plano-convex  lens  was  found  to  produce  at  a  distance  of  62  cm.  a  sharp 
image  of  an  infinitely  distant  object.  In  front  of  the  same  lens,  at  a  distance  84  cm., 
a  millimetre  scale  was  placed,  and  a  sharp  image  was  formed  at  a  distance  of  250  cm. 
It  was  thus  found  that  10  millimetres  in  the  object  corresponded  to  29  in  the  image. 


Problems  and  Examples  in  Physics.  885 

From  these  three  observations  determine  the  focal  distance  of  the  lens.     Ans.    The 
mean  of  the  three  results  is  62*4. 

159.  The  image  of  a  distant  tree  was  sharply  formed  at  a  distance  of  31  cm.  from 
the  centre  of  a  concave  mirror. 

In  another  case  the  image  of  an  object  18  mm.  in  length  at  a  distance  of  405  mm. 
from  the  mirror  was  formed  at  1350  mm.  from  the  mirror  and  had  a  length  of  61  mm. 
In  another  experiment  the  distances  of  object  and  image  and  the  size  of  the  image  were 
respectively  2200,  355  and  3  mm. 

Deduce  from  these  several  data  the  focal  distance  of  the  mirror.     A)is.  31 '2;  30*5. 

160.  A  compass  needle  at  the  magnetic  equator  makes  15  oscillations  in  a  minute  ; 
how  many  will  it  make  in  a  place  where  the  horizontal  force  of  the  earth's  magnetism  is 

? — as  great?  A?is.  12. 

25 

161.  A  compass  needle  makes  q  oscillations  a  minute  under  the  influence  of  the 
earth's  magnetism  alone  ;  how  many  will  it  make  when  re-magnetised  so  as  to  be 
half  as  strong  again  as  before?  Ans.  11. 

162.  On  a  table  where  the  earth's  magnetism  is  counteracted,  the  north  pole  of  a 
compass  needle  makes  20  oscillations  in  a  minute  under  the  attraction  of  a  blue  pole 
4  inches  distant ;  how  many  will  it  make  when  the  blue  pole  is  3  inches  distant  ? 

Ans.  26 "6. 

163.  If  the  oscillating  magnet  be  re-magnoitised  so  as  to  be  twice  as  strong  as 
before,  how  many  oscillations  in  a  minute  will  it  make  ?  Ans.  3771. 

163a.  At  one  end  of  a  light  glass  thread,  carefully  balanced  so  as  to  oscillate  in  a 
vertical  plane,  is  a  pith  ball.  Over  this  and  in  contact  with  it  is  a  fixed  pith  ball  of  the 
same  dimensions.  Both  balls  being  charged  with  the  same  electricity  it  is  found  that 
to  keep  them  i  "4  inch  apart,  a  weight  of  '9  mgr.  must  be  placed  at  the  free  end  of  the 
glass  thread.    .What  weight  must  be  placed  there  to  keep  the  balls   i"os  inch  apart  ? 

Ans.   I  "6  mgr. 

163<5.  A  small  insulated  sphere  A  charged  with  the  quantity  of  +  electricity  2  is 
at  a  distance  of  25  mm.  from  a  second  similar  sphere  B  charged  with  the  quantity  5  ; 
the  latter  is  momentarily  touched  with  an  unelectrified  sphere  B,  of  the  same  size,  and 
the  distance  altered  to  20  mm.  What  is  the  ratio  of  the  repulsive  forces  in  the  two 
cases  ?  Ans.  25  :  32. 

163c.  Two  insulated  spheres  whose  diameters  are  respectively  as  7  :  10  have  equal 
quantities  of  electricity  imparted  to  them.     In  what  ratio  are  their  electrical  densities  ? 

Ans.   100  :  49, 

163d.  Two  such  spheres  whose  diameters  are  as  3  :  5  contain  respectively  the 
quantities  of  electricity  7  and  10.     In  what  ratio  are  their  densities?       Ans.  35  :  18. 

164.  A  galvanometer  offering  no  appreciable  resistance  is  connected  by  short  thick 
wires  with  the  poles  of  a  cell,  and  deflects  20°.  By  how  much  will  it  be  deflected  if  two 
exactly  similar  cells  are  connected  with  the  first  side  by  side  ?  Ans.  47° '30. 

165.  By  how  much  if  the  three  cells  are  connected  in  series  ?  Ans.  20°. 

166.  Two  cells  each  of  i  ohm  resistance  are  connected  in  series  by  a  wire  the 
resistance  of  which  is  also  i  ohm.  If  each  of  these  when  connected  singly  by  short 
thick  wires  to  a  galvanometer  of  no  appreciable  resistance  deflects  it  25°,  how  much 
will  the  combination  deflect  it,  the  connections  being  made  by  short  thick  wires? 

Ans.  17° -1 6. 
A  Siemens'  unit  is  equal  to  the  resistance  of  a  column  of  pure  mercury  a  metre  in 
length  and  a  square  mm.  in  cross  section.     It  is  equal  to  0-9536  of  an  ohm  or   B  A 
unit;  or  a  B  A  unit  equals  i'0485  Siemens'  unit,  or  equals  a  column  of  mercury  i'0485 
metre  in  length  and  a  square  mm.  in  cross  section. 

167.  A  single  thermo-electric  couple  deflects  a  galvanometer  of  100  ohms  resis- 
tance 30';  how  much  will  a  series  of  such  couples  deflect  it,  the  connections  being  made 
by  short  thick  wires?  Ans.  14° '40. 

168.  Suppose  a  sine  galvanometer  had  been  used  in  the  last  question,  and  the 
first  reading  had  been  30',  what  would  the  second  be?  Ans.  i5°'io. 

169.  The  internal  resistance  of  a  cell  is  half  an  ohm  ;  when  a  tangent  galvan- 
ometer of  I  ohm  resistance  is  connected  with  it  by  short  thick  wires  it  is  deflected  15° ; 
by  how  much  will  it  be  deflected  if  for  one  of  the  thick  wires  a  thin  wire  of  i^  ohm 
resistance  is  substituted?  Ans.  7° •37. 


886  Problems  and  Examples  in  Physies. 

170.  What  will  be  the  deflection  if  each  of  the  wires  is  replaced  by  a  thin  wire  of 
i^  ohm  resistance  ?  Ans.  5°  5', 

171.  A  ceU  of  one-third  of  an  ohm  resistance  deflects  a  tangent  galvanometer  of 
unknown  resistance  45°,  the  connection  being  made  by  two  short  thick  wires.  If  a  wire 
of  3  ohms  resistance  be  substituted  for  one  of  the  short  wires  the  deflection  is  30°.  What 
is  the  resistance  of  the  galvanometer?  Ans.  3*42  ohms. 

172.  What  would  be  the  deflection  if  for  the  cell  in  the  last  question  three  exactly 
similar  cells  in  series  were  substituted  {a)  when  the  galvanometer  alone  is  in  circuit  ; 
ib)  when  both  the  galvanometer  and  the  thin  wire  are  in  circuit  ? 

Atis.  a  66°- 10.  b  =  55° '30. 

173.  A  galvanometer  offering  no  sensible  resistance  is  deflected  50°  by  a  cell 
connected  with  it  by  short  thick  wires.  If  a  resistance  of  3  ohms  be  put  in  the  circuit 
the  deflection  is  20°.     Find  the  internal  resistance  of  the  cell.  Ans.  1-49. 

174.  Suppose  the  results  in  the  last  question  were  produced  by  two  exactly  similar 
cells  in  series,  find  the  internal  resistance  of  each.  Ans.  0-65. 

175.  Suppose  they  were  produced  by  two  exactly  similar  cells  placed  side  by  side, 
^nd  the  internal  resistance  of  each.  Ans.  2-63. 

176.  If  the  resistance  of  130  yards  of  a  particular  copper  wire  — -  of  an  inch   in 

16 

diameter  is  an  ohm,  express  in  that  unit  the  resistance  of  8242  yards  of  copper  vnre  — 

12 
of  an  inch  in  diameter.  .  Ans.  35*66. 

177.  One  form  of  fuse  for  firing  mines  by  voltaic  electricity  consists  of  a  platinum 
wire  f  of  an  inch  long,  of  which  a  yard  weighs  2  grains.  Required  its  resistance  in 
terms  of  a  Siemens  unit.  Specific  gravity  of  platinum  22,  and  its  conducting  power 
1 1 -25  that  of  mercury.  Ans.  o'l^i. 

178.  Express  in  ohms  the  resistance  of  one  mile  of  copper  wire  |  of  an  inch  in 
diameter.  Ans.  07577. 

179.  The  whole  resistance  of  a  copper  wire  going  round  the  earth  (24800  miles)  is 

221650  ohms.     Find  its  diameter  in  inches.  Ans.  — . 

13 

180.  How  much  platinum  wire  0-05  of  an  inch  in  diameter  must  be  taken  to  get  a 
resistance  equal  to  i  ohm,  the  specific  resistance  of  platinum  being  taken  at  5*55  that  of 
copper?  Ans.  14-26. 

181.  160  yards  of  iron  wire  0-0625  of  an  inch  in  diameter  have  the  same  electrical 
resistance  as  a  mile  of  copper  wire  0-0416  of  an  inch  in  diameter.  Find  the  specific  re- 
sistance of  iron,  that  of  copper  being  unity.  Ans.  6. 

182.  Ten  exactly  similar  cells  in  series  produce  a  deflection  of  46°  in  a  tangent 
galvanometer,  the  external  resistance  of  the  circuit  being  10  ohms.  If  arranged  so 
that  there  is  a  series  of  5  cells,  of  two  abreast,  a  deflection  of  33° '42  is  produced  ; 
find  the  internal  resistance  of  the  cell.  Ans.  ^  ohm. 

183.  On  the  bobbins  of  the  new  Post  Ofiice  pattern  of  a  single  needle  instrument 
are  coiled  225  yards  of  No.  35  copper  wire  o'oo87  inch  in  diameter,  the  resistance  of 
which  is  about  92  ohms.  Required  the  conducting  power  of  the  wire  in  terms  of 
mercury.  Ans.  56. 

184.  Ten  exactly  similar  cells  each  of  |  of  an  ohm  resistance  give,  when  arranged 
in  five  series  of  2  each,  a  deflection  of  23^-57  ;  but  when  arranged  in  2  series  of  5  each 
a  deflection  of  33^-40.  Required  the  external  resistance  of  the  circuit  including  that 
of  the  galvanometer.  Ans.  \. 

185.  A  cell  in  a  certain  circuit  deflects  a  tangent  galvanometer  18°  26' ;  two  such 
cells  abreast  in  the  same  circuit  deflect  it  23°  57' ;  two  such  cells  in  the  same  circuit 
diminished  by  i  ohm  deflect  it  29° -2.  Find  the  internal  resistance  of  one  cell  and  that 
of  the  circuit.  Ans.  R  =  r  =  i*66. 

186.  What  is  the  best  arrangement  of  6  cells,  each  of  |  of  an  ohm  resistance, 
against  an  external  resistance  of  2  ohms  ? 

Ans.  Indifferent  whether  in  6  cells  of  i  each  or  in  3  cells  of  2. 

187.  What  is  the  best  arrangement  of  20  cells,  each  of  0*8  ohm  resistance,  against 
•an  external  resistance  of  4  ohms  ?  Ans.  10  cells  of  2  each. 

188.  In  a  circuit  containing  a  galvanometer  and  a  voltameter,  the  current  which 
deflects  the  galvanometer  45°  produces  10-32  cubic  centimetres  of  mixed  gas  in  a 


Problems  and  Examples  in  Physics.  ^Zj 

minute.     The  electrodes  are  put  farther  apart,   and  the  deflection  is  now  20°  ;  find 
how  much  gas  is  now  produced  per  minute.  Ans.  375  cc. 

189.  100  inches  of  copperwire  weighing  100  grains  has  a  resistance  of  o'i5i6  ohm. 
Required  the  resistance  of  50  inches  weighing  200  grains.  '  Ans.  c'oiSgs. 

190.  A  knot  of  nearly  pure  copper  wire  weighing  one  pound  has  a  resistance  of 
1200  ohms  at  i5°"5  C.  ;  what  is  the  resistance  of  a  knot  of  the  same  quality  of  wire 
weighing  125  pounds?  Ans.  9*6  ohms. 

191.  Find  the  length  in  yards  of  a  wire  of  .the  same  diameter  and  quality  as  the- 
knot  pound  in  178,  having  a  resistance  of  2  ohms.  Ans.  3-38  yards. 

192.  Find  the  length  in  yards  of  a  wire  of  the  same  quality  and  total  resistance  as 
the  knot  pound  in  178,  but  of  three  times  the  diameter.  Ans.  18261  yards. 

193.  The  specific  gravity  of  platinum  is  2J  times  that  of  copper  ;  its  resistance  5^ 

9 
as  great.  What  length  of  platinum  wire  weighing  100  grains  has  the  same  resistance 
as  ICO  inches  of  copper  wire  also  weighing  100  grains?  Ans.  7*2. 

194.  A  cell  with  a  resistance  of  an  ohm  is  connected  by  very  short  thick  wires, 
with  the  binding  screws  of  a  galvanometer,  the  resistance  of  which  is  half  an  ohm,  and 
the  deflection  is  45°  ;  if  the  screws  be  also  connected  at  the  same  time  by  a  wire  of  i 
ohm  resistance,  find  the  deflection.  Ans.  36°  52'. 

195.  The  resistance  of  a  galvanometer  is  half  an  ohm,  and  the  deflection  when 
the  current  of  a  cell  is  passed  through  it  is  30°.  When  a  wire  of  2  ohms  resistance  is 
introduced  into  the  circuit  the  deflection  is  15°  ;  find  the  internal  resistance  of  the  cell. 

Ans.  I '23. 

196.  When  the  current  of  a  cell,  the  resistance  of  which  is  f  of  an  ohm,  is  passed 
through  a  galvanometer  connected  with  it  by  very  short  thick  wires,  the  deflection  is 
45° ;  when  the  binding  screws  are  also  connected  by  a  shunt  having  a  resistance  of  i 
the  deflection  is  33° "42.     Find  the  resistance  of  the  galvanometer.  Ans.  2. 

197.  A  cell  whose  internal  resistance  is  2  ohms  has  its  copper  pole  connected  with 
the  binding  screw  A  of  a  galvanometer  formed  of  a  thick  band  of  copper.  From 
the  other  screw  B  a  wire  of  20  ohms  resistance  passes  to  the  zinc  pole,  and  the  deflection 
read  off  is  7°'8.  Find  the  deflection  when  B  is  at  the  same  time  connected  with  the 
zinc  pole  by  a  second  wire  of  30  ohms  resistance.  Ans.  11  •6. 

198.  What  would  be  the  deflection  in  185  if  the  second  wire  instead  of  passing 
from  B  to  the  zinc  pole  passed  directly  from  the  zinc  pole  to  the  copper  pole  ? 

Ans.  6° "43. 

199.  A  Leclanch^  cell  deflects  a  galvanometer  30°  when  200  ohms  resistance  are 
introduced  into  the  circuit,  15°  when  50  ohms  are  introduced ;  a  standard  Daniell's 
cell  deflects  at  30'  when  100  ohms  are  in  circuit  and  15°  when  250  additional  ohms  are 
introduced.  Required  the  electromotive  force  of  the  Leclanch^  in  terms  of  that  of  the 
Daniell.  Ans.  1-48. 

200.  A  Bunsen  and  a  Daniell  cell  are  placed  in  the  same  circuit  in  the  first  case 
so  that  the  carbon  of  the  first  is  united  to  the  zinc  of  the  Daniell ;  and  in  the  second 
case  so  that  their  currents  oppose  each  other.  The  currents  are  respectively  30° "2, 
and  in  the  second  10° '6.  Required  the  electromotive  force  of  the  Bunsen  in  terms  of 
the  Daniell.  Ans.  \-?,(^. 

201.  A  telegraph  line  constructed  of  copper  wire,  a  kilometre  of  which  weighs  30*5 
kilogrammes  is  to  be  replaced  by  iron  wire  a  kilometre  of  which  weighs  135 '6  kilo- 
grammes. In  what  ratio  does  the  resistance  alter?  Ans.  The  resistance  of  the  iron 
wire  will  be  i"i8  times  that  of  the  copper  wire  for  which  it  is  substituted. 

202.  A  telegraph  line  which  has  previously  consisted  of  copper  wire  weighing  30*5 
kilogrammes  to  the  kilometre  is  to  be  replaced  by  an  iron  wire  of  the  same  diameter 
which  shall  offer  the  same  resistance.  What  must  be  the  section  of  the  latter,  and 
what  its  weight  per  kilometre  ? 

Ans.  The  section  of  the  copper  wire  is  3*4357  sq.  mm.,  that  of  the  iron  by  which 
it  is  replaced  is  2o'6  sq.  mm.,  and  its  weight  per  kilometre  is  160 '4  kilogrammes. 


i  • 


INDEX. 


(THE   NUMBERS   REFER  TO   THE   ARTICLES.) 


ABE 

ABEL'S  electrical  fuse,  746 
Aberration,     chromatic,      546  ; 
spherical,  501 

Absolute  expansion  of  mercury,  300 
•  Absorbent  power  of  aqueous  vapour,  909 

Absorbing  power,  397 

Absorption,  139  ;  of  gases,  140;  of  gases 
by  liquids,  175  ;  of  heat  by  liquids, 
407  ;  by  vapours,  408  ;  heat  pro- 
duced by,  452 

Acceleration  of  a  force,  27,  74 

Accidental  haloes,  590  ;  images,  589  ; 
magnetic  variations,  656 

Accommodation  (of  the  eye),  583 

Achromatism,  547  ;  of  the  microscope, 

555 

Achromatopsy,  595 

Acidometer,  123 

Acierage,  805 

Aclinic  lines,  660 

Acoustics,  208-272 

Acoustic  foci,  223 

Actinic  rays,  409,  538 

Action  and  reaction,  39 

Adhesion,  83 

Aerial  meteors,  900 

Aerolites,  450 

-^sculine,  545 

Affinity,  82 

Agents,  6 

Agonic  line,  654 

Air,  aspirating  action  of  currents  of, 
186  ;  causes  which  modify  tempera- 
ture of,  929  ;  heating  by,  461  ;  ther- 
mometer, 311 

Air  balloons,  177;  chamber,  196 

Air  pump,  438  ;  Bianchi's,  184  ;  con- 
densing, 181 ;  gauges,  182  ;  rarefac- 
tion in,  181  ;  receiver  of,  181  ;  Spren- 
gel's,  185  ;  uses  of,  189 


AQU 

Ajutage,  203 

Alarum,  electric,  840 

Alcarrazas,  349 

Alcoholic  value  of  wines,  354 

Alcoholometer,     125 ;      Gay-Lussac's, 

125  ;  centesimal,  125 
'Alcohol  thermometer,  285 
Alloys,  317 
Amalgam,  708 
Amalgamated  zinc,  768 
Amber,  682 
Amici's     microscope,     5  54 ;      camera 

lucida,  566 
Ampere's      memoria '  technica^     772  ; 

theory  of  magnetism,  827 
Amplitude  of  vibration,  5 1 
Analogous  pole,  691 
Analyser,  618 
Analysis,  spectral,  540;  of  solar  light, 

403 

Anelectrics,  683,  702  f 

Anelectrotonus,  779 

Anemometer,  900 

Aneroid  barometer,  173 

Angle  of  deviation,  512  ;  optic,  580  ; 
of  polarisation,  616  ;  reflection  and 
incidence,  480,  504  ;  of  repose,  39  ; 
refraction,   504  ;  visual,  580 

Angular  currents,  laws  of,  808 

Animal  heat,  455 

Anione,  791 

Annealing,  87 

Annual  variations,  655 

Anode,  791 

Antilogous  pole,  691 

Anvil,  863 

Aqueous  humour,  575 

Aqueous  vapour,  its  influence  on  cli- 
mate, 909;  tension  of,  331,  332, 
333 


QQ 


890 


Index. 


ARA 

Arago's  experiment,  167 

Arbor  Dianse,  801  ;  Satumi,  801 

Arc  of  vibration,  51  ;  voltaic,  784 

Archimedes'  principle,  1 10  ;  applied  to 
gases,  176 

Area,  unit  of,  22 

Armatures,  678  ;  Siemens',  858 

Arms  of  levers,  40 

Armstrong's  hydro-electric  machine,  712 

Artesian  wells,  108 

Artificial  magnets,  642 

Ascent  of  liquids  in  capillary  tubes, 
129  ;  between  surfaces,  130 

Astatic  currents,  821  ;  needle  and  sys- 
tem, 662 

Astronomical  telescope,  558 

Athennancy,  407 

Atmosphere,  its  composition,  146  ; 
crushing  force  of,  148  ;  amount  of, 
determination  of,  152  ;  electricity  in 
the,  917,  918  ;  moisture  of,  374 

Atmospheric  electricity,  causes  of,  916, 
919  ;  pressure,  147 

Atomic  heat,  429 ;  weight  deduced 
from  specific  heat,  429 

Atoms,  3 

Attraction,  capillary,  131  ;  and  repul- 
sion produced  by  capillarity,  131  ; 
molecular,  80  ;  universal,  63 

Attractions,  magnetic,  laws  of,  665  ; 
electrical,  laws  of,  692 

Atwood's  machine,  74 

Aura,  719 

Aurora  borealis,  656,  927 

Aurum  musivum,  708 

Austral  pole,  651 

Avoirdupois,  23 

Axis  of  crystal,  603  ;  electric,  691  ; 
lenses,  519;  optic,  580;  of  a  mag- 
net, 643  ;  of  oscillation,  76  ;  visual, 
926 

Azimuthal  circle,  657 


BABINET'S  stopcock,  183 
Bain's  electrochemical  telegraph, 
838 

Bad  cond^tors,  378 

Balancd^^j^^j  beam  of,  69  ;  compensat- 
ing, -^98 ;  delicacy  of,  70 ;  hydro- 
static, 117;  knife  edge  of,  68  ;  physi- 
cal and  chemical,  71  ;  torsion,  86, 
666,  692 

Ballistic  pendulum,  78 

Balloons,  177-180;  construction  and 
management  of,  178  ;  Mongolfier,  177 


BOI 

Bands  of  spectrum,  541 

Barker's  mill,  205 

Barometers,  153;  aneroid,  173; 
Bunten's,  156  ;  cistern,  154  ;  correc- 
tions in,  159  ;  determination  of 
heights  by,  165;  fixed,  164;  For- 
tin's,  155  ;  Gay-Lussac's,  156  ;  pre- 
cautions with,  157  ;  wheel,  163 ; 
variations  of  height  of,  160 

Barometric  formula,  Laplace's,  165  ; 
height  of,  corrected  for  heat,  305  ; 
manometer,  172  ;  variations,  161 

Baroscope,  176 

Battery,  Bunsen's,  763  ;  Callan's,  763  ; 
chemical  effects  of,  790  ;  Daniell's, 
761;  electric,  729  ;  gas,  798  ;  gravity, 
765 ;  Grove's,  762 ;  Leclanche's, 
765  ;  Leyden,  constant,  760  ;  charged 
by  coil,  864  ;  local,  825  ;  luminous 
effects,  784 ;  magnetic,  677;  measure- 
ment of  charge,  732  ;  mechanical 
effects  of,  789 ;  Menotti's,  765  ; 
Marie  Davy's,  765  ;  postal,  825 ; 
Smee's,  764  ;  sulphate  of  mercury, 
765  ;  tension  of,  767  ;  thermo-electric, 
876  ;  voltaic,  757,  758  ;  Walker's, 
764 ;  Wollaston's,  758 

Beam  of  a  balance,  69  ;  of  a  steam-en- 
gine, 438 

Beats,  246 

Beaume's  hydrometer,  124 

Becquerel's  pyrometer,  880 ;  thermo- 
electric battery,  876  ;  electrical  ther- 
mometer, 879 

Bell  of  a  trumpet,  223 

Bellows,   229  ;  hydrostatic,  98 

Bennett's  electroscope,  705 

Berthollet's  experiment,  174 

Bertin's  commutator,  818 

Bertsch's  machine,  714 

Bianchi's  air  pump,  184 

Biaxial  crystals,  double  refraction  in, 
607  ;  optic  axes  of,  607  ;  rings  in,  629 

Bifurcation,  602 

Binnacle,  659 

Binocular  vision,  584 

Biot's  apparatus,  638 

Black's  experiments  on  latent  heat,  432 

Bladder,  swimming,  115 

Block  and  tackle,  44 

Blood  globules,  15 

Bodies,  properties  of,  7,  119 

Bohnenberger's  electroscope,  770 

Boiler,  437 

Boiling,  326 ;  by  cooling,  343  ;  laws  of, 
339 


Ifidex, 


891 


Bor 

Boiling  point,  influence  of  dissolved 
substances  on,  341  ;  of  nature  of 
vessel,  342 ;  of  pressure  on,  343  ;  in 
a  thermometer,  281  ;  measure  of 
heights  by,  345 

Boreal  pole,  651 

Boutigny's  experiments,  360 

Boyle  and  Mariotte's  law,  166-168 

Bramah's  hydraulic  press,  105 

Breaking  weight,  88 

Breezes,  land  and  sea,  902 

Breguet's  thermometer,  288 

Bridge,  Wheatstone's,  886 

British  Association  unit,  884 

British  imperial  yard,  22  ;  and  French 
system  of  M'eights  and  measures,  1 22 

Browning's  regulator,  787 

Brush  discharge,  739 

Bull's  eye,  554 

Bunsen's  battery,  763  ;  burner,  541  ; 
ice    calorimeter,    423  ;    photometer, 

479 
Bunsen  and  Kirchhoff's  researches,  542 
Bunten's  barometer,  156 
Buoyancy  of  liquids,  97 
Burning  mirrors,  393 


C.^SIUM,  542 
Cagniard-Latour's    syren,     228  ; 
experiments    on    formation    of    va- 
pour, 346 

Callan's  battery,  763 

Calorescence,  406 

Caloric,  AI9 

Calorific  effects  of  electrical  discharge, 
742  ;  of  current  electricity,  780,  781  ; 
of  RuhmkorfTs  coil,  864  ;  of  the 
spectrum,  538 

Calorimeter,  421;  Bunsen's  ice,  422; 
Black's,  422 ;  Favre  and  Silber- 
mann's,  434 ;  Lavoisier  and  La- 
place's, 422 

Calorimetry,  418 

Camera  lucida,  557  ;  Amici's,  566  ; 
obscura,  565  ;  Porta's  obscura,  483 

Campani's  eye-piece,  555 

Capacity,  specific  inductive,  702 

Capillarity,  128  ;  attraction  and  repul- 
sion produced  by,  131  ;  correction 
for,  158 

Capillary  phenomena,  128-134  ;  tubes, 
129  ;  ascent  and  depression  in,  129  ; 
between  parallel  or  inclined  surfaces, 
130 

Capsule,  of  the  eye,  575 


CLO 

Cardan's  suspension,  155 

Carre's  mode  of  freezing,  350  ;  dielec- 
trical  machine,  715 

Carriage  lamps,  503  _ 

Cartesian  diver,    113 

Cascade,  charging  by,  731 

Cathetometer,  85 

Catoptric  telescopes,  561 

Caustics,  501,  502 

Celsius'  scale,  282 

Centesimal  alcoholometer,  125 

Centigrade  scale,  282 

Centimetre,  122 

Centre,  optical,  523  ;  of  gravity,  65  ; 
of  parallel  forces,  37  ;  of  pressure,  99 

Charge  of  a  Leyden  jar,  penetration  of, 
728  ;  measurement  of,  732  ;  laws  of, 
733,;  residual,  728 

Charging  by  cascade,  731 

Chatterton's  compound,  832 

Chemical  affinity,  82  ;  combination, 
453  ;  effects  of  the  battery,  745  ;  of 
electrical  discharge,  745  ;  of  voltaic 
currents,  773  ;  of  Ruhmkorff's  coil, 
864  ;  harmonicon,  262  ;  hygrorpeter, 
368;  properties  of  the  spectrum,  538 

Chemistry,  i 

Chevallier's  microscope,  554 

Cheval-vapeur,  444 

Chimes,  electrical,  718 

Chimney,  457 

Chladni's  experiments,  266 

Chlorophylle,  544 

Chords,  major  and  minor,  233  ;  physi- 
cal constitution  of,  248  ;  tones 
dominant  and  subdominant,  233  ; 
vocal,  245 

Choroid,  575 

Chromatic  scale,  236  ;  aberration,  546 

Chromium,  magnetic  limit  of,  680 

Ciliary  processes,  575 

Circle,  azimuthal,  657 

Circular  polarisation,  631 

Cirrocumulus,  905 

Cirrostratus,  905 

Cirrus,  905 

Cistern  barometer,  154 

Clarke's  magneto-electrical  machine,  85  5 

Cleavage,  electricity  produced  by,  690 

Clement  and  Desorme's  experiment,  186 

Climate,  932  ;  constant  932  ;  inrtuence 
of  aqueous  vapour  on,  909 

Climatology,  927-934 

Clocks,  78  ;  electrical,  841 

Clouds,  905  ;  electricity  of,  920  ;  for- 
mation of,  906 


QQ?. 


89? 


Index. 


COA 

Coatings,  724  ;  Leyden  jar  with  mov- 
able, 726 

Cobalt,  680 

Coercive  force,  649 

Coefficients  of  linear  expansion,  292, 
294 

Cohesion,  81 

Coil,  primary,  837  ;  Ruhmkorff's,  862  ; 
effects  produced  by,  864  ;  secondary, 

837 

Cold,  apparent  reflection  of,  395  ;  pro- 
duced by  evaporation,  349;  expansion 
of  gases,  464  ;  by  nocturnal  radiation, 
465  ;  sources  of,  463 

Colladon  and  Sturm's  experiments,  221 

Collecting  plate,  734 

Collimation,  558 

Collision  of  bodies,  55 

Colloids,  136 

Coloration  produced  by  rotatory  polari- 
sation, 637 

Colour,  7  ;  of  (bodies,  555  ;  of  heat, 
409  ;  of  thin  pktes,  612 

Colour  disease,  595 

Colours,  contrast  of,  5904  mixed,  536  ; 
simple,  532  ;  complementary,  536  ; 
produced  by  polarised  light,  624-630; 
by  compressed  glass,  630 

Combustion,  453  ;  heat  diisergaged 
during,  454 

Comma,  musical,  234 

Common  reservoir,  685 

Communicator,  832 

Commutator,  833,  835,  856,  863  ; 
Berlin's,  818 

Compass,  correction  of  errors,  658  ; 
declination,  657  ;  mariner's,  659; 
inclination,  660  ;  sine,  776  ;  tangeitt, 

775 
Compensating  cube,  411 
Compensation  pendulum,  298;  balance, 

298  ;  gridiron,  298  ;  strips,  298 
Complementary  colours,  536 
Component  forces,  32 
Composition  of  velocities,  48 
Compound  microscope,  52 
Compressed  glass,  colours  produced  by, 

630 
Compressibility,  7,  16;  of  gases,    166; 

of  liquids,  92 
Concave  mirrors,  392,  496 
Concert  pitch,  237 
Concordant  tones,  233 
Condensation  of  vapours,  351 
Condensed  gas,  140  ;  wave,  213 
Condenser,    438,    713,  720 ;   limits  to 


ctm 

charge  of,  723  ;  of  Ruhmkorff's  coil, 

863  ;  Liebig's,  353 
Condensing   engine,    443  ;    air  pump. 

188  ;     force,    calculation    of,     722  ; 

electroscope,    734  ;   plate,    734  ;  hy- 
grometers, 369 
Conical  pendulum,  53 
Conduction  of  heat,  377  ;  of  electricity, 

684  ;  lightning,  925 
Conductivity  of  bodies  for  heat,  378  ; 

coefficient  of,  378  ;  of  gases,  382  ;  of 

liquids,  380  ;  for  electricity,  885,  888 
Conductors,      684 ;      equivalent,  885  ; 

good  and  bad,  378  ;  lightning,  925  ; 

l^rime,  707  ;  resistance  of,  883 
Congelation,  320 
Conjugate   mirrors,    393 ;    focus,    493, 

520 
Connecting  rod,  438  -^ 

Conservation  of  energy,  62 
Constant  currents,  760 
Contact  theory  of  electricity,  751 
Contractile  force,  297 
Convection,  381 
Convex  meniscus,    128 ;  mirrors,   494, 

497 
Cooling,    method   of,    426  ;    Newton's 

law  of,  390 
Cornea,  575 
Corpuscular  theory,  469 
Corti's  fibres,  245 
Cosine,  law  of  the,  387,  478 
Coulomb's  law,  665 
Couple,  36  ;  terrestrial  magnetic,  652  ; 

voltaic,  754  ;  thermo-electric,  874 
Couronne  des  tasses,  758 
Coxwell's  balloon,  177 
Critical  angle,  508  ;  temperature,  346 
Cross- wire,  558 
Crutch  of  a  clock,  78 
Cryophorus,  349 
Crystal,  hemihedml,  691 
Crystalline,  575 
Crystallisation,  321 
Crystalloids,  136 
Crystals,     321  ;     expansion   of,      294  ; 

doubly    refracting,    602,    614,   625  ; 

uniaxial,  605  ;  positive  and  negative, 

606 
Cube,  Leslie's,  396 
Cumulostratus,  905 
Cumulus,  905 
Current  electricity,  753 
Currents,  action  on  currents,  810,  811  ; 

action  of  magnets,   814  ;    action    of 

earth    on,     820,     821  ;     action     on 


Index, 


89s 


CUR 

solenoids,  822,  827  ;  constant,  760 ; 
derived,  891 ;  detection  and  measure- 
ment of  voltaic,  771  ;  diaphragm, 
789  ;  direct  and  inverse,  851  ;  effects 
of  enfeeblement  of,  759  ;  extra,  850, 
851  ;  of  inclination,  893  ;  intensity 
of>  777  j  induction  by,  843  ;  laws  of 
angular,  808  ;  laws  of  sinuous,  809  ; 
local,  768  ;  magnetisation  by,  829  ; 
motion  and  sounds  produced  by, 
831  ;  muscular,  892  ;  rotation  of 
magnets  by,  814  ;  secondary,  759  ; 
terrestrial,  828  ;  thermal  effects  of, 
781,  782  ;  transmissions  by,  793 
Curvature  of  liquid  surfaces,  132  ;  in- 
fluence of,  on  capillary  phenomena, 

133 

Curves,  magnetic,  666 

Cushions,  707 

Cyanogen  gas,  356 

Cylinder,  438  ;  electrical  machine,  71 1 


DAGUERREOTYPE,  571 
Daltonism,  595 

Dalton's  laM^s  on  gases  and  vapours, 
358  ;  method  of  determining  the  ten- 
sion of  aqueous  vapour,  332 

Damper,  263,  848 

Daniell's  battery,  761  ;  hygrometer, 
370  ;  pyrometer,  290 

Dark  lines  of  the  spectrum,  539  ;  of 
solar  spectrum,  543 

Davy's  battery,  765 

Davy's  experiment,  394 

Day,  apparent,  21 

Decimetre,  24,  122 

Declination,  compass,  657  ;  magnetic, 
653  ;  of  needle,  653  ;  variations  in, 
654 ;  of  a  star,  563 

Decomposition,  chemical,  790 ;  of 
white  light,  530  ;  of  salts,  792 

Deflagrator,  Hare's,  758,  780 

Degrees  of  a  thermometer,  282 

De  la  Rive's  floating  battery,  815  ;  ex- 
periments, 867 

Delezenne's  circle,  849 

Delicacy  of  balance,  70  ;  of  thermo- 
meter, 286 

Densimeter,  127 

Density,  24  ;  of  the  earth,  64  ;  electric, 
694  ;  of  gases,  312-314  ;  maximum 
of  water,  307 ;  of  vapours,  Gay- 
Lussac's  method,  361  ;  Dumas's, 
362  ;  Deville  and  Troost's,  363 


DOU 

Depolarisation,  627 

Depolarising  plate,  625 

Depression  of  liquids  in  capillary  tube, 
129  ;  between  surfaces,  130 

Derived  currents,  891 

Descartes'  laws  of  refraction,  505 

Despretz's  experiment,   378 

Developer,  572 

Deviation,  angle  of,  512 

Deville  and  Troost's  method,  363 

Dew,  911  ;  point,  369 

Diabetic  urine,  analysis  of,  640 

Dial  telegraphs,  834 

Dialyser,  136 

Dialysis,   136 

Diamagnetism,  870 

Diapason,  243 

Diaphanous  iDodies,  470 

Diaphragm,  554  ;  currents  789 

Diathermancy,  407 

Dielectrical  machine,  Carre's,  715 

Dielectrics,  702 

Differential  barometer,  1 72 

Differential  galvanometer,  773  ;  ther- 
mometer, Leslie's,  287;  Matthiessen's, 
287  ;  tone,  247 

Diffraction,  473,  611  ;  fringes,  609 

Diffusion  of  heat,  410  ;  of  liquids,  136 

Digester,  Papin's,  347 

Dioptric  telescopes,  561 

Diplopy,  594 

Dip,  magnetic,  660  • 

Dipping  needle,  660 

Discharge,  electrical,  721  ;  effects  of 
the,  736  ;  lateral,  925  ;  slow  and 
instantaneous,  721  ;  universal,  736 

Discharging  rod,  721 

Disc,  Newton's,  533 

Dispersion,  512 

Dispersive  power,  530 

Dissipation  of  energy,  468 

Distance,  estimation  of,  581  ;  adapta- 
tion of  eye  to,  583 

Distillation,  352 

Distribution  of  free  electricity,  693  ;  of 
magnetism,  681  ;  of  temperature, 
933  ;  of  land  and  water,  935 

Diurnal  variations,  655 

Diver,  Cartesian,  113 

Dividing  machine,  1 1 

Divisibility,  7,  12 

Dobereiner's  lamp,  452 

Dominant  chords,  234 

Doppler's  principle,  220 

Double  action  steam  engine,  438,  439 

Double  refraction,  614 


894 


Index, 


DOU 

Doublet,  Wollaston's,  549 

Dove's  law  of  storms,  903 

Draught  of  fire-places,  458 

Driving  wheels,  441 

Drummond's  light,  569 

Dry  piles,  769 

Duboscq's  microscope,  569  ;  regulator, 
786 

Ductility,  7,  89 

Duhamel's  graphic  method,  231 

Dulong  and  Arago's  experiments  on 
Boyle's  law,  167  ;  method  of  deter- 
mining the  tension  of  aqueous  va- 
pour, 333 

Dulong  and  Petit's  determination  of  ab- 
solute expansion  of  mercury,  300 

Dulong  and  Petit's  method  of  cooling, 
426  ;  law,  429 

Dumas's  method  for  vapour  density,  362 

Duplex  telegraphy,  837 

Duration  of  electrical  spark,  747 

Dutiochet's  endosmometer,  135 

Dynamical  theory  of  heat,  402 

Dynamic  radiation  and  absorption,  415 

Dynamo-magnetic  machine,  860 


EARTH,  its  action  on  currents,  819- 
821  ;  action  of  solenoids,  826  ; 
flattening  of,  by  rotation,  79;  magnetic 
poles  of  the,  660 ;  magnetisation  by, 
674 

Earth's  magnetism,  663 

Earnshaw  on  velocity  of  sound,  2 1 7 

Ear  trumpet,  225 

Ebullition,  326  ;  laws  of,  339 

Eccentric,  438,  439 

Echelon  lenses,  570 

Echoes,  223  ;  monosyllabic,  trisyllabic, 
multiple,  223 

Efflux,  velocity  of,  199  ;  quantity  of, 
202  ;  influence  of  tubes  on,  203 

Eff"usion  of  gases,  138 

Elastic  bodies,  55 

Elastic  force,  141  ;  of  vapours,  327 

Elasticity,  7,  17  ;  limit  of,  17,  85;  of 
traction,  85  ;  modulus  of,  85  ;  of 
torsion,  86  ;  of  flexure,  87 

Electrical  machines,  706-715  ;  precau- 
tions in,  708 

Electrical  attractions  and  repulsions, 
692  ;  resistance,  unit  of,  884  ;  con- 
ductivity, 888 

Electric  alarum,  840  ;  axis,  691  ;  bat- 
teries, bottle,  741,  729;  charge,  733; 


-ENE 

chimes,  718  ;  clocks,  841  ;  density, 
694 ;  discharge,  736  ;  egg,  740  ; 
fish,  897;  fuse,  746;  glow,  739; 
light,  782-784  ;  stratification  of  the, 
865  ;  pendulum,  683  ;  pistol,  745  ; 
poles,  691  ;  residue,  728  ;  shock,  725, 
737;  spark,  717;  telegraphs,  832- 
842  ;  whirl,  719;  tube,  741 

Electricity,  6,  682  ;  application  of,  to 
medicine,  898 ;  atmospheric,  916- 
925  ;  current,  753  ;  bodies  in  contact, 
696 ;  communication  of,  703  ;  de- 
velopment of,  by  friction,  689  ;  by 
pressure  and  cleavage,  690 ;  distri- 
bution of,  693  ;  dynamical,  749-891 ; 
disengagement  of,  in  chemical 
actions,  745,  751  ;  frictional,  689; 
loss  of,  697 ;  mechanical  effects, 
744 ;  produced  by  induction,  699  ; 
velocity    of,     748;    theories   of,  687 

Electrified  bodies,  motion  of,  688,  704 

Electrochemical  telegraph,  838  ;  series, 
791 

Electrodes,  756  ;  polarisation  of,  759 

Electrodynamics,  806 

Electrogilding,  803 

Electrolysis,  791 ;  laws  of,  795 

P-^lectrolyte,  791 

Electromagnetic  force,  830  ;  machines, 
842 

Electromagnets,  830 

Electrometallurgy,  802-804 

Electrometer,  705  ;  Lane's,  732 ;  quad- 
rant, 710  ;  Thomson's,  735 

Electromoter,  832 

Electromotive  series,  754 ;  force,  755, 
766,  777 ;  determination  of,  889  ; 
force  of  elements,  766 

Electrophorus,  706 

Electropyrometer,  880 

Electroscope,  683  ;  Bohnenberger's, 
770  ;  Volta's  condensing,  734  ;  gold 
leaf,  705 

Electrosilvering,  804 

Electrotonus,  779 

Elements,  electronegative  and  electro- 
positive, 791 

Elliptical  polarisation,  634 

Emergent  rays,  510, 

Emission  theory,  469 

Emissive  power,  398 

Endosmometer,  132 

Endosmose,  135 ;  electrical,  789 ;  of 
gases,  137 

Endosmotic  equivalent,  135 

Energy,  59 ;  conservation  of,   62  ;  dis- 


Index. 


895 


ENG 

sipation  of,  468  ;  transformations  of, 
61  ;  varieties  of,  60 

Engines,  gas,  446 ;  steam,  436 ;  double 
action,  438  ;  low  and  high  pressure, 
443 ;  single  action,  440 ;  locomotive, 
441  ;  fire,  198  ;  transformation  of,  61 

Eolipyle,  442 

Equator,  643;  magnetic,  660 

Equilibrium  of  forces,  35  ;  of  floating 
bodies,  1 12  ;  of  heavy  bodies,  66  ;  of 
liquids,  103-104;  mobile  of  tempera- 
ture, 388  ;  neutral,  67  ;  stable,  67  ; 
unstable,  67 

Equivalent,  endosmotic,  135  ;  conduc- 
tors, 885 

Escapement,  78  ;  wheel,  78 

Ether,  402  ;  luminiferous,  469 

Evaporation,  326  ;  causes  which  accele- 
rate it,  328  ;  cold  due  to,  349 ;  latent 
heat  of,  348 

Evaporation  and  ebullition,  340 

Exchanges,  theory  of,  388 

Exhaustion,  produced  by  air-pump,  184; 
by  Sprengel's  pump,  185 

Exosmose,  135 

Expanded  wave,  213 

Expansibility  of  gases,  141 

Expansion,  275  ;  appai-ent  and  real, 
299  ;  absolute,  of  mercury,  300  ;  ap- 
parent, of  mercury,  301  ;  of  liquids, 
304  ;  of  solids,  292  ;  of  gases,  308- 
310  ;  linear  and  cubical,  coefficients 
of,  292  ;  measurement  of  linear,  293  ; 
of  crystals,  296  ;  applications  of,  297  ; 
force  of,  306 

Expansion  of  gases,  cold  produced  by, 
464  ;  problems  on,  309 

Expansive  force  of  ice,  323 

Experiment,  Berthollet's,  1 74  ;  Frank- 
Im's,  344 ;  Florentine,  94  ;  Pascal's, 
151  ;  Torricellian,  150 

Extension,  7,  9 

Extra  current,  850,  851  ;  direct,  851  ; 
inverse,  851 

Eye,  575  ;  accommodation  of,  583  ; 
not  achromatic,  591  ;  refractive  in- 
dices of  media  of,  576  ;  path  of  rays 
in,  578  ;  dimensions  of  various  parts 
of,  577 

Eye-glass,  512,  593  ;  lens,  555  ;  piece, 
549,  553,  555  ;  Campani's,  555 


FAHRENHEIT'S  hydrometer,  120; 
scale,  282 
Falling  bodies,  laws  of,  73 


FOR 

Faraday's  wheel,  588  ;  theory  of  indue" 
tion,  701  ;  voltameter,  795 

Favre   and    Sil  Hermann's    calorimeter, 
434  ;  determination  of  Jbeat  of  com^ 
bustion,  453  ^ 

Field  of  a  microscope,  554;  of  view,  556; 
magnetic,  669 

Field  lens  and  glass,  555  ;  of  micro- 
scope, 554 

Figures,  Lichtenberg's,  727 

Finder,  558 

Fire  engine,  198;  places,  457;  works, 
205 

Fish,  electrical,  897 

Fishes,  swdmming  bladder  of,  114 

Fizeau's  experiments,  477 

Flame,  453^ 

Flask,  specific  gravity,  118 

Flattening  of  the  earth,  79 

Flexure,  elasticity  of,  87 

Float,  437 

Floating  bodies,  112 

Florentine  experiment,  13,  94 

Fluid,  4 ;  imponderable,  6  \  elastic  144 ; 
magnetic,  645 

Fluidity,  7 

Fluorescence,  545 

Flute,  264 

Fluxes,  317 

Fly-wheel,  438 

Focal  distance,  392 

Foci,  acoustic,  223  ;  of  convex  mirrors, 
494  ;  in  double  convex  lenses,  520 

Focus,  392,  493  ;  conjugate,  determi- 
nation of  the  principal,  495  ;  of  a 
spherical  concave  mirror,  493 

Focussing  the  microscope,  550 

Fogs,  904 

Foot,  22 

Foot-pound,  56,  444 

Force,  26  ;  conservation  of,  62  ;  coer- 
cive, 649  ;  direction  of,  30 ;  elastic, 
of  gases,  141;  lines  of  magnetic,  669; 
of  expansion  and  contraction,  297  ; 
electromotive,  755,  766  ;  representa- 
tion of,  30  ;  parallelogram  of,  33  ;  of 
liquids,  306 ;  portative,  679 

Forces,  6;  along  the  same  line,  31  ; 
equilibrium  of,  38  ;  impulsive,  57  ; 
magnetic,  660  ;  molecular,  80  ;  mo- 
ments of,  38 ;  polygon  of,  35  ;  triangle 
of,  35 

Formulae  for  expansion,  296  ;  barome- 
tric, 163  ;  for  sound,  218  ;  for  spheri- 
cal mirrors,  498,  499  ;  for  lenses,  527 

Fortin's  barometer,  155 


896 


Index. 


FOU 

Foucault's  determination  of  velocity  of 
light,  476  ;  experiment,  785 

Fountain  in  vacuo,  189  ;  at  Giggles- 
wick,  193;  intermittent,  191 ;  Hero's, 
190 

Franklin's  experiment,  344,  916;  plate, 
724 ;  theory  of  electricity,  687 

Fraunhofer's  lines,  539,  540 

Freezing,  apparatus  for,  350 

Freezing  mixtures,  324 ;  point  in  a 
thermometer,  281 

French  weights  and  measures,  1 20 ; 
boiler,  437 

Fresnel's  experimentum  crucis,  608  ; 
rhomb,  633 

Friction,  26,  45  ;  heat  of,  447  ;  hy- 
draulic, 203  ;  development  of  electri- 
city by,  689 

Friction  wheels,  74 

Frigorific  rays,  395 

Fringes,  609 

Frog,  rheoscopic,  894 

Frost,  901 

Frozen  mercury,  349,  356,  360 

Fulcrum,  43 

Fulgurites,  923 

Fulminating  pane,  724 

-Fuse,  Abel's,  746;  Chatham,  780,  781 

Fusing  point,  315 

Fusion,  laws  of,  315  ;  vitreous,  315  ; 
latent  heat  of,  432  ;  of  ice,  421 


GALILEAN  telescope,  560 
Galleries,  whispering,  223 

Gallon,  122 

Galvani's  experiment,  749 

Galvanometer,  773  ;  differential,  773 ; 
vSir  W.  Thomson's,  774 

Galvanoscope,  773 

Galvanothermometer,  781 

Gas  battery,  798  ;  engines,  446 

Gases,  absorption  of,  by  liquids,  175  ; 
application  of  Archimedes'  principle 
to,  1 76  ;  cold  produced  by  expansion 
of,  464  ;  compressibility  of,  143, 
166  ;  conductivity  of,  382  ;  diamag- 
netism  of,  869  ;  density  of,  312,  314 ; 
expansion  of,  142,  308-311  ;  endos- 
mose  of,  137  ;  effusion  and  transpira- 
tion of,  1 38  ;  Gay-Lussac's  method, 
308;  index  of  refraction  of,  518; 
laws  of  mixture  of,  1 74  ;  and  vapours, 
mixtures  of,  358  ;  permanent,  356  ; 
problems  in,  359  ;  liquefaction  of, 
356  ;    physical   properties   of,    141  ; 


HAM 

pressure  exerted  by,  145  ;  radiation  of 
414  ;  Regnault's  method,  313  ;  speci- 
fic heat  of,  43 1  ;  velocity  of  sound  in, 
217,  218,  219  ;  weight  of,  144 

Gaseous  state,  4 

Gassiott's  battery,  767 

Gauge,  air-pump,  182  ;  rain,  907 

Gay-Lussac's  alcoholometer,  125  ;  baro- 
meter, 156;  determination  and  ex- 
pansion of  gases,  308 ;  of  vapour- 
density,  361  ;  stopcock,  358 

Geissler's  tubes,  185,  542,  866 

Generating  plate,  754 

Geographical  meridian,  653 

Geometrical  shadows,  473 

Gififard's  injector,  186 

Gimbals,  659 

Glacial  pole,  933 

Glaciers,  915 

Glashier's  balloon  ascents,  177;  factors, 
372 

Glasses,  periscopic,  592  ;  weather,  163 

Glass,  expansion  of,  303  ;  magnifying, 
549;  object,  553  ;  opera,  560 

Globe  lightning,  923 

Glow,  electrical,  739 

Gold  leaf  electroscope,  705 

Goniometers,  502 

Good  conductors,  378 

Gramme,  24,  122 

Gramme's  magneto-electrical  machine, 
861 

Graphic  method,  Duhamel's,  231  ; 
Foster's,  782 

Gratings,  610 

Gravesande's  ring,  274 

Gravitation,  6,  79  ;  terrestrial,  64  ;  ac- 
celerative  effect  of,  27 

Gravity,  battery,  765 

Gravity,  centre  of,  65 

Gregorian  telescope,  562 

Gridiron  pendulum,  298 

Grimaldi's  experiment,  608 

Grotthiiss'  hypothesis,  794 

Grove's  battery,  762  ;  gas,  798 

Guericke's  air  pump,  181 

Gulf  Stream,  930 


HADLEY'S  reflecting  sextant,  490 
Hail,  913 
Hair  hygrometer,  373 
Haldat's  apparatus,  98 
Hallstrom's  experiments,  307 
Haloes,  590 
Hammer,  263,  863 


Index, 


897 


HAR 

Hardening,  87 

Hardness,  7  ;  scale  of,  90 

Hare's  deflagrator,  758,  780,  781 

Harmonicon,  chemical,  262 

Harmonics,  240,  257 

Harmonic  triad,  233  ;  grave,  247 

Harp,  265 

Harris's  unit  jar,  733 

Heat,  273  ;  animal,  455  ;  absorption  of, 
by  vapours,  &c.,  408,  412;  diffusion 
of,  410  ;  developed  by  induction,  868; 
dynamical  theory  of,  402  ;  hypothesis 
on,  273  ;  influence  of  the  nature  of, 
408;  latent,  318;  mechanical,  equi- 
valent of,  467  ;  polarisation  of,  641  ; 
produced  by  absorption  and  imbibi- 
tion, 452  ;  radiated  377  ;  radiant, 
384;  reflection  of,  391;  scattered, 
397;  sources  of,  447-466;  specific, 
419 ;  transmission  of,  377 ;  terres- 
trial, 451 

Heaters,  437 

Heating,  456 ;  by  steam,  460  ;  by  hot 
air,  461  ;  by  hot  water,  462 

Height  of  barometer,  154,  160;  varia- 
tions in,  160 

Heights  of  places,  determination  of,  by 
barometer,  165  ;  by  boiling  point,  345 

Heliostat,  502 

Helix,  44,  829 

Helmholtz's  analysis  of  sound,  241  ; 
researches,  244 

Hemihedral  crystal,  691 

Hemispheres  Magdeburg,  149 

Henley's  electrometer,'7 10 ;  discharger, 

744 
Henry's  experiment,  852 
Herepath's  salt,  620 
Hero's  fountain,  190 
Herschelian  rays,  403  ;  telescope,  564 
Hirn's  experiments,  445 
Hoar  frost,  911 
Holmes'    magneto-electrical    machine, 

857 
Holtz's  electrical  machine,  713 
Homogeneous  light,  537  ;  medium,  472 
Hope's  experiments,  307 
Horizontal  line,  64  ;  plane  64 
Horse  power,  444 
Hotness,  276 
Hour,  21 

Howard's  nomenclature  of  clouds,  905 
Humour,  aqueous,  575 
Hyaloid  membrane,  575 
Hydraulic   press,    105  ;  friction,    203  ; 

tourniquet,  205 


IND 

Hydraulics,  92 

Hydrodynamics,  92 

Hydro-electric  machine,  712 

Hydrometers,  116;  Nicholson's,  117-; 
Fahrenheit's  120 ;  with  variable 
volume,  123;  Beaume's,  124;  of 
constant  volume,  123  ;  specific  gra- 
vities, 116  ;  uses  of  tables  of,  122 

Hydrostatic  bellows,  98 ;  paradox,  JOO  ; 
balance,  117 

Hydrostatics,  92-95 

Hygrometers,  367 ;  of  absorption, 
373  ;  chemical,  368  ;  condensing^ 
369  ;  wet-bulb,  372  ;  Mason's,  372  ; 
Regnault's,  371 

Hygrometric   state,    366  ;    substances, 

365 
Hygrometry,  365  ;  problem  on,  375 
Hygroscope,  373 
Hypothesis,  5 
Hyposometer,  345 


ICE,  914";  method  of  fusion  of,  421 
Ice    caloi-imeter,  421  ;    Bunsen's, 
422  ;  expansive  force  of,    323  ;  ma- 
chine, 464 

Iceland  spar,  621 

Idioelectrics,  683 

Image  and  object,  magnitudes  of,  528 

Images,  accidental,  589  ;  condition  of 
distinctness  of,  550  ;  formation  of,  in 
concave  mirrors,  496  ;  in  convex 
mirror,  497  ;  in  plane  mirrors,  482  ; 
of  multiple,  485  ;  magnitude  of,  500  ; 
produced  by  small  apertures,  474  ; 
virtual  and  real,  483  ;  inversion  of, 

579 
Imbibition,  139  ;  heat  produced  by,  452 
Impenetrability,  7 
Imperial  British  yard,  22 
Imponderable  matter,  6 
Impulsive  forces,  54 
Inch,  122 
Incident  ray,  504 
Inclination,  660;  compass,  661 
Inclined  plane,  42  ;  motion  on,  47 
Index  of  refraction,  506  ;  measurement 

of,  in  solids,    516;  in  liquids,   517; 

in  gases,  518 
Indicator,  832,  834,  835 
Indices,  refractive,  table  of,  518 
Indium,  542 

Induced  currents,  843-855 
Induction,  apparatus  founded  on,  855  ; 


QQ3 


8gS 


Index. 


IND 

by  the  earth,  849  ;  by  currents,  843  ; 
of  a  current  on  itself,  850 ;  electrical, 
699  ;  in  telegraph  cables,  836  ;  limit 
to,  700  ;  Faraday's  theory  of,  701  ; 
heat  developed  by,  868 ;  by  magnets, 
847  ;  magnetic,   648  ;  vertical,   675 

Inductive  capacity,  specific,  702 

Inductorium,  862 

Inelastic  bodies,  55 

Inertia,  19  ;  applications  of,  20 

Influence,  magnetic,  648 ;  electrical, 
699 

Ingenhousz's  experiment,  378 

Injector,  186 

Insects,  sounds  produced  by,  228 

Insulating  bodies,  685;  stool,  717 

Insolation,  598,  599 

Insulators,  684 

Instruments,  optical,  548  ;  polarising, 
618;  mouth,  254;  reed,  256; 
stringed,  263  ;  wind,   254,  264 

Intensity  of  the  current,  777  ;  of  the 
electric  light,  788  ;  illumination, 
478  ;  of  reflected  light,  488  ;  of  a 
musical  tone,  232  ;  of  radiant  heat, 
387  ;  of  sound,  causes  vi'hich  influ- 
ence, 214;  of  terrestrial  magnetism, 
663  ;  of  terrestrial  gravity,  79 

Interference  of  light,  608 

Intermittent  fountain,  191  ;  springs, 
193  ;  syphon,  193 

Interpolar,  777 

Intervals,  musical,  233 

Intrapolar  region,  779 

Inversion  of  images,  579 

lones,  791 

Iris,  575 

Iron,  passive  state  of,  799  ;  electrical 
deposition  of,  805 

Iron  ships,  magnetism  of,  675 

Irradiation,  590 

Irregular  reflection,  487 

Isochimenal  line,  931 

Isoclinic  lines,  660 

Isodynamic  lines,  663 

Isogeothermic  lines,  931 

Isogonic  lines,  654 

Isotheral  lines,  931 

Isothermal  lines,  931  ;  zone,  931 


I 


ACOBI'S  unit,  884 

Jar,   Leyden,  725-735 
r,    luminous,     741  ;    Harris's    unit, 
732 


LEN 

Jet,  lateral,  ^00  ;  height  of,  201  ;  form 

of,  204 
Joule's  experiment  on  heat  and  work, 

467  ;  equivalent,  467 
Jupiter,  475 


KALETDOPHONE,  588 
Kaleidoscope,  485 
Kamsin,  902 
Kathode,  791 
Kathelectrotonus,  779 
Katione,  791 
Keepers,  678 

Key,  833,  849,  856,  863  ;  note,  235 
Kienmayer's  amalgam,   708 
Kilogramme,  24,  122 
Kilogrammetre,  444 
Kinetic  energy,  59 
Kinnersley's  thermometer,  744 
Kirk's  Ice  machine,  464 
Knife  edge,  68 
Konig's  apparatus,    242 ;    manometric 

flames,  272 
Kravogl's  machine,  842 
Kiilp's  method  of  compensation,  679 
Kundt's  velocity  of  sound,  261 


LACTOMETER,  126 
Ladd's     dynamomagnetic     ma- 
chine, 860 

Land  and  water,  935 

Lane's  electrometer,  732 

Lantern,  magic,  567 

Laplace's  barometic  formula,  165 

Laryngoscope,  529 

Latent  heat,  318  ;  of  fusion,  4;j2  ;  of 
vapours,  433 

Latitude,  influence  on  the  air,  929 ; 
parallel  of,  79 

Lavoiser  and  Laplace's  calorimeter, 
421  ;  method  of  determining  linear 
expansion,  293 

Law,  5 

Lead  tree,  801 

Leclanche's  elements,  766 

Ledger  lines,  238 

Leidenfrost's  phenomenon,  360 

Lemniscate,  629 

Length,  unit  of,  22  ;  of  undulation,  213 

Lenses,  519-527  ;  achromatic,  545  ; 
aplanatic,  526  ;  foci  in  double  con- 
vex, 520;  in  double  concave,  521  ; 
formation  of  images  in  double  con- 
vex, 524  ;  in  double  concave,    525  ; 


Index. 


899 


LEN 

formulae  relating  to,  527;  lighthouse, 
570;  optical  centre,  secondary  axis 
of,  523 

Leriz's  law,  845 

Leslie's  cube,  396  ;  experiment,  349  ; 
thermometer,  287 

Level,  water,  106  ;  spirit,  107 

Level  surface,  64 

Levelling  staff,  106 

Lever,  40 

Leyden  discharge,  inductive  action  of, 
846 

Leyden  jars,  725-735 ;  charged  by 
Ruhmkorff's  coil,  864 

Lichtenberg's  figures,  727 

Liebig's  condenser,  353 

Ligament,  suspensory,  575 

Light,  469  ;  diffraction  of,  609  ;  homo- 
geneous, 535,  537;  intensity  of,  478; 
interference  of,  608  ;  laws  of  reflec- 
tion of,  480 ;  medium,  472  ;  oxy- 
hydrogen,  569  ;  polarisation  of,  614  ; 
sources  of,  597  ;  theory  of  polarised 
light,  623 ;  undulatory  theory  of, 
469,  600 ;  velocity  of,  475-477 

Lighthouse  lenses,  570 

Lightning,  921  ;  ascending,  923  ;  effects 
of,  923  ;  conductor,  925 ;  globe,  923  ; 
heat,  921  ;  brush,  921  ;  flashes,  921 ; 
zigzag,  921 

Limit,  magnetic,  680  ;  to  induction,  7(X) ; 
of  perceptible  sounds,  230 

Line,  aclinic,  660;  of  collimation,  558  ; 
isoclinic,  660  ;  agonic,  654  ;  isogonic, 
654;  isodynamic,  663  ;  of  sight,  558 

Linear  expansion,  coefficients  of,  292, 
294 

Liquefaction  of  gases,  356,  357  ;  of 
vapours,  351 

Liquids,  96  ;  active  and  inactive,  638 
buoyancy  of,  97  ;  compressibility  of, 
94 ;  conductivity  of,  380  ;  calcula 
tion  of  density  of,  104  ;  diffusion  of, 
136  ;  diamagnetism  of,  870  ;  expan 
sion  of,  299  ;  equilibrium  of,  10 1 
manner   in   which   they  are  heated 

•  381  ;  pressure  on  sides  of  vessel,  99 
refraction  of,  517";  rotatory  power  of, 
638  ;  spheroidal  form  of,  81  ;  spheroi 
dal  state  of,  360  :  specific  heat  of, 
427  ;  volatile  and  fixed,  325  ;  ten 
sions  of  vapours  of,  335  j  of  mixed 
liquids,  336 

Lissajous'  experiments,  268-270 

Lithium,  542 

Litre,  24,  122 


MAG 

Local  action,  759  ;  attraction,  675  ', 
battery,  835  ;  currents,  768 

Locatelli's  lamp,  401 

Locomotives,  441,  442 

Lodestone,  642  ^ 

Long-sight,  592 

Loops  and  nodes,  253 

Loss  of  electricity  in  vacuo,  698  ;  of 
weight  in  air,  correction  for,  376 

Loudness  of  a  musical  tone,  232 

Luminiferous  ether,  469 

Luminous  bodies,  470  ;  effects  of  the 
electric  discharge,  738,  784  ;  of  the 
electric  current,  864 ;  of  RuhmkorfPs 
coil,  864  ;  jar,  741  ;  meteors,  916  ; 
pane,  741  ;  pencil,  471  ;  ray,  471  ; 
tube,  741  ;  square,  and  bottle,  741 

Luminous  radiation,  405  ;  heat,  407 


MACHINE,   Atwood's,  74  ;  elec- 
trical, 706-715  ;  Von  Ebner's, 
746  ;  electromagnetic,  832 

Mackerel  sky,  905 

Magazine,  677 

Magdeburg  hemispheres,  149 

Magic  lantern,  567 

Magnetic  attractions  and  repulsions,  664 ; 
battery,  677;  couple,  652;  curves, 
668  ;  declination,  657  ;  dip,  660  ; 
effects  of  the,  electrical  discharge, 
743  ;  equator,  660 ;  field,  669 ; 
fluids,  645  ;  induction,  648 ;  in- 
fluence, 648  ;  limit,  680  ;  meridian, 
653  ;  needle,  653,  654;  observatories, 
664  ;  poles,  660 ;  saturation,  676  ; 
storms,  656 

Magnetisation,  670  ;  by  the  action  of 
the  earth,  674  ;  by  currents,  829 

Magnetism,  6,642  ;  earth's,  663  ;  of  iron 
ships,  675  ;  Ampere's  theory  of,  827  ; 
remanent,  830 ;  theory  of,  645  ;  ter- 
restrial distribution  of  free,  681 
•  Magneto-electrical  apparatus,  855; 
Gramme's,  861  ;  machines,  857-860 

Magnets,  artificial  and  natural,  642  ; 
broken,  647 ;  action  of  earth  on,  65 1  ; 
equator  of,  643  ;  north  and  south 
poles  of,  644  ;  portative  force  of,  679  ; 
saturation  of,  676  ;  influence  of  heat, 
680  ;  induction  by,  847  ;  inductive 
action  on  moving  bodies,  848  ;  action 
on  cun-ents,  815  ;  on  solenoids,  825  ; 
rotation  of  induced  currents  by,  867  ; 
optical  effects  of,  869 

Magnification,    linear    and   superficial, 


900 


Index. 


MAG 
552  ;  measure  of,  552  ;  of  a  telescope, 
558 

Magnifying  power,  557 

Magnitude,  9  ;  apparent,  of  an  object, 
551  ;  of  images  in  mirrors,  550 

Major  chord,  233  ;  triads,  234 

Malleability,  807 

Manganese,  magnetic  limit  of,  680 

Manhole,  437 

Manipulator,  834 

Manometer,  94,    169;  open-air,    170  ; 
-     with  compressed  air,  171  ;  Regnault's 
barometric,  172 

Manometric  flames,  272 

Mares'  tails,  905 

Marie  Davy  battery,  765 

Marine  galvanometer,  774 

Mariner's  card,  900  ;  compass,  659 

Mariotte  and  Boyle's  law,  166 

Mariotte's  tube,  166  ;  bottle,  207 

Marloye's  harp,  265 

Maskelyne's  experiment,  64 

Mason's  hygrometer,  372 

Mass,  measure  of,  23  ;  unit  of,  23 

Matter,  2 

Matteucci's  experiment,  846 

Matthiessen's  thermometer,  287 

Maximum  and  minimum  thermometers, 
289  ;  of  tension,  709 

Mean  temperature,  928 

Measure  of  force,  29  ;  of  work,  57 

Measure  of  magnification,  552,  557  ;  of 
mass,  23  ;  of  space,  22  ;  of  time,  21  ; 
of  velocity,  25 

Measurement  of  small  angles  by  re- 
flection, 491 

Mechanical  equivalent  of  heat,  467  ; 
effects  of  electrical  discharge,  744 

Melloni's  researches,  401  ;  thermomul- 
tiplier,  385,  877 

Melting  point,  influence  of  pressure  on, 
316 

Membranes,  vibrations  of,  267 

Memoria  technica,  772 

Meniscus,  129  ;  in  barometer,  158  ; 
Sagittaof,  158 

Menotti's  battery,  765 

Mercury  frozen,  349,  357,  360  ;  pendu- 
lum, 298  ;  coefficient  of  expansion, 
301  ;  expansion  of,  300  ;  pump,  187 

Meridian,  21  ;  geographical  and  mag- 
netic, 653 

Metacentre,  112 

Metal,  Rose's  and  Wood's  fusible,  317 

Metals,  conductivity  of,  888 

Meteoric  stones,  450 


MUS 

Meteorology,  899 

Metre,  22,  122 

Mica,  626 

Micrometer  lines,  557;  screw,  II 

Microscope,  12  ;  achromatism  of,  555  ; 
Amici's,  554  ;  compound,  553  ;  fo- 
cussing, 550  ;  magnifying  powers  of, 
557 ;  photo-electric,  569  ;  simple, 
549  ;  solar,  568 

Microspectroscope,  544 

Mill,  Barker's,  205 

Millimetre,  122 

Mineral  waters,  924 

Mines,  firing  by  electricity,  746,  780 

Minimum  thermometer,  289  ;  deviation, 

515 

Minor  chord,  233 

Minute,  21 

Mirage,  509 

Mirrors,  applications  of,  502  ;  burning, 

393  ;  concave,  392  ;  conjugate,  393  ; 

glass,  484  ;  parabolic,  503  ;  rotating, 

489,  747  ;  spherical,  492 
Mists,  904 
Mixture   of  gases,    174;  of  gases  and 

liquids,  175 
Mixtures,  freezing,  324  ;  method  of,  423 
Mobile  equilibrium,  388 
Mobility,  7,  18 
Modulus  of  elasticity,  85 
Moisture  of  the  atmosphere,  374 
Molecular   forces,    3 ;    attraction,    8c  ; 

state  of  bodies,  4 
Molecular  state,  relation  of  absorption 

tor,  416 
Molecules,  3 
Moments  of  forces,  38 
Momentum,  28 
Mongolfier's  balloon,  177 
Monochord,  250 
Monochromatic  light,  535 
Monosyllabic  echo,  223 
Morgagni's  humour,  575 
Morin's  apparatus,  75 
Morren's  mercury  pump,  187 
Morse's  telegraph,  835 
Motion,  18  ;  on  an  inclined  plane,  47  ; 

curvilinear,  25  ;  in  a  circle,  49,  50  \ 

rectilinear,  25  ;  uniformly  accelerated 

rectilinear,  46  ;  quantity  of,  29  ;  of  a 
'    pendulum,  51 
Mouth  instruments,  255 
Multiplier,  773 
Multiple  echoes,   223  ;  images   formed 

by  mirrors,  484,  485,  486 
Muscular  currents,  892,  893 


Index, 


901 


MUS 

Music,  205  ;  physical  theoiy  of,  232- 
248 

Musical  boxes,  265  ;  intervals,  233 ; 
scale,  234 ;  temperament,  236 ;  tones, 
properties  of,  232 ;  intensity,  notation, 
238  ;  pitch,  and  timbre,  232  ;  sound, 
211  ;  range,  238 

Myopy,  582,  592 


NAIRNE'S  electrical  machine,  711 
Nascent  state,  82 

Narer's  apparatus,  357 
Needle,    dipping,    660 ;   astatic,    662  ; 

magnetic,  653 
Negative  plate,  754 
Negatives  on  glass,  572 
Nerve  currents,  896 
Neutral   line,    699  ;    equilibrium,    67  ; 

point,  699 
Newtonian  telescope,  563 
Newton's   disc,    533  ;  law   of  cooling, 

389  ;  rings,    983,   612,    613  ;  theory 

of  light,  534 
Nicholson's  hydrometer,  117 
Nickel,    electrical  deposition  of,    805; 

magnetic  limit  of,  680 
Nicol's  prism,  622 
Nimbus,  905 
Nobili's   battery,     875  ;     rings,     800  ; 

thermomultipliers,  877  ;  thermo-elec- 
tric pile,  401,  404,  875 
Nocturnal  radiation,  465 
Nodal  points,  253,  608 
Nodes   and   loops,    253  ;  of  an   organ 

pipe,  258  ;  explanation  of,  260 
Noises,  209 
Nonconductors,  684 
Norremberg's  apparatus,  619 
Northern  light,  927 
Norwegian  stove,  383 
Notation,  musical,  238 
Notes  in  music,  233  ;  musical,  of  women 

and  boys,  245  ;  wave  length  of,  239 
Nut  of  a  screw,  44 


OBSCURE   radiation,    405  ;   rays, 
406  ;  transmutation  of,  406 
Object  glass,  553 
Objective,  553 

Observatories,  magnetic,  664 
Occlusion  of  gases,  140 
Octave  233 


.    PER 

Oersted's  experiment,  772 

Ohm's  law,  777 

Opaque  bodies,  470 

Opera  glasses,  560  __ 

Ophthalmoscope,  596 

Optics,  469 

Optic  axis,  570  ;  axes  of  biaxial  crystals, 

607  ;  angle,  570  ;  nerve,  575 
Optical  centre,  523  ;  effects  of  magnets, 

869  ;  instruments,  548 
Optometer,  582 
Organ  pipes,  258  ;  nodes  and  loops  of^ 

258 
Orrery,  electrical,  719 
Oscillations,  5 1  ;  axis  of,    76  ;  method 

of,  667 
Otto  von  Guericke's  air-pump,  181 
Outcrop,  108 
Overshot  wheels,  206 
Oxyhydrogen  light,  569 
Ozone,  745,  923 


PALLET,  78 
Pane,   fulminating,    724  ;   lumi- 
nous, 742 

Papin's  digester,  347 

Parabolic  mirrors,  503 ;  curve,  57, 
200 

Parachute,  179 

Paradox,  hydrostatic,  1 00 

Parallel  of  latitude,  79  ;  forces,  36 ; 
centre  of,  27 

Parallel  rays,  471 

Parallelogram  of  forces,  33 

Paramagnetic  bodies,  870 

Partial  current,  890 

Pascal's  law  of  equality  of  pressures,  95  ; 
experiments,  151 

Passage  tint,  639 

Passive  state  of  iron,  799 

Pedal,  263 

Peltier's  cross,  881 

Pendulum,  51  ;  application  to  clocks, 
78  ;  ballistic,  78  ;  conical,  53  ;  com- 
pensation, 298  ;  electrical,  660  ;  grid- 
iron, 298  ;  mercurial,  298  ;  length  of 
compound,  76  ;  verification  of,  laws 
of,  77 

Penumbra,  473 

Percussion,  heat  due  to,  449 

Periscopic  glasses,  592 

Permanent  gases,  356 

Persistence  of  impression  on  the  retina, 
588 

Perturbations,  magnetic,  654,  655 


902 


hidex. 


PHE 

Phenakistoscope,  588 

Phenomenon,  5 

Phial  of  four  elements,  103 

Phonautograph,  271 

Phosphoi-escence,  598,  599 

Phosphorogenic  rays,  538 

Phosphoroscope,  599 

Photo-electric  microscope,  569 

Photogenic-apparatus,  569 

Photographs  on  paper,  572  ;  on  albu- 
menised  paper  and  glass,  574 

.Photography,  571-574 

Photometers,  479,  480 

Physical  phenomena,  5  ;  agents,  6  ; 
shadows,  473 

Physics,  object  of,  i 

Physiological  effects  of  the  electric  dis- 
charge, 737  ;  of  the  current,  778  ;  of 
Ruhm.korff's  coil,  864 

Piezometer,  94 

Pigment  colours,  536 

Pile,  voltaic,  757-770 

Pipes,  organ,  258 

Pisa,  tower  of,  66 

Pistol,  electric,  745 

Piston  of  air-pump,  181  ;  rod,  438 

Pitch,  concert,  237  ;  of  a  note,  232  ;  a 
screw,  44 

Plane,  44;  electrical  inclined,  719; 
wave,  605 

Plants,  absorption  in,  139 

Plante's  secondary  battery,  797 

Plate  electrical  machine,  707 

Plates,  colours  of  thin,  612  ;  vibrations 
of,  266 

Plumb-line,  64 

Pluviometer,  907 

Pneumatic  syringe,  143,  449 

Poggendorff 's  law,  745 

Point,  boiling,  342,  343 

Points,  power  of,  695 

Polar  aurora,  927 

Polarisation,  797  ;  angle  of,  616  ; 
current,  797 ;  of  electrodes,  759  ; 
by  double  refraction,  614  ;  by  reflec- 
tion, 615  ;  by  single  refraction,  617; 
elliptical  and  circular,  631,  632,  634  ; 
of  heat,  641  ;  galvanic,  759,  797 ;  of 
the  medium,  701  ;  plane  of,  616  ; 
plate,  759  ;  rotatory,  635 

Polarised  light,  theory  of,  623  ;  colours 
produced  by  the  interference  of,  624, 
630  ;  rays,  624 

Polariser,  618 

Polarising  instruments,  618 

Polarity,  759;  boreal,  austral,  651 


PYR 

Poles,  756  ;  analogous  and  antilogous, 
791  ;  of  the  earth,  660  ;  of  a  mag- 
net, 643  ;  mutual  action  of,  644  ; 
precise  definition  of,  646  ;  austral 
and  boreal,  651 

Polygon,  offerees,  35 

Polyprism,  512 

Ponderable  matter,  6 

Pores,  13 

Porosity,  7,  13  ;  application  of,  15 

Portative  force,  679 

Positive  plate,  754 

Positives  on  glass,  573 

Postal  battery,  835 

Potential  energy,  59  ;  of  electricity, 
752 

Pound,  122  ;  avoirdupois,  23,  29  ; 
foot,  56 

Powders,  radiation  from,  416 

Power  of  a  lever,  40  ;  of  a  microscope, 
557 

Presbytism,  582,  592 

Press,  hydraulic,  105 

Pressure,  centre  of,  99  ;  on  a  body  in  a 
liquid,  109  ;  atmospheric,  147  ; 
amount  of,  on  human  body,  152  ; 
experiment  illustrating,  189 ;  in- 
fluence on  melting  point,  317  ;  heat 
produced  by,  449 ;  electricity  pro- 
duced by,  690 

Pressures,  equality  of,  95  ;  vertical 
downward,  96 ;  vertical  upward,  97  ; 
independent  of  form  of  vessel,  98  ; 
on  the  sides  of  vessels,  99 

Prevost's  theory,  388 

Primary  coil,  837 

Primitive  current,  891 

Principal  current,  891 

Principle  of  Archimedes,  no 

Prisms,  510-515  ;  double  refracting, 
621  ;  Nicols',  622  ;  with  variable 
angle,    512 

Problems  on  expansion  of  gases,  309  ; 
on  mixtures  of  gases  and  vapours, 
359;  on  hygrometry,  375 

Proof  plane,  693 

Propagation  of  light,  472 

Protoplasm,  778 

Protuberances,  543 

Pulley,  41 

Pump,  air,  181  ;  coixlensing,  188 

Pumps,  different  kinds  of,  194  ;  suction, 
195  ;  suction  and  force,  196 

Pupil,  575 

Psychrometer,  372 

Pyroelectricity,  691 


Index. 


903 


PYR 


Pyrheliometer,  450 
Pyrometers,  290;  electric,  880 


QUADRANTAL  deviation,  675 
Quadrant  electrometer,  710 


RADIANT  heat,  484 ;  detection 
and  measurement  of,  385  ; 
causes  which  modify  the  intensity 
of,  387 ;  Melloni's  researches  on, 
401  ;  relation  of  gases  and  vapours 
to,  411 

Radiated  heat,  377,  384 

Radiating  power,  398  ;  identity  of  ab- 
sorbing and  radiating,  399  ;  causes 
which  modify,  &c. ,  400  ;  of  gases, 
414 

Radiation,  cold  produced  by,  465  ; 
from  powders,  416  ;  of  gases, 
luminous,  and  obscure,  405  ;  laws  of, 
386  ;  solar,  450 

Radiative  power,  909 

Rain,  907  ;  clouds,  907  ;  bow,  926  ; 
fall,  907  ;  gauge,  907 

Ramsden's  electrical  machine,  707 

Rarefaction  in  air  pump,  181  ;  by 
Sprengel's  pump,  185 

Ray,  incident,  504  ;  luminous,  471  ; 
ordinary  and  extraordinary,  604 

Rays,  actinic,  or  Ritteric,  335  ; 
divergent  and  convergent,  471  ; 
frigorific,  395  ;  of  heat,  384,  402  ; 
invisible,  402  ;  obscure,  406;  path  of, 
in  eye,  578;  polarised,  624  ;  trans- 
mutation of  thermal,  407 

Reaction  and  action,  39 

Reaction  machines,  442 

Real  volume,  14  ;  foci,  .520  ;  focus,  493; 
image,  496,  524 

Reaumur  scale,  282 

Receiver  of  air-pump,  181 

Recomposition  of  white  light,  533 

Reed  instruments,  256 

Reeds,  free  and  beating,  256 

Reflected  light,  intensity  of,  488 

Reflecting  power,  396 ;  goniometer, 
502  ;  sextant,  490;  stereoscope,  586; 
telescope,  561 

Reflection,  apparent,  of  cold,  395  ;  of 
heat,  391  ;  from  concave  mirrors, 
392  ;  irregular,  487  ;  laws  of,  390  ; 
verification  of  laws  of,  393  ;  in  a 
vacuum,  394  ;  of  light ;  480-509  ;  of 
sound,  222 


ROT 

Refracting  stereoscope,  587  ;  telescope, 

561 
Refraction,     504-509 ;     double,     602 ; 

polarisation  by,  614;  explanation  of 

single,  601  ;  of  sound,  224 
Refractive  index,    506;  of  gases,  518; 

of  liquids,  517  ;  of  solids,  516  ;  table 

of,  518  ;  indices  of  media  of  eye,  576 
Refractory  substances,  315 
Refrangibility  of  light,    alteration   of, 

545 
Regelation,  914, 
Regnault's  determination  of  density  of 

gases,       313 ;      manometer,       172  ; 

methods  of  determining  the  expansion 

of  gases,  310  ;  of  specific  heat,  425  ; 

of  tension  of  aqueous   vapour,  332, 

334;  hygrometer,  371 
Regulator   of  the   electric  light,    786, 

787 
Relay,  835 

Remanent  magnetism,  830 
Repulsions,    magnetic,   665  ;  electrical 

laws  of,  690 
Reservoir,  common,  685 
Residual  charge,  728 
Residue,  electric,  728 
Resinous  electricity,  686,  687 
Resistance  of  a  conductor,  777  ;  of  an 

element,  887 
Resonance,  223;  box,  237  ;  globe,  241 
Rest,  18 

Resultant  of  forces,  32-34 
Retina,  575  ;  persistance  of  impression 

on,  588 
Return  shock,  924 
Reversion,  method  of,  658 
Rheometer,  773 
Rheoscope,  773 
Rheoscopic  frog,  894 
Rheostat,  882 
Rhomb,  Fresnel's,  633 
Rhumbs,  659,  900 
Right  ascension,  563 
Rime,  901 
Rings,     coloured,     628  ;      in     biaxial 

crystals,    629  ;   Newton's,  612,  613  ; 

Nobili's,  800 
Ritchie's  experiment,  399 
Ritteric  rays,  406 
Rock  salt,   head  transmitted  through, 

410 
Rods,  vibrations  of,  265 
Roget's  vibrating  spiral,  807 
Rose's  fusible  metal,  317 
Rotating  min-or,  747 


904 


Itidex. 


ROT 

Rotation,  electrodynamic  and  electro- 
magnetic, of  liquids,  817 

Rotation  of  the  earth,  77  ;  of  magnets, 
by  currents,  814 ;  of  currents  by 
magnets,  816  ;  of  induced  currents 
by  magnets,  867 

Rotatory  power  of  liquids,  638 ;  polari- 
sation, 635,  636;  coloration  produced 
by,  637 

Rousseau's  densimeter,  127 

Roy  and  Ramsden's  measurement  of 
linear  expansion,  294 

Rubbers,  707 

Rubidium,  542 

Ruhmkorff's  coil,  862  ;  effects  produced 
by,  864 

Rumford's  photometer,  479 

Rutherford's  thermometers,  289 


SACCHARIMETER,  639 
Saccharometer,  123 
Safety-valve,     105,     347  ;     tube    355 ; 

whistle,  437 
Sagitta  of  meniscus,  158 
Salimeters,  126 
Salts,  decomposition  of,  792 
Saturation,  degree  of,   366  ;  magnetic, 

676  ;  of  colours,  536 
Saussure's  hygrometer,  373 
Savart's  toothed  wheel,  227 
Scale  of  hardness,  90 
Scales  in  music,  234  ;  chromatic,  236  ; 

of  a  thermometer,   282  ;  conversion 

of,  into  one  another,  282 
Scattered  heat,  397  ;  light,  487 
Schehallien  experiment,  64 
Sclerotica,  575 
Scott's  phonautograph,  271 
Screw,  II,  44 
Secondary  axis,    523  ;  batteries,    797  ; 

currents,  759  ;  coil,  837 
Second  of  time,  21,  25 
Seconds  pendulum,  76 
Secular  magnetic  variations,  654 
Segments,  ventral  and  nodal,  204 
Segner's  water-M^heel,  206 
Selenite,  626 

Semicircular  deviation,  675 
Semi-conductox's,  684 
Semi-tones,  235 
Senarmont's  experiment,  379 
Serein,  909 

Series,  thermo-electric,  872 
Serum,  12 
Sextant,  490 


SOU 

Shadow,  473 

Shaft,  438 

Shock,  electric,  725-735  ;  return,  924 

Short  sight,  592 

Siemens'  armature,  858  ;  unit,  884  ; 
electrical  thermometer,  890 

Sight,  line  of,  558 

Silver,  voltameter,  795 

Simoom,  902 

Sine  compass,  776 

Singing  of  liquids,  339 

Sinuous  currents,  809 

Sirocco,  902 

Size,  estimation  of,  581 

Sleet,  912 

Slide  valve,  438 

Smee's  battery,  764 

Snow,  912  ;  line,  915 

Soap  bubble,  colours  of,  612 

Solar  microscope,  568  ;  light,  thermal 
analysis  of,  403  ;  radiation,  450  ; 
spectrum,  530 ;  properties  of  the, 
538  ;  dark  lines  of,  539,  543  ;  time, 
21  ;  day,  21 

Soleil's  saccharimeter,  639 

Solenoids,  822-826  ;  action  of  currents 
on,  823;  of  magnets  and  of  earth  on, 
824,  825  ;  on  solenoids,  826 

Solidification,  320  ;  change  of  volume 
on,  320,  323  ;  retardation  of,  322 

Solidity,  4,  7 

Solids,  conductivity  of,  378  ;  index  of 
refraction  in,  516  ;  diamagnetism  of, 
870;  linear  and  cubical  expansion  of, 
292,  297 

Solids,  formulae  of  expansion,  296 

Solution,  319 

Sondhauss's  experiments,  224 

Sonometer,  250 

Sonorous  body,  210 

Sound,  209  ;  cause  of,  210  ;  not  propa- 
gated in  vacuo,  211  ;  propagated  in 
all  elastic  bodies,  212  ;  propagation 
of,  in  air,  213  ;  causes  which  influ- 
ence intensity  of,  214  ;  apparatus  to 
strengthen,  215  ;  velocity  of,  in 
gases,  217-219  ;  in  liquids  and 
solids,  221  ;  reflection  of,  222  ;  re- 
fraction of,  224  ;  transmission  of,  216 

Sound,  Helmholtz's  analysis  of,  241 

Sound,  Konig's  apparatus,  241  ; 
Kundt's,  261 

Sounder,  839 

Sounds,  limit  of  perceptible,  230 ; 
synthesis  of,  243  ;  perceptions  of, 
245  ;  produced  by  currents,  813 


Index. 


905 


SPA 

Space,  measure  of,  22 

Spar,  Iceland,  621 

Spark  and  brush  discharge,  739  ;  elec- 
trical, 717,  739  ;  board,  747  ;  dura- 
tion and  velocity  of,  747 

Speaking  trumpet,  225  ;  tubes,  216 

Specific  gravity,  24,  116,  121  ;  flask, 
118  ;  of  solids,  117  ;  of  gases,  312  ; 
of  liquids,  120  ;  tables  of,  121,  122 

Specific  heat,  419-432  ;  compound 
bodies,  530  ;  determination  of,  by 
fusion  of  ice,  421  ;  by  method  of 
mixtures,  423  ;  by  Regnault's  appa- 
ratus, 425  ;  of  solids  and  liquids, 
427,  428;  of  gases,  431 

Specific  inductive  capacity,  702 

Spectacles,  593 

Spectral  analysis,  540 

Spectroscope,   541  ;  experiments  with, 

542  ;  uses  of  the,  544 
.Spectrum,  calorific,  538;  chemical,  538 

Spectrum,  403  ;  colours  of,  532  ;  pure 
531  ;  solar,  530,  542 

Spectrum,  dark  lines  of,  539 

Spectrum,  diffraction,  611 

Spctrum,  luminous  properties,  538 

Spectrum  of  aurora  borealis,  927  ;  pro- 
perties of,  538  ■ 

Specular  reflection,  487 

Spherical  aberration,  501,  526 ;  mir- 
rors, 492  ;  focus  of,  493  ;  formulae 
for,  498 

Spheroidalform  of  liquids,  81;  state,  360 

Spherometer,  11 

Spiral,  829  ;  Roget's  vibrating,  807 

Spirit-level,  107 

Sprengel's  air-pump,  185 

Stable  equilibrium,  67 

Stars,  spectral  analysis  of,  545 

Staubbach,  73 

Steam  engines,  436 ;  boiler,  437  ; 
double  action,  or  Watt's,  438  ;  pipe, 
186;  various  kinds  of,  443  ;  work  of, 
444 ;  heating  by,  460 

Steeling,  805 

Stereoscopes,  585-587 

Stethoscope,  226 

Stills,  352 

Stool,  insulating,  717 

Stopcock,  doubly  exhausting,  183  ; 
Gay-Lussac's,  358 

Storms,  magnetic,  656 

Stoves,  459  ;  Norwegian,  383  ' 

Stratification  of  electric  light,  865 

Stratus,  905 

Stringed  instruments,  263 


TER 

Strings,  249  ;  transverse   vibration  of, 

249 
Subdominant  chords,  234 
Suction  pump,    195  ;  and  force  pump, 

196  ;  load  which  piston  supports,  197 
Sulphate  of  mercury  battery,  765 
Sun,  analysis  of,   543  ;  constitution  of, 

543 
Sun  spots,  663 
Surface  level,  64 

Suspension,  axis  of,  68  ;  Cardan's,  155 
Suspensory  ligament,  575 
Swimming,  115  ;  blader  of  fishes,  114 
Symmer's  theory  of  electricity,  687 
Syphon,  192  ;  intermittent,  193 
Syphon  barometer,  156 
Syren,  228 

Syringe,  pneumatic,  143,  448 
Synthesis  of  sounds,  243 


TAMTAM  metal,  91 
Tangent   compass,    or  galvano- 
meter, 775,  796 
Telegraph,  cables,  induction  in,  836  ; 
electric,    832  ;    dial,    834 ;  Morse's, 

835 

Telescopes,  558-564;  astronomical, 
558  ;  Galilean,  560;  Gregorian,  562; 
Herschelian,  564  ;  Newtonian,  562  ; 
reflecting  Rosse's,  564 

Telluric  lines,  539 

Temper,  91 

Temperature,  276,  419  ;  correction  for, 
in  barometer,  159  ;  critical,  346  ; 
of  a  body,  276 ;  determined  by 
specific  heat,  428 

Temperature,  absolute  zero  of,  466 ; 
mfluence  of,  on  specific  gravity,  120  ; 
mean,  928  ;  how  modified,  929  ;  dis- 
tribution of,  933  ;  of  lakes,  springs,  934 

Temperatures,  different  remarkable, 
291  ;  influence  on  expansion,  296 

Tempering,  87,  91 

Tenacity,  7,  88 

Tension,  1 14,  694,  863  ;  maximum  ot 
electrical  machine,  709  ;  maximum 
of  vapours,  329  ;  of  aqueous  vapour 
at  various  temperatures,  333-337  ;  of 
vapours  of  different  liquids,  335  ;  of 
mixed  liquids  in  two  communicating 
vessels,  337 

Terquem's  experiment,  693 

Terrestrial  currents,  828  ;  heat,  45 1  ; 
magnetic  couple,  652  ;  telescope,  559 

Terrestrial  gravitation,  64,  79 


go6 


Index, 


TER  » 

Terrestrial  magnetic  couple,  652 

Tetanus,  778 

Thallium,  542 

Thaumatrope,  588 

Theodolite,  10 

Theory,  5  ;  of  induction,  701 

Thennal  analysis,  403  ;  unit,  418,  454  ; 
springs,  934 

Thermal  effects  of  the  current,  780,  781 

Thermal  rays,  transmutation  of,  407  ; 
unit,  418 

Thermocrose,  409 

Thermo-electric  battery,  385,  876 ; 
couples,  874 ;  currents,  873,  875, 
878  ;  pile,  385,  404,  875  ;  series,  872 

Thermo-electricity,  871 

Thermo-element,  872 

Thermometers,  277  ;  Becquerel's  elec- 
trical, 879  ;  division  of  tubes  in,  278 
filling,     279 ;    graduation    of,     280 
determination  of  fixed  points  of,  281 
scale  of,  282  ;  displacement  of  zero, 
283  ;  limits  to  use  of,  284  ;  alcohol 
285  ;  conditions  of  delicacy  of,  286 
Kinnersley's,    744 ;    Leslie's,    287 
Matthiessen's,   287  ;  Breguet's,    288 
maximum     and      minimum,      289 
Siemens'    electrical,     890 ;     weight, 
302  ;  air,  308,  309 

Thermo-barometer,  345 

Thermometer,  electric,  744 

Thermometry,  276-289 

Thermo-multiplier,  Melloni's,  877, 

Thermoscope,  287 

Thomson's  electrometer,  735  ;  galva 
nometer,  774  ;  apparatus  for  atmo 
spheri'c  electricity,  917 

Thread  of  a  screw,  44 

Thunder,  922 

Timbre,  232 

Time,  measure  of,  21  ;  mean  solar,  21 

Tint,  536  ;  transition,  639 

Tones,  combinational,  247  ;  differential 
247 

Tonic,  234 

Torricelli's  experiment,  150  ;  theorem 
199  ;  vacuum,  157 

Torsion,  angle  of,  86 ;  balance  86 
666,  692 ;  force  of,  86 

Total  reflection,  508 

Tourmaline,  620,  691  ;  pincette,  628 

Tourniquet,  hydraulic,  205 

Traction,  elasticity  of,  85 

Trajectory,  25 

Transformation  of  energy,  6i 

Transition  tint,  639 


VAP 

Transparency,  7,  470 
Transparent  media,  51 0-5 1 7 
Transpiration  of  gases,  138 
Translucent  bodies,  470 
Transmission  of  heat,    377  ;    of  light, 

469,  510  ;  by  the  current,  793 
Transmission  of  sound,  216 
Triad,  harmonic,  233 
Triangle,  265 
Triangle  of  forces,  35 
Trumpet,  speaking,  ear,  225 
Tubes,  Geissler's,  185,  866  ;  luminous, 

741  ;  safety,  355  ;  speaking,  216 
Tuning  fork,  237,  265 
Turbines,  206 
Tyndall's  researches,  404,  910 


UNANNEALED     glass,     colours 
produced  by,  630 
Undershot  wheels,  206 
Undulation,  length  of,  213,  600 
Undulatory  theory,  469 
Uniaxial  crystals,  603;  double  refraction 

in,  605  ;  positive  and  negative,  606 
Unit  jar,  Harris's,  733  ;  Siemens',  884  ; 

thermal,  418 
Unit  of  length,  area  and  volume,   22 ; 

heat,  418  ;  of  work,  58 
Unstable  equilibrium,  67 
Urinometer,  126 


\  7ACU0,  loss  of  electricity  in,  698 
V  Vacuum,  application  of,  to 
construction  of  air  pump,  181 ;  ex- 
tent of,  produced  by  air  pump,  182  ; 
fall  of  bodies,  in  a,  73  ;  formation 
of  vapour  in,  328  ;  heat  radiated 
in,  386  ;  reflection  in  a,  394  ;  Torri- 
cellian, 157 

Valve,  safety,  105,  347  ;  chest,  437 

Vane,  electrical,  719 

Vaporisation,  326  ;  latent  heat  of,  347, 

433 

Vapour,  aqueous,  tension  of,  at  various 
temperatures,  333-337  ;  formation  of, 
in  closed  tube,  346;  latent  heat  of,  348 

Vapours,  325  ;  absorption  of  heat  by, 
408 ;  absorptive  powers  of,  413  ; 
density  of,  Gay-Lussac's  method, 
361  ;  determination  of  latent  heat  of, 
432  ;  Dumas's  method,  362  ;  elastic 
force  of,  327  J  formation  of,  in  vacuo. 


Index. 


907 


VAR 

328;  saturated, 329 ;' unsaturated,  330; 
tension  of  different  liquids,  335  ;  of 
mixed  liquids,  336;  in  communicating 
vessels,  337 

Variations,  annual,  655 ;  accidental, 
656;  barometric,  160;  causes  of, 
161  ;  diurnal,  655  ;  relation  of,  to 
weather,  161  ;  in  magnetic  declina- 
tion, 653,  657 

Varley  unit,  884 

Velocity,  25  ;  direction  of,  52 ;  of 
efflux,  199  ;  of  electricity,  747  ;  of 
light,  475-477  ;  graphic  representa- 
tion of  changes  of,  52  ;  of  sound  in 
gases,  217,  218;  formula  for  calcula- 
ting, 218;  of  winds,  900 

Velocities,  composition  of,  48  ;  ex- 
amples of,  25 

Vena  contracta,  202 

Ventral  and  nodal  segment,  204,  253, 
258 

Vernier,  10 

Vertical  line,  64 

Vibrating  spiral,  Roget's,  807 

Vibration,  210  ;  arc  of,  51  ;  produced 
by  currents,  831 

Vibrations,  246 ;  formulae,  259 ;  of 
membranes,  267  ;  laws  of,  251  ; 
measurement  of  number  of,  227 ; 
number  of,  producing  each  note,  237  ; 
of  musical  pipe,  259  ;  of  rods,  265  ; 
of  plates,  266;  of  strings,  249,  251, 
252 

View,  field  of,  556 

Vinometers,  126 

Virtual  and   real   images,  483;   focus, 

.493 

Vision,  distance  of  distinct,  582  ;  bino- 
cular, 584 

Visual  angle,  580 

Vis  viva,  56,  419,  467 

Vital  fluid,  749 

Vitreous  body,  575  ;  electricity,  686  ; 
fusion,  315  ;  humour,  575 

Vocal  chords,  245 

Volatile  liquids,  325 

Volta's  condensing  electroscope,  734; 
electrophorus,  706 ;  fundamental  ex- 
•  periment,  750 

Voltaic  arc,  784 ;  couple,  754 ;  cur- 
rents, 771  ;  induction,  843  ;  pile  and 
battery,  757,  758,  783 

Voltameter,  silver,  795  ;  Faraday's,  795 

Volume,  22 ;  unit  of,  22,  24  ;  deter- 
mination of,  III  ;  change  of,  on 
solidification,   323  ;   of  a  liquid  and 


WOR 
that  of  its  vapour,  relation  between, 

364 
Von  Ebner's  electrical  machine,  746 


WALKER'S  battery,  764 
Water  bellows,  186  ;    decom- 
position of,  120  ;  hammer,    73  ;  hot, 
heating  by,  462  ;  level,  1 06 

Water,  maximum  density  of,  307 ; 
spouts,  908  ;  wheels,  206 

Watt's  engine,  438 

Wave,  condensed,  213  ;  expanded, 
213 ;  lengths,  600  ;  plane,  605 

Weather,  its  influence  on  barometric 
variations,  160,  161  ;  glasses,  163 

Wedge,  43 

Wedgewood's  pyrometer,  290 

Weighing,  method  of  double,  72 

Weight,  23,  79  ;  of  bodies  weighed  in 
air,  correction  for  loss  of,  376  ;  of 
gases,  145  ;  thermometer,  302 

Weights  and  measures,  122 

Wells,  artesian,  108 

Wells's  theory  of  dew,  901 

Wet  bulb  hygrometer,  372 

Wheatstone's  bridge,  886  ;  photometer, 
479  ;  rheostat,  882  ;  rotating  mirror, 
747  ;  and  Cooke's  telegraph,  833 

Wheel  barometer,  163 

Wheels,  friction,  74 ;  escapement,  78  ; 
water,  206 

Whirl,  electrical,  719 

Whispering  galleries,  223 

Whistle,  safety,  437 

White  light,  decomposition  of,  530  ;  re- 
composition  of,  533 

W^hite's  pulley,  41 

Wiedemann  and  Franz's  tables  of  con- 
ductivity, 378 

Wild's  magneto-electrical  machine,  859 

Winckler's  cushions,  707 

Windchest,  256 ;  instruments,  254,  264 

Winds,  causes  of,  901  ;  direction  and 
velocity  of,  890,  929  ;  law  of  rotation 
of,  903 ;  periodical,  regular,  and 
variable,  902 

Wines,  alcoholic  value  of,  354 

Wollaston's  battery,  758  ;  cryophorus, 
349  ;  doublet,  549 

Wood,  conductivity  of,  378 

Wood's  fusible  metal,  317 

Work,  34,  56  ;  measure  of,  57  ;  of  an 
engine,  443  ;  rate  of,  443  ;  unit  of, 
58  ;  internal  and  external,  of  bodies, 


9o8 


Index. 


YAR 


274;  of  a"voltaic  battery,  783;  re- 
quired ^r  the  production  of  elec- 
tricity, 716 


YARD,  British,  22,  122 
Young  and  Fresni&l's  experiment, 
608 


ZON 

ZAMBONI'S  pile,  769 
Zero,  absolute,  466  ;  aqueous  va- 
pours below,  331  ;  displacement  of, 
283 
Zinc,   amalgamated,    768  ;  carbon  bat- 
.  tery,  763 
Zone,  isothermal,  931 


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I187D    P^y^"!f  Tr!  and  ed.  from 
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